problem solving multiplication lesson 4.10 answer key

• Texas Go Math
• Big Ideas Math
• enVision Math
• EngageNY Math
• McGraw Hill My Math
• 180 Days of Math
• Math in Focus Answer Key
• Math Expressions Answer Key
• Privacy Policy

Go Math Grade 3 Chapter 4 Answer Key Pdf Multiplication Facts and Strategies

Go math answer key for grade 3 chapter 4 multiplication facts and strategies.

Go Math Grade 3 Chapter 4 Answer Key Pdf: Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies helps thousands of students to achieve excellent grades. Students can effectively solve problems and grab knowledge and skills by using Go Math Grade 3 Answer Key. Help your students keep up and catch up to do the math with the reference of HMH Go Math Solution Key Grade 3. It’s important to know the process of solving a problem more than finding the correct answer to improve the skills of your students. Go Math Answer Key Grade 3 Chapter 4 Multiplication Facts and Strategies will give all that flexibility to build their confidence to do math in an easy way.

Multiplication Facts and Strategies Go Math Grade 3 Chapter 4 Answer Key Pdf

In order to move successfully, refer to Grade 3 Multiplication Facts. Help your children to move to the next grade level by encouraging them with a lot of practice. Use Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies and achieve your goals easily.

Lesson 1: Multiply with 2 and 4

Multiply with 2 and 4 Page No 195

Multiply with 2 and 4 lesson check page no 196.

Lesson 2: Multiply with 5 and 10

Multiply with 5 and 10 Page No 201

Multiply with 5 and 10 lesson check page no 202.

Lesson 3: Multiply with 3 and 6

Multiply with 3 and 6 Page No 207

Multiply with 3 and 6 lesson check page no 208.

Lesson 4: Algebra • Distributive Property

Distributive Property Page No 213

Distributive property lesson check page no 214.

Lesson 5: Multiply with 7

Multiply with 7 Page No 219

Multiply with 7 lesson check page no 220.

Mid-Chapter Checkpoint

Mid-Chapter Checkpoint Page No 221

Mid-chapter checkpoint page no 222.

Lesson 6: Algebra • Associative Property of Multiplication

Associative Property of Multiplication Page No 227

Associative property of multiplication lesson check page no 228.

Lesson 7: Algebra • Patterns on the Multiplication Table

Patterns on the Multiplication Table Page No 233

Patterns on the multiplication table lesson check page no 234.

Lesson 8: Multiply with 8

Multiply with 8 Page No 239

Multiply with 8 lesson check page no 240.

Lesson 9: Multiply with 9

Multiply with 9 Page No 245

Multiply with 9 lesson check page no 246.

Lesson 10: Problem Solving • Multiplication

Multiplication Page No 251

Multiplication lesson check page no 252.

Chapter 4 Review/Test

Review/Test Page No 253

Review/test page no 254, review/test page no 255, review/test page no 256, review/test page no 257, review/test page no 258.

Write a multiplication sentence for the model.

Answer: 2 × 5 = 10

Explanation: Draw 2 counters. Place 5 Objectives in 2 counters. Count the total number of objectives and them. Add 5 + 5 to get the answer. Finally, you get 10 .

Find the product.

Answer: 4×3 = 12

Explanation: Look at the above figure. You can see 4 Counters and 3 objectives on each counter. So, you have to multiply 4×3 . When you multiply with 4, you can first multiply with 2 and then double the product. Multiply 3 with 2. You will get 2×3 is 6 . Now, double the number 6. The final answer is 12 .

Question 3. 2 × 6 ——– ________

Answer: 2×6 = 12

Explanation: When there is a multiplication requires with 2, you can double the given number 6 to get the final answer . The answer is 6+6 = 12 .

Question 4. 4 × 8 ——— ________

Answer: 4×8 = 32

Explanation: You can double 2×8 to get 4×8 . Multiply 8 with 2. You will get 16. Then, double the product to get the answer to 4×8. You will get 16+16 = 32. So, you get the final answer as 32 .

Go Math 3rd Grade Homework Book Answers Question 5. 2 × 3 ——– ________

Answer: 2×3 = 6

Explanation: Draw two counters. Place three objectives in two counters. Now, add the objectives in two counters. The final answer is 3+3 = 6. So, 2×3=6 is the answer.

Question 6. 4 × 6 ——— _________

Answer: 4×6 = 24

Explanation: You can double 2×6 to get 4×6. Multiply 6 with 2. You will get 12. Then, double the product to get the answer to 4×6. You will get 12+12 = 24 . So, you get the final answer as 24 .

Question 7. 4 × 4 ——— _________

Answer: 4×4 = 16

Explanation: Multiply 4 with 2. 2×4 = 8. Now, double the number 8. 8+8 = 16. The answer for 4×4 is 16

Question 8. 2 × 7 ——– _________

Answer: 2×7 = 14

Explanation: The given multiplication is 2×7. The answer to any number multiplies with 2 is double of that number. So, the 2×7 can find by doing 7+7. The answer is 7+7 = 14. So, the final answer is 2×7 = 14.

Question 9. 4 × 5 ——— _________

Answer: 4×5 = 20

Explanation: Firstly, multiply 2×5 to get the answer for 4×5. Then, double the answer of 2×5 to get the final answer. So, do 2×5 = 10. Double the number 10 to get the 4×5 Answer. The double of 10 is 10+10 = 20. The answer to 4×5 is 20 .

Question 10. 2 × 4 ——– _________

Answer: 2×4 = 8

Explanation: The multiplication begins with 2. So, you can double 4 to get the answer of 2×4. The double of 4 is 4+4 = 8. The answer for 2×4 is 8 .

Problem Solving

Question 11. On Monday, Steven read 9 pages of his new book. To finish the first chapter on Tuesday, he needs to read double the number of pages he read on Monday. How many pages does he need to read on Tuesday? __________ pages

Explanation: Steven read 9 pages of his new book on Monday. He wants to finish his first chapter on Tuesday. To finish the chapter, he needs to double the number of pages he read on Monday.

Double of pages read on Monday = 9 x 2 =18.

Steven needs to read 18 pages on Tuesday.

Go Math Grade 3 Chapter 4 Answer Key Pdf Question 12. Courtney’s school is having a family game night. Each table has 4 players. There are 7 tables in all. How many players are at the game night? __________ players

Explanation: From the given information Courtney’s school is having a family game night. Each table has 4 players. There are 7 tables in all. So, every table has 4 players. To know the total number of players at the game night, we need to multiply 7 with 4.

Total Number of players at the game night = 7 x 4 = 28.

Lesson Check

Explanation: The above figure consists of 4 counters. Also, each counter has two objectives in it. So, we need to multiply the number of counters with a number of objectives. The answer is 4×2 = 8 .

Question 2. Find the product. 2 × 8 ——- ________ Options: a. 10 b. 14 c. 16 d. 18

Explanation: To solve the 2×8, double the number 8. The answer for 2×8 is 8+8. S o, the final answer is 2×8 = 16.

Question 3. Sean made a picture graph to show his friends’ favorite colors. This is the key for the graph. Each Ο = 2 friends. How many friends does Ο Ο Ο Ο stand for? Options: a. 4 b. 8 c. 20 d. 40

Explanation: Sean made 4 picture graphs to show his friends’ favorite colors. Each Ο represents 2 friends. So, to find the final answer, we need to add all the colors. As there are 4 picture graphs you need to do 2+2+2+2 = 8. There are 8 friends available.

Explanation: In the above table, we can see three different walking trails lengths of three persons. The walking trail length of the Mountain is 844feets. The walking trail length of Lake is 792 feet. Also, the Harmony walking trail length is 528 feet. To get How many feet longer is Mountain Trail than Harmony Trail, we need to subtract Harmony walking trail length from Mountain Trail length. So, now we have to do 844-528 which is equal to 316 feet. S o, Mountain Trail walked 316 feet than Harmony trail.

Question 5. Find the sum. 5 2 7 + 1 5 4 ———- Options: a. 373 b. 581 c. 671 d. 681

Explanation: Break apart the addends from the given values. Start with the hundreds. Then, add each place value. Let’s write 527 as 500+20+7 and 154 as 100+50+4. Sum up the above two values. Then you get 600+70+11. Add the ones and then add the 10’s and 100’s. The final answer is 681 .

Question 6. A bar graph shows that sports books received 9 votes. If the scale is 0 to 20 by twos, where should the bar end for the sports books? Options: a. between 8 and 10 b. on 10 c. on 8 d. between 6 and 8

Explanation: As per the given data, the sports books received 9 votes. If we take a bar graph with a scale of 0 to 20 by twos, the graph is 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. So, the number 9 will lie between numbers 8 to 10. Therefore, the answer is between 8 and 10 .

Question 1. 5 × 7 = 35

Explanation: Skip count by 5’s until you say 7 numbers. 5, 10, 15, 20, 25, 30, 35. Now, the count of the number is 7. So, the answer for 5 x 7 is 35 .

Question 2. 5 × 1 = _______

Explanation: Any number multiplied by 1 is the same number. So, the answer is 5 .

Question 3. 2 × 10 = _______

Explanation: A multiple of 10 is any product that has 10 as one of its factors. So, the multiplication of any number with 10 is 10’s of that particular number. The answer is 20.

Question 4. ________ = 8 × 5

Explanation: From Commutative Law of Multiplication, you can write 8 x 5 = 5 x 8. So, to find the multiplication of 5 x 8, Skip count by 5’s until you say 8 numbers. 5, 10, 15, 20, 25, 30, 35, 40. Now, the count of the number is 8. So, the answer for 5 x 8 is 40. Therefore, the answer for 8 x 5 is 40 .

Question 5. 1 × 10 = ________

Explanation: Multiplication of any number with 1 is the same number. So, 1 x 10 = 10 .

Question 6. _______ = 4 × 5

Explanation: Using the Commutative Law of Multiplication, you can write 4 x 5 = 5 x 4. Now, Skip count by 5’s until you say 4 numbers. 5, 10, 15, 20. Therefore, the answer for 5 x 4 is 20.

Question 7. 5 × 10 = _______

Explanation: Skip-count by 5’s 10 times. You can write as 5, 10, 15, 20, 25, 30, 35, 40, 45, 50. The answer for 5 x 10 is 50 .

Question 8. 7 × 5 = ________

Explanation: Write 7 x 5 as 5 x 7 according to the Commutative Law of Multiplication. Now do multiply for 5 x 7. Skip-count by 5’s seven times. Now, you can write as 5, 10, 15, 20, 25, 30, 35. The answer for 5 x 7 is 35. So, the answer for 7 x 5 is also 35.

Question 9. _______ = 5 × 5

Explanation: Skip-count by 5’s 5 times. You can get 5, 10, 15, 20, 25. The answer for 5 x 5 is 25.

Chapter 4 Review Test Go Math 3rd Grade Question 10. 5 × 8 = _________

Explanation: You can Skip-count by 5’s 8 times. Write like 5, 10, 15, 20, 25, 30, 35, 40. So, the answer for 5 x 8 is 40.

Question 11. ______ = 5 × 9

Explanation: The multiplication of 5 × 9 is calculated as Skip-count by 5’s 9 times. You can write as 5, 10, 15, 20, 25, 30, 35, 40, 45. The final answer for 5 × 9 is 45.

Question 12. 10 × 0 = _________

Explanation: Multiplication of any number with 0 is 0. So, the answer for 10 x 0 is 0.

Question 13. 5 × 6 ——– ________

Explanation: Skip count by 5’s until you say 6 numbers. 5, 10, 15, 20, 25, 30. So, the answer for 5 x 6 is 35.

Question 14. 10 × 7 ——— ________

Explanation: Add 10’s until you say 7 numbers. Now, you can write as 10 + 10 + 10 + 10 + 10 + 10 + 10. Now, add the 10’s to get the final answer. There are seven 10’s available. So, the answer is 70.

Question 15. 5 × 3 ——– ________

Explanation: Skip count by 5’s until you say 3 numbers. Write like 5, 10, 15. The answer for 5 x 3 is 15.

Question 16. 10 × 4 ——– _________

Explanation: Add 10’s until you say 4 numbers. Then, write like 10 + 10 + 10 + 10 to get the answer. The answer for 10 x 4 is 40.

Question 17. 5 × 0 ——- _________

Explanation: Multiplication of any number with 0 is 0. So, the answer for 5 x 0 is 0.

Question 18. 10 × 8 ——- __________

Explanation: You have to add 10’s until you say 8 numbers. Write as 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10. Now, add the 10’s to get the final answer. There are eight 10’s available. So, the answer for 10 x 8 is 80.

Question 19. 5 × 2 ——- __________

Explanation: Skip count by 5’s until you say 2 numbers. Write like 5, 10. The answer for 5 x 2 is 10.

Question 20. 10 × 6 ——– _________

Explanation: Add 10’s until you say 6 numbers. Write as 10 + 10 + 10 + 10 + 10 + 10. Now, add the 10’s to get the final answer. So, the answer for 10 x 6 is 60.

Question 21. Ginger takes 10 nickels to buy some pencils at the school store. How many cents does Ginger have to spend? ________ cents

Explanation: From the given data, Ginger takes 10 nickels to buy some pencils at the school store. One nickel can be treated as 5 cents. So, 10 nickels value is 10 nickels x 5 cents = 50 cents.

Ginger has to spend 50 cents to buy some pencils at the school store.

Question 22. The gym at Evergreen School has three basketball courts. There are 5 players on each of the courts. How many players are there in all? __________ players

Explanation: As per the given data, the gym at Evergreen School has three basketball courts. There are 5 players on each of the courts. The number of players in there in all = 3 basketball courts x 5 players = 15 players.

15 players are available in total.

Question 1. Mrs. Hinely grows roses. There are 6 roses on each of her 10 rose bushes. How many roses in all are on Mrs. Hinely’s rose bushes? Options: a. 16 b. 54 c. 60 d. 66

Explanation: There are 10 rose bushes available. In each rose bush, Mrs. Hinely growing 6 roses. So, to find the number of roses, you need to multiply 10 x 6. The multiplication of 10 x 6 is 60. The number of roses in all are on Mrs. Hinely’s rose bushes are 60.

Question 2. Find the product. 5 × 8 ——- Options: a. 8 b. 16 c. 35 d. 40

Explanation: Skip-count by 5’s 8 times. Write like 5, 10, 15, 20, 25, 30, 35, 40. So, the answer for 5 x 8 is 40.

Spiral Review

Answer: c. Zoo

Explanation: From the given figure, Mr. Miller’s class voted for a field trip. From the table, every start represents 2 votes. It is mentioned that for the Science Center, Mr. Miller’s given two starts. As one star represents 2 votes, he gave 4 votes for Science Center. Similarly, Aquarium = 3 and a half stars. The half star represents one vote. So, the number of votes given for the Aquarium is 7. For Zoo, he has given 4 stars. So, every start means 2 votes. The total number of votes is 8. Finally, the number of starts for the Museum is 2. So, the total number of votes is 4.

Mr. Miller’s class is given a high number of votes for Zoo. So, Mr. Miller’s class wishes to go for Zoo.

Answer: c. 47

Explanation: Zack prepared a table of flavors and votes. So, every vote represents one person. By adding the total number of votes, we can get the total number of students participated in ina survey. Add 16 + 10 + 9 + 12 = 47. 47 students were surveyed in all to vote for their favorite juice.

Question 5. Which of the following numbers is even? 25, 28, 31, 37 Options: a. 25 b. 28 c. 31 d. 37

Answer: b. 28

Explanation: Even numbers are divided by 2. Also, even numbers end with a digit of 0, 2, 4, 6, or 8. So, the given number out of the given numbers is 28. It is ended with 8 and also it can divide by 2.

Question 6. Estimate the sum. 4 7 9 + 8 9 ——— Options: a. 568 b. 400 c. 500 d. 600

Answer: a. 568

Explanation: Add the ones. Regroup the ones as tens and ones. So, 9 + 9 = 18. Remain the 8 same and add the 1 to the tens. Add the tens. Regroup the tens as hundreds and tens. Now, add 7 + 8 + 1 = 16. place the 6 in the tens place and move the 1 to hundreds. Add the hundreds now. 4 + 1 = 5. So, now place the numbers in order. The final answer is 568.

Note: The option is modified for the above question. There is no correct answer available in the given options. So, option a is changed to the correct answer. The answer is explained with the place value to add two addends method.

Question 1. 6 × 4 = 24 Think: You can use doubles. 3 × 4 = 12 12 + 12 = 24

Explanation: By using doubles, we can find a 6 x 4 value. First, multiply the factor with half of 6. So, now we can do 3 x 4 = 12. Now, we can double the value of 3 x 4. That is 12 + 12 = 24. So, the answer for 6 x 4 = 24.

Question 2. 3 × 7 = _______

Explanation: Skip count by 3’s until you say 7 numbers. 3, 6, 9, 12, 15, 18, 21. So, the answer for 3 x 7 is 21.

Question 3. ________ = 2 × 6

Explanation: With the Commutative Law of Multiplication, you can write 2 x 6 as 6 x 2. Multiply the factor 2 with 5 and then add the factor to it to get the final answer. First, multiply the factor with 5. That is 5 x 2 = 10. Now, add the factor with the answer of 5 x 2. 10 +2 = 12. The answer for 6 x 2 is 12. So, the answer for 2 x 6 is 12.

Question 4. ________ = 3 × 5

Explanation: You can skip count by 3’s until you say 5 numbers. 3, 6, 9, 12, 15. So, the final answer for 3 x 5 is 15.

Question 5. 1 × 3 = ________

Explanation: Multiplication of any number with 1 is the same number. So, 1 x 3 = 3.

Question 6. ________ = 6 × 8

Explanation: Use doubles to find the answer of 6 x 8. Firstly, multiply 3 x 8 = 24. Then, double the value of 3 x 8. 24 + 24 = 48. The answer for 6 x 8 is 48.

Question 7. 3 × 9 = ________

Explanation: Skip count by 3’s until you say 9 numbers. Write like 3, 6, 9, 12, 15, 18, 21, 24, 27. The answer for 3 x 9 is 27.

Question 8. _______ = 6 × 6

Explanation: Use doubles to find the answer of 6 x 6. Firstly, multiply 3 x 6 = 18. Then, double the value of 3 x 6. 18 + 18 = 36. The answer for 6 x 6 is 36.

Question 9. 4 × 3 —— ________

Explanation: Write 4 x 3 as 3 x 4 according to the Commutative Law of Multiplication. Now do multiplication for 3 x 4. Skip-count by 3’s four times. Now, you can write as 3, 6, 9, 12. The answer for 3 x 4 is 12. So, the answer for 4 x 3 is also 12.

Go Math Grade 3 Chapter 4 Pdf Question 10. 6 × 5 —— _________

Explanation: Multiply the given factor 5 with 5. Then, add 5 to the answer to get the answer for 6 x 5. Firstly, multiply 5 x 5 = 25. Add 5 to 25. 5 + 25 = 30. So, the answer for 6 x 5 is 30.

Question 11. 2 × 3 —— _________

Explanation: Using the Commutative Law of Multiplication, you can write 2 x 3 = 3 x 2. Now, Skip count by 3’s until you say 2 numbers. 3, 6. Therefore, the answer to 3x 2 is 6. The answer for 2 x 3 is 6.

Question 12. 6 × 3 ——– _________

Explanation: Double the value of 3 x 3 to get the answer for 6 x 3. The answer for 3 x 3 = 9. Now, double the value of 9. The answer for 6 x 3 is 9 + 9 = 18.

Question 13. 10 × 6 ——- _________

Explanation: Using the Commutative Law of Multiplication, you can write as 10 x 6 = 6 x 10. Now, multiply the 10 with 5. The answer is 5 x 10 = 50. Now, add the 10 to 50 to get the answer. The answer for 6 x 10 is 10 + 50 = 60. So, the answer for 10 x 6 is 60.

Question 14. 3 × 6 ——- __________

Explanation: Skip-count by 3’s 6 times. You can write as 3, 6, 9, 12, 15, 18. The answer for 3 x 6 is 18.

Question 15. 7 × 6 ——- __________

Explanation: With the help of the Commutative Law of Multiplication, you can change 7 x 6 to 6 x 7. Double the value of 3 x 7 to get 6 x 7. Now, do 3 x 7 = 21. Double the 21. 21 + 21 = 42. The answer for 6 x 7 = 42. So, the answer for 7 x 6 is 42.

Question 16. 3 × 0 ——- _________

Explanation: Multiplication of any number with 0 is 0. So, the answer for 3 x 0 is 0.

Question 17. 9 × 6 ——- __________

Explanation: Write 9 x 6 as 6 x 9 using the Commutative Law of Multiplication. Multiply the 9 with 5. 5 x 9 = 45. Now add the 45 to the 9. So, the answer for 6 x 9 is 45 + 9 = 54. Therefore, the answer for 9 x 6 is 54.

Question 18. 3 × 3 ——- __________

Explanation: Skip count by 3’s until you say 3 numbers. 3, 6, 9. So, the answer for 3 x 3 is 9.

Question 19. 10 × 3 ——– ___________

Explanation: Use Commutative Law of Multiplication to write 10 x 3 to 3 x 10. Now, skip count by 3’s until you say 10 numbers. 3, 6, 9, 12, 15, 18, 21, 24, 27, 30. So, the answer for 3 x 10 is 30. Therefore, the answer for 10 x 3 is 30.

Question 20. 1 × 6 ——– ________

Explanation: Multiplication of any number with 1 is the same number. So, 1 x 6 = 6.

Question 21. James got 3 hits in each of his baseball games. He has played 4 baseball games. How many hits has he had in all? _________ hits

Answer: 12 hits

Explanation: As per the given data, James got 3 hits in each of his baseball games. He has played 4 baseball games. To find the number of hits has he had in all, we need to multiply, 3 hits x 4 baseball games. So, the answer is 3 x 4 = 12 hits.

Question 22. Mrs. Burns is buying muffins. There are 6 muffins in each box. If she buys 5 boxes, how many muffins will she buy? __________ muffins

Answer: 30 muffins

Explanation: From the provided information, Mrs. Burns is buying muffins. She is going to buy 5 boxes each has 6 muffins in it. So, to find the total number of muffins, we need to multiply, number of boxes and number of muffins in it. The total number of muffins = 6 x 5 = 30. She is going to buy 30 muffins.

Question 1. Paco buys a carton of eggs. The carton has 2 rows of eggs. There are 6 eggs in each row. How many eggs are in the carton? Options: a. 8 b. 12 c. 14 d. 24

Answer: b. 12

Explanation: From the given data, Paco buys a carton of eggs. The carton has 2 rows in it. Every row has 6 eggs. To find the number of eggs, we need to multiply the number of rows and the number of eggs for each row. Therefore, the number of eggs in the carton are 2 x 6 = 12. 12 eggs are available in the carton.

Question 2. Find the product. 9 × 3 —— Options: a. 18 b. 24 c. 27 d. 36

Answer: c. 27

Explanation: Use Commutative Law of Multiplication to write 9 x 3 to 3 x 9. Now, skip count by 3’s until you say 9 numbers. 3, 6, 9, 12, 15, 18, 21, 24, 27. So, the answer for 3 x 9 is 27. Therefore, the answer for 9 x 3 is 27.

Question 3. Find the difference. 5 6 8 – 2 8 3 ——— Options: a. 285 b. 325 c. 385 d. 851

Answer: a. 285

Explanation: Subtract the ones. 8 – 3 = 5. Then, Subtract the tens. 6 < 8. So, regroup 5 hundreds 6 tens equal to 4 hundreds 8 tens. 16 – 8 = 8. Subtract the hundreds and add them to check the answer. 4 – 2 = 2. The final answer is 285.

Go Math Grade 3 Chapter 4 Test Pdf Question 4. Dwight made double the number of baskets in the second half of the basketball game than in the first half. He made 5 baskets in the first half. How many baskets did he make in the second half? Options: a. 7 b. 9 c. 10 d. 20

Answer: c. 10

Explanation: Given that Dwight made double the number of baskets in the second half of the basketball game than in the first half. He made 5 baskets in the first half. So, to find the second-half baskets, we need to double the baskets in the first half. Baskets in the second half = 5 x 2 = 10.

Question 5. In Jane’s picture graph, the 😊  smile symbol represents two students. One row in the picture graph has 8 symbols. How many students does that represent? Options: a. 40 b. 32 c. 24 d. 16

Answer: d. 16

Explanation: From Jane’s picture graph, the 😊 smile symbol represents 2 students. The one row in the picture graph has 8 symbols. To find the total number of students, we need to multiply the number of smiles and the number of students for each smile. The number of students for a row is 8 x 2 = 16.

Answer: a. 5 × 6 = 30

Explanation: The given array shows that it has 6 boxes for a row and 5 boxes for a column. So, by multiplying the number of rows x number of columns the correct answer is 6 x 5 = 30. By using the Commutative Law of Multiplication, we can write 6 x 5 = 5 x 6. So, the answer from the given options is 5 × 6 = 30.

Write one way to break apart the array. Then find the product.

Explanation: The given array is 6 x 7. Use the Distributive Property to get the final answer. Break the array rows to make two smaller arrays with the facts 3 and 3. Now, you can write the given array as (3 + 3) x 7. Then, multiply each addend with 7. The equation becomes (3 x 7) +(3 x 7). Now simplify and add them to get the final answer. 21 + 21 = 42.

Explanation: The given array has 8 columns and 4 rows. Simplify the answer using Distributive Property. Now, break the array rows to make two smaller arrays with the facts 2 and 2. To get the answer, we have to write 4 x 8. By doing smaller arrays, you can write it as (2 + 2) x 8. Multiply each addend with 8. The equation becomes (2 x 8) +(2 x 8). Now simplify and add them to get the final answer. 16 + 16 = 32.

Explanation: The given figure has 9 columns and 6 rows. Use Distributive Property to get the answer of a given array. Let’s break the array rows with two smaller arrays with the facts 3 and 3. Now, write the equation as 6 x 9 = (3 + 3) x 9. Multiply each 3 with 9. 27 + 27. The final answer is 54.

Explanation: The given array has 8 columns and 7 rows. With the help of Distributive Property, you can solve the given array. Break the array columns with two smaller arrays with the facts 4 and 4. Write the equation as (7 x 4) + (7 x 4) = 28 + 28 = 56.

Question 5. There are 2 rows of 8 chairs set up in the library for a puppet show. How many chairs are there in all? Use the Distributive Property to solve. ____________ chairs

Explanation: From the given information, there are 2 rows of 8 chairs set up in the library for a puppet show. So, in the array, there are 2 rows and 8 columns. To find the answer, we have to multiply 2 x 8. Using Distributive Property, we can solve 2 x 8. Sum the number 2 with facts 1 and 1. So, we can write as (1 + 1) x 8. Simplify the answer by multiplying each addend to 8. (1 x 8) + (1 x 8) = 8 + 8 = 16. There are 16 chairs available in 2 rows.

Go Math Grade 3 Chapter 4 Pdf Lesson 4.4 Extra Practice Answer Key Question 6. A marching band has 4 rows of trumpeters with 10 trumpeters in each row. How many trumpeters are in the marching band? Use the Distributive Property to solve. ___________ trumpeters

Explanation: From the given information, a marching band has 4 rows of trumpeters with 10 trumpeters in each row. To know the number of trumpeters, we have to calculate 4 x 10. With the help of Distributive Property, you can separate the one number with its sums. Now write the 4 with its sums 2 and 2. (2 + 2) x 10. Now, you can multiply each addend with 10. (2 x 10) + (2 x 10) = 20 + 20 = 40. 40 trumpeters are in the marching band.

Question 1. Which number sentence is an example of the Distributive Property? Options: a. 7 × 6 = 6 × 7 b. 7 × (2 × 3) = (7 × 2) × 3 c. 7 × 6 = (7 × 3) + (7 × 3) d. 7 + 6 = 7 + 3 + 3

Answer: c. 7 × 6 = (7 × 3) + (7 × 3)

Explanation: Distributive Property: The Distributive Property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. So, from the given options, c. 7 × 6 = (7 × 3) + (7 × 3) is the correct answer.

Answer: a. (2 × 6) + (2 × 6)

Explanation: The given figure has 6 columns and 4 rows. By using Distributive Property, you can find the answer easily. Let’s break the array rows with two smaller arrays with the facts 2 and 2. Now, write the equation as 4 x 6 = (2 + 2) x 6. Multiply each 2 with 6. the equation can be written as (2 x 6) + (2 x 6).

Question 3. The school auditorium has 448 chairs set out for the third-grade performance. What is 448 rounded to the nearest ten? Options: a. 500 b. 440 c. 450 d. 400

Answer: c. 450

Explanation: Given that the school auditorium has 448 chairs set out for the third-grade performance. The 448 number lies between 440 and 450. 448 is closer to 450 than it is to 440. So, 448 rounds to 450.

Go Math 3rd Grade Chapter 4 Mid Chapter Checkpoint Question 4. Find the difference. 4 0 0 – 2 9 6 ———- Options: a. 104 b. 114 c. 204 d. 296

Answer: a. 104

Explanation: Subtract the ones. 0<6. so regroup 0 tens 0 ones = 1 tens 4 ones. Now, do 10 – 6 = 4. Then, Subtract the tens. 9 = 9. So, so regroup. 4 hundred 9 tens = 3 hundred 4 tens. 9 – 9 = 0. Subtract the hundreds and add them to check the answer. 3 – 2 = 1. The final answer is 104.

Question 5. There are 622 fruit snacks in one crate and 186 in another crate. How many fruit snacks are there in all? 6 2 2 + 1 8 6 ———- Options: a. 436 b. 708 c. 768 d. 808

Answer: d. 808

Explanation: Break apart the addends from the given values. Start with the hundreds. Then, add each place value. Let’s write 622 as 600 + 20 + 2 and 186 as 100 + 80 + 6. Sum up the above two values. Then you get 700 + 100 + 8. Add the ones and then add the 10’s and 100’s. The final answer is 808.

Answer: a. Football

Explanation: From the given picture, it is mentioned that the sports students play and the number of students for that game. As mentioned, Football needs 6 students. Baseball needs 12 students. Basketball needs 10 students. Also, Soccer needs 16 students. So, the answer is Football sport required 6 students to play.

Question 1. 6 × 7 = 42

Explanation: By using doubles, we can find a 6 x 7 value. First, multiply the factor with half of 6. So, now we can do 3 x 7 = 21. Now, we can double the value of 3 x 7. That is 21 + 21 = 42. So, the answer for 6 x 7 = 42.

Question 2. ________ = 7 × 9

Explanation: Use the Distributive Property to find the value of 7 x 9. If we take 7 rows and 9 columns of an array, then we can break the array into two smaller arrays with the facts of 9. Now, write the 7 x 9 as 7 x (6 + 3). Multiply the facts with the 7. Then, you get (7 x 6) + (7 x 3). Therefore, you get the answer as 42 + 21 = 63.

Question 3. _______ = 1 × 7

Explanation: Multiplication of any number with 1 is the same number. So, 1 x 7 = 7.

Question 4. 3 × 7 = _______

Question 5. 7 × 7 = ________

Explanation: Let us take the array has 7 columns and 7 rows. Simplify the answer using Distributive Property. Now, break the array rows to make two smaller arrays with the facts 4 and 3. To get the answer, we have to write 7 x 7. By doing smaller arrays, you can write it as (4 + 3) x 7. Multiply each addend with 7. The equation becomes (4 x 7) +(3 x 7). Now simplify and add them to get the final answer. 28 + 21 = 49.

Question 6. _______ = 2 × 7

Explanation: Draw two counters. Place seven objectives in two counters. Now, add the objectives in two counters. The final answer is 7 + 7 = 14. So, 2×7 = 14 is the answer.

Question 7. 7 × 8 = _________

Explanation: Distributive Property: The Distributive Property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. So, from the given options, c. 7 × 8 = (7 × 4) + (7 × 4) = 28 + 28 = 56.

Question 8. ______ = 4 × 7

Explanation: Firstly, multiply 2×7 to get the answer for 4×7. Then, double the answer of 2×7 to get the final answer. So, do 2×7 = 14. Double the number 14 to get the 4×7 Answer. The double of 14 is 14 +14 = 28. The answer to 4×7 is 28.

Go Math Grade 3 Chapter 4 Answer Key Question 9. 7 × 5 ——- __________

Explanation: From Commutative Law of Multiplication, you can write 7 x 5 = 5 x 7. So, to find the multiplication of 5 x 7, skip count by 5’s until you say 7 numbers. 5, 10, 15, 20, 25, 30, 35. Now, the count of the number is 7. So, the answer for 5 x 7 is 35. Therefore, the answer for 7 x 5 is 35.

Question 10. 7 × 1 ——- _________

Explanation: Using the Commutative Law of Multiplication, you can write 7 x 1 = 1 x 7. Multiplication of any number with 1 is the same number. So, 1 x 7 = 7.

Question 11. 6 × 7 ——- __________

Explanation: Use doubles to find the answer of 6 x 7. Firstly, multiply 3 x 7 = 21. Then, double the value of 3 x 7. 21 + 21 = 42. The answer for 6 x 7 is 42.

Question 12. 7 × 4 ——- __________

Explanation: Write 7 x 4 as 4 x 7 according to the Commutative Law of Multiplication. Now, do multiplication for 4 x 7. You can double 2×7 to get 4×7. Multiply 7 with 2. You will get 14. Then, double the product to get the answer to 4×7. You will get 14 +14 = 28. So, you get the final answer as 28.

Question 13. 2 × 7 ——- ___________

Explanation: The given multiplication is 2×7. The answer to any number multiplies with 2 is double of that number. So, the 2×7 can find by doing 7+7. The answer is 7+7 = 14. So, the final answer is 2×7 = 14.

Question 14. 10 × 7 —— ____________

Explanation: A multiple of 10 is any product that has 10 as one of its factors. So, the multiplication of any number with 10 is 10’s of that particular number. The answer is 70.

Question 15. 3 × 7 ——- ____________

Explanation: Skip count by 3’s until you say 7 numbers. Write like 3, 6, 9, 12, 15, 18, 21. The answer for 3 x 7 is 21.

Question 16. 7 × 9 —— ___________

Question 17. 8 × 7 ——- __________

Explanation: Distributive Property: The Distributive Property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. So, from the given options, c. 8 x 7 = (4 + 4) x 7 = (4 x 7) + (4 x 7) = 28 + 28 = 56 is the correct answer.

Go Math Grade 3 Chapter 4 Review/Test Pdf Question 18. 7 × 0 —— __________

Explanation: Multiplication of any number with 0 is 0. So, the answer for 7 x 0 is 0.

Question 19. Julie buys a pair of earrings for $7. Now she would like to buy the same earrings for 2 of her friends. How much will she spend for all 3 pairs of earrings? $ __________

Answer: $21

Explanation: From the given information, Julie buys a pair of earrings for $7. She also wants to buy 2 more pairs of earrings for her 2 friends. So, a total she needs to but 3 pairs of earrings. To know the total amount she is going to spend on earrings, we need to multiply the total number of earrings pair with a cost for each earring. So, we can do 3 x $7 = $21. Julie needs to spend $21 to buy 3 pairs of earrings.

Question 20. Owen and his family will go camping in 8 weeks. There are 7 days in 1 week. How many days are in 8 weeks? _________ days

Answer: 56 days

Explanation: Given that Owen and his family will go camping in 8 weeks. There are 7 days in 1 week. So, to calculate the total number of days in 8 weeks, multiply 8 x 7 = 56. There are 56 days in 8 weeks.

Question 1. Find the product. 7 × 8 —— Options: a. 54 b. 56 c. 64 d. 66

Answer: b. 56

Answer: c. 21

Explanation: The given array has 7 columns and 3 rows. Simplify the answer using Distributive Property. Now, break the array rows to make two smaller arrays with the facts 1 and 2. To get the answer, we have to write 3 x 7. By doing smaller arrays, you can write it as (1 + 2) x 7. Multiply each addend with 8. The equation becomes (1 x 7) +(2 x 7). Now simplify and add them to get the final answer. 7 + 14 = 21.

Question 3. Which statement is true about the numbers below? 6, 12, 18, 24, 30 Options: a. All of the numbers are odd. b. Some of the numbers are odd. c. All of the numbers are even. d. Some of the numbers are even.

Explanation: All the given numbers are divided by 2. So, the answer is All of the numbers are even

Answer: b. 39

Explanation: To know more people chose retriever than poodle, we have to do subtraction from retriever to poodle. So, 65 – 26 = 39. 39 more people chose retriever than poodle.

Question 5. What is 94 rounded to the nearest ten? Options: a. 90 b. 94 c. 95 d. 100

Answer: a. 90

Explanation:

94 is between 90 and 100. 94 is closer to 90 than is to 100. 94 rounded to the nearest ten is 90.

Question 6. Jack has 5 craft sticks. He needs 4 times that number for a project. How many craft sticks does Jack need altogether? Options: a. 9 b. 16 c. 20 d. 24

Answer: c. 20

Explanation: Jack has 5 craft sticks. He needs 4 times that number for a project. To find the total number of craft sticks does Jack needs altogether are 5 x 4 = 20. 20 craft sticks need to Jack.

Question 1. A __________ of 4 is any product that has 4 as one of its factors. _________

Answer: Commutative Property of Multiplication

Question 2. This is an example of the ______________ . 3 × 8 = (3 × 6) + (3 × 2) This property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. __________

Answer: Distributive Property of Multiplication

Concepts and Skills

Answer: 7 x 5 = 35

The provided array has 7 columns and 5 rows. Let’s simplify the answer by using Distributive Property. Now, break the array rows to make two smaller arrays with the facts 2 and 3. Now, do 7 x 5. By doing smaller arrays, you can write it as 7 x (2 + 3). Multiply 7 with 2 and 7 with 3. Write (7 x 2) + (7 x 3). Now add them to get the final answer. 14 + 21 = 35.

Answer: 9 x 4 = 36

Explanation: The given array has 9 columns and 4 rows. Now, do 9 x 4. Using Distributive Property break the array rows to make two smaller arrays with the 4 facts 2 and 2. Now, add 9 x (2 + 2). Multiply 9 with 2 and 9 with 2. Write (9 x 2) + (9 x 2). Now add them to get the final answer. 18 + 18 = 36.

Go Math Grade 3 Chapter 4 Multiplication Facts and Answers Question 5. 3 × 1 = __________

Explanation: Using the Commutative Law of Multiplication, Write 3 x 1 = 1 x 3. Multiplication of any number with 1 is the same number. So, 1 x 3 = 3.

Question 6. 5 × 6 = _________

Explanation: Skip-count by 5’s 6 times. You can write as 5, 10, 15, 20, 25, 30. The answer for 5 x 6 is 30.

Question 7. ________ = 7 × 7

Explanation: Use Distributive Property, to get the answer. Given 7 x 7. Write the facts for 7. 7 = 4 + 3. Now, write 7 x 7 = 7 x (4 + 3). Multiply 7 with 4 and 7 with 3. (7 x 4) + (7 x 3) = 28 + 21 = 49.

Question 8. 2 × 10 = _________

Explanation: Double the 10 to get the answer for 2 x 10. So, now write 10 + 10 = 20. The answer for 2 x 10 = 20.

Question 9. 2 × 1 ——– _________

Explanation: Add 1 + 1 to get 2 x 1. 1 + 1 = 2. The answer for 2 x 1 = 2.

Question 10. 6 × 6 ——– _________

Explanation: Use doubles to get 6 x 6. First, multiply 3 x 6 = 18. Then, double the value of 3 x 6. 18 + 18 = 36. The answer for 6 x 6 is 36.

Question 11. 8 × 7 ——- __________

Explanation: Use Distributive Property to find 8 x 7 = (4 + 4) x 7 = (4 x 7) + (4 x 7) = 28 + 28 = 56 is the correct answer.

Question 12. 6 × 0 —— ___________

The multiplication of any number with 0 is 0. So, the answer for 10 x 0 is 0.

Question 13. 3 × 8 ——- __________

Explanation: Skip-count by 3’s 8 times. You can write as 3, 6, 9, 12, 15, 18, 21, 24. The answer for 3 x 8 is 24.

Question 14. Lori saw 6 lightning bugs. They each had 6 legs. How many legs did the lightning bugs have in all? __________ legs

Explanation: Given that, Lori saw 6 lightning bugs. Each lightning bug had 6 legs. To find the total number of legs, do 6 x 6 = 36. The lightning bugs have 36 in all.

Question 15. Zach walked his dog twice a day, for 7 days. Moira walked her dog three times a day for 5 days. Whose dog was walked more times? How many more? Type below: _________

Answer: Moira’s dog walked more than Zach’s dog. It walked one time more than Zach’s dog.

Explanation: Zach walked his dog twice a day, for 7 days. So, Zach’s dog walked 7 x 2 = 14 times in total. Moira walked her dog three times a day for 5 days. Moira’s dog walked 3 x 5 = 15 days. So, Moira’s dog walked more times than Zach’s dog. It walked one time more than Zach’s dog.

Question 16. Annette buys 4 boxes of pencils. There are 8 pencils in each box. Jordan buys 3 boxes of pencils with 10 pencils in each box. Who buys more pencils? How many more? Type below: __________

Answer: Annette has more pencils than Jordan. He has 2 pencils more than Jordan.

Explanation: Annette buys 4 boxes of pencils. Each box has 8 pencils in it. So, Annette has 4 x 8 = 32 pencils. Jordan buys 3 boxes of pencils with 10 pencils in each box. So, he has 3 x 10 = 30 pencils. Annette has 2 pencils more than Jordan.

Question 17. Shelly can paint 4 pictures in a day. How many pictures can she paint in 7 days? _________ pictures

Explanation: Shelly can paint 4 pictures in a day. In 7 days, she can paint 7 x 4 = 28 pictures.

Write another way to group the factors. Then find the product.

Question 1. (3 × 2) × 5 3 × (2 × 5) 30

Explanation: Using the Associative Property of Multiplication, we can write (3 × 2) × 5 = 3 × (2 × 5). Find (3 × 2) × 5. Multiply 3 x 2 = 6. Then, multiply 6 x 5 = 30. Find 3 x (2 x 5). Multiply 2 x 5 = 10. Then, multiply 3 x 10 = 30. So, (3 × 2) × 5 = 3 × (2 × 5). The product value is 30.

Question 2. (4 × 3) × 2 = ________

Answer: (4 × 3) × 2 = 4 x (3 x 2) 24

Explanation: Use Associative Property of Multiplication to write other groups the factors. (4 × 3) × 2 = 4 x (3 x 2). Now, multiply 4 x 3 = 12. Then, multiply 12 x 2 = 24. So, (4 × 3) × 2 = 24.

Question 3. 2 × (2 × 8) = ________

Answer: 2 × (2 × 8) = (2 x 2) x 8 32

Explanation: With Associative Property of Multiplication, 2 × (2 × 8) = (2 x 2) x 8. Now, multiply 2 x 8 = 16. Then, multiply 16 x 2 = 32. So, 2 × (2 × 8) = 32.

Question 4. 9 × (2 × 1) = ________

Answer: 9 × (2 × 1) = (9 × 2) × 1 18

Explanation: Using Associative Property of Multiplication, we can write 9 × (2 × 1) = (9 × 2) × 1. Now, multiply 2 x 1 = 2. Then, multiply 2 x 9 = 18. So, 9 × (2 × 1) = 18.

Question 5. 2 × (3 × 6) = ________

Answer: 2 × (3 × 6) = (2 x 3) x 6 36

Explanation: With the help of Associative Property of Multiplication, we can write 2 × (3 × 6) = (2 x 3) x 6. Now, multiply 2 x 3 = 6. Then, multiply 6 x 6 = 36. So, 2 × (3 × 6) = 36.

Question 6. (4 × 2) × 5 = ________

Answer: (4 × 2) × 5 = 4 x (2 x 5) 40

Explanation: Use Associative Property of Multiplication, to write (4 × 2) × 5 = 4 x (2 x 5). Now, multiply 2 x 5 = 10. Then, multiply 4 x 10 = 40. So, (4 × 2) × 5 = 40.

Use parentheses and multiplication properties. Then, find the product.

Question 7. 9 × 1 × 5 ( 9 × 1 ) × 5 = ________

Answer: ( 9 × 1 ) × 5 = 9 x (1 x 5) 45

Explanation: Use Associative Property of Multiplication. ( 9 × 1 ) × 5 = 9 x (1 x 5). Now, multiply 9 x 1 = 9. Then, multiply 9 x 5 = 45. So, ( 9 × 1 ) × 5 = 45.

Mathematics Grade 3 Pdf Lesson 4.6 Answer Key Question 8. 3 × 3 × 2 ( 3 × 3 ) × 2 = _________

Answer: ( 3 × 3 ) × 2 = 18

Explanation: Use Associative Property of Multiplication. ( 3 × 3 ) × 2 = 3 x (3 x 2). Now, multiply 3 x 3 = 9. Then, multiply 9 x 2 = 18. So, ( 3 × 3 ) × 2 = 18.

Question 9. 2 × 4 × 3 ( 2 × 4 ) × 3 = _________

Answer: ( 2 × 4 ) × 3 = 2 x (4 x 3) 24

Explanation: Now use Associative Property of Multiplication. ( 2 × 4 ) × 3 = 2 x (4 x 3). Now, multiply 2 x 4 = 8. Then, multiply 8 x 3 = 24. So, ( 2 × 4 ) × 3 = 24.

Question 10. 5 × 2 × 3 ( 5 × 2 ) × 3 = _________

Answer: ( 5 × 2 ) × 3 = 5 x (2 x 3) 30

Explanation: Use Associative Property of Multiplication. ( 5 × 2 ) × 3 = 5 x (2 x 3). Now, multiply 5 x 2 = 10. Then, multiply 10 x 3 = 30. So, ( 5 × 2 ) × 3 = 30.

Question 11. 7 × 1 × 5 ( 7 × 1 ) × 5 = ________

Answer: ( 7 × 1 ) × 5 = 7 x (1 x 5) 35

Explanation: Use Associative Property of Multiplication. ( 7 × 1 ) × 5 = 7 x (1 x 5). Now, multiply 7 x 1 = 7. Then, multiply 7 x 5 = 35. So, ( 7 × 1 ) × 5 = 35.

Question 12. 8 × 2 × 3 ( 8 × 2 ) × 3 = _________

Answer: ( 8 × 2 ) × 3 = 8 x (2 x 3) 48

Explanation: Use Associative Property of Multiplication. ( 8 × 2 ) × 3 = 8 x (2 x 3). Now, multiply 8 x 2 = 16. Then, multiply 16 x 3 = 48. So, ( 8 × 2 ) × 3 = 48.

Question 13. 7 × 2 × 3 ( 7 × 2 ) × 3 = ________

Answer: ( 7 × 2 ) × 3 = 7 x (2 x 3) 42

Explanation: Use Associative Property of Multiplication. ( 7 × 2 ) × 3 = 7 x (2 x 3). Now, multiply 2 x 3 = 6. Then, multiply 7 x 6 = 42. So, ( 7 × 2 ) × 3 = 42.

Question 14. 4 × 1 × 3 ( 4 × 1 ) × 3 = ________

Explanation: Use Associative Property of Multiplication. ( 4 × 1 ) × 3 = 4 x (1 x 3). Now, multiply 4 x 1 = 4. Then, multiply 4 x 3 = 12. So, ( 4 × 1 ) × 3 = 12.

Question 15. 10 × 2 × 4 ( 10 × 2 ) × 4 = ________

Explanation: Use Associative Property of Multiplication. ( 10 × 2 ) × 4 = 10 x (2 x 4). Now, multiply 2 x 4 = 8. Then, multiply 10 x 8 = 80. So, ( 10 × 2 ) × 4 = 80.

Question 16. Beth and Maria are going to the county fair. Admission costs $4 per person for each day. They plan to go for 3 days. How much will the girls pay in all? $ _________

Answer: $24

Explanation: From the given information, County fair admission costs $4 per person for each day. To go for 3 days, it costs, 3 x $4 = $12. Beth and Maria are going to the county fair. So, 2 members are going to the county fair. The total amount is 2 X $12 = $24.

Question 17. Randy’s garden has 3 rows of carrots with 3 plants in each row. Next year he plans to plant 4 times the number of rows of 3 plants. How many plants will he have next year? _________ plants

Explanation: From the given information, Randy’s garden has 3 rows of carrots with 3 plants in each row. So, 3 x 3 = 9. To plant 4 times the number of rows of 3 plants, 9 x 4 = 36. 36 plants will have to plant by Randy’s garden next year.

Question 1. There are 2 benches in each car of a train ride. Two people ride on each bench. If a train has 5 cars, how many people in all can be on a train? Options: a. 4 b. 9 c. 10 d. 20

Answer: d. 20

Explanation: Given that there are 2 benches in each car of a train ride. If a train has 5 cars in total, the number of benches = 5 x 2 = 10. From the given information, two people ride on each bench. So, 10 x 2 = 20 people will travel on a train if the train has 5 cars.

Question 2. Crystal has 2 CDs in each box. She has 3 boxes on each of her 6 shelves. How many CDs does Crystal have in all? Options: a. 6 b. 12 c. 18 d. 36

Answer: d. 36

Explanation: The crystal has 3 boxes on each of her 6 shelves. So, she has 3 x 6 = 18 boxes with her. Each box has 2 CDs in it. So, 2 x 18 = 36 CDs available at crystal.

Question 3. Find the sum. 4 7 2 + 1 8 6 ——– Options: a. 658 b. 648 c. 558 d. 286

Add the ones. Add 2 + 6 =8. Then, Add the tens. Regroup hundreds and tens. Add 7 + 8 = 15. Remember to carry over. Add the hundreds. Add 4 + 1 + 1 = 6. Place the one’s, ten’s and hundreds to get the sum. The sum is 658.

Answer: d. 25 minutes

Question 5. Madison has 142 stickers in her collection. What is 142 rounded to the nearest ten? Options: a. 40 b. 140 c. 150 d. 200

Answer: b. 140

Explanation: The 142 lies between 140 and 150. But the 142 is closer to 140 than it is to 150. So, 142 is rounded to the 140.

Question 6. There are 5 pages of photos. Each page has 6 photos. How many photos are there in all? Options: a. 12 b. 20 c. 24 d. 30

Answer: d. 30

Explanation: Given that there are 5 pages of photos. And, each page has 6 photos. Total photos = 5 x 6 = 30.

Is the product even or odd? Write even or odd.

Question 1. 2 × 7 = even Think: Products with 2 as a factor are even.

Answer: even

Explanation: Products with 2 as a factor are even.

Question 2. 4 × 6 = ________

Explanation: The numbers end with 0, 2, 4, 6, 8 are even numbers. So, 24 is even number. The 4 × 6 an even number.

Go Math Grade 3 Algebra Lesson 4.7 Question 3. 8 × 3 = ________

Explanation: 8 is an even number. 3 is an odd number. The product of an odd number and an even number is even. The answer is even.

Question 4. 2 × 3 = _________

Question 5. 9 × 9 = ________

Answer: odd

Explanation: 9 is an odd number. The product of two odd numbers is an odd number. The answer is odd.

Question 6. 5 × 7 = _________

Explanation: The numbers end with 1,3, 5, 7, 9 are odd numbers. So, 35 is an odd number. The 5 × 7 an odd number.

Question 7. 6 × 3 = ________

Explanation: 6 is an even number. 3 is an odd number. The product of an odd number and an even number is even. The answer is even.

Use the multiplication table. Describe a pattern you see.

Question 8. in the column for 5 _________

Answer: The one’s digits repeat 0 and 5. Each number is 5 more than the number above it.

Explanation: Each number is added with 5. One’s digit is repeated with 0 and 5.

Question 9. in the row for 10 ________

Answer: Add 10. All the products are even. The one’s digit is always 0.

Explanation: All the products are even. Also, the one’s digit is always 0. Add 10 for every product to get the next number to it.

Question 10. in the rows for 3 and 6 Type below: _________

Answer: The products of 6 are the products of 3 doubled.

Explanation: Add 3 for row 3. The products of 6 are the products of 3 doubled.

Question 11. Carl shades a row in the multiplication table. The products in the row are all even. The ones digits in the products repeat 0, 4, 8, 2, 6. What row does Carl shade? Carl shaded row for _________

Answer: The row for 4.

Explanation: From the given data, the answer is row 4.

Question 12. Jenna says that no row or column contains products with only odd numbers. Do you agree? Explain. _________

Answer: Yes, Either the products are all even, or there is an even and odd number pattern.

Explanation: Jenna said correctly. Either the products are all even, or there is an even and odd number pattern.

Question 1. Which has an even product? Options: a. 1 × 9 b. 3 × 3 c. 5 × 7 d. 4 × 9

Answer: d. 4 × 9

Explanation: The product of an odd number and an even number is even. The answer is 4 × 9.

Question 2. Which describes this pattern? 10, 15, 20, 25, 30 Options: a. Even and then odd b. Add 10. c. Subtract 5. d. Multiply by 5.

Answer: a. Even and then odd

Explanation: The given pattern is the combination of even and add.

Question 3. Lexi has 2 cans of tennis balls. There are 3 tennis balls in each can. She buys 2 more cans. How many tennis balls does she now have in all? Options: a. 12 b. 9 c. 7 d. 6

Answer: a. 12

Explanation: Lexi has 2 cans of tennis balls. There are 3 tennis balls in each can. So, she has 2 x 3 = 6 balls. She buys 2 more cans. So, again 2 cans with 3 tennis balls = 2 x 3 =6. Total = 6 + 6 = 12. 12 tennis balls she is going to have with her.

Explanation: From the given picture, Green eyes have 4 circles. Each circle =4. 4 x 4 = 16. 16 students have green eyes.

Question 5. Sasha bought 3 boxes of pencils. If each box has 6 pencils, how many pencils did Sasha buy in all? Options: a. 9 b. 12 c. 18 d. 24

Explanation: Sasha bought 3 boxes of pencils. If each box has 6 pencils, 3 x 6 = 12 pencils Sasha can buy in all.

Question 6. Find the sum. 2 1 9 + 7 6 3 ———– Options: a. 992 b. 982 c. 976 d. 972

Answer: b. 982

Explanation: Break apart the addends from the given values. Start with the hundreds. Then, add each place value. Let’s write 219 as 200+10+9 and 763 as 700+60+3. Sum up the above two values. Then you get 900+70+12. Add the ones and then add the 10’s and 100’s. The final answer is 982.

Question 1. 8 × 10 = 80

Explanation: 8 × 10 = (2 x 4) x 10 Use the Associative Property. 8 × 10 = 2 x (4 x 10) Multiply. 4 × 10 8 × 10 = 2 x 40 Double the product. 8 × 10 = 40 + 40 8 × 10 = 80

Question 2. 8 × 8 = ________

Explanation: Factor 8 is an even number. 4+ 4 8 x 4 = 32. 32 doubled is 64. 8 x 8 = 64.

Question 3. 8 × 5 = ________

Explanation: 8 × 5 = (2 x 4) x 5 Use the Associative Property. 8 × 5 = 2 x (4 x 5) Multiply. 4 × 5 8 × 5 = 2 x 20 Double the product. 8 × 5 = 20 + 20 8 × 5 = 40

Question 4. 3 × 8 = ________

Explanation: Factor 8 is an even number. 4+ 4 3 x 4 = 12. 12 doubled is 24. 3 x 8 = 24.

Question 5. _______ = 4 × 8

Explanation: Factor 8 is an even number. 4+ 4 4 x 4 = 16. 16 doubled is 32. 4 x 8 = 32.

Question 6. 8 × 7 = ________

Explanation: 8 × 7 = (2 x 4) x 7 Use the Associative Property. 8 × 7 = 2 x (4 x 7) Multiply. 4 × 7 8 × 7 = 2 x 28 Double the product. 8 × 7 = 28 + 28 8 × 7 = 56.

Question 7. 6 × 8 = ________

Explanation: Factor 8 is an even number. 4+ 4 6 x 4 = 24. 24 doubled is 48. 6 x 8 = 48.

Question 8. _______ = 9 × 8

Explanation: Factor 8 is an even number. 4+ 4 9 x 4 = 36. 36 doubled is 72. 9 x 8 = 72.

Question 9. 8 × 2 —— ________

Explanation: Using the Commutative Law of Multiplication, 2 x 8 = 8 x 2. Factor 8 is an even number. 4+ 4 2 x 4 = 8. 8 doubled is 16. 2 x 8 = 16. So, 8 x 2 =16.

Question 10. 6 × 8 ——- ________

Question 11. 8 × 7 —— _________

Explanation: Using the Commutative Law of Multiplication, 8 x 7 = 7 x 8. Factor 8 is an even number. 4+ 4 7 x 4 = 28. 28 doubled is 56. 7 x 8 = 56.

Question 12. 0 × 8 ——- ____________

Multiplication of any number with 0 is 0. So, the answer for 0 x 8 is 0.

Question 13. 8 × 5 —— ___________

Explanation: 8 × 5 = (2 x 4) x 5 Use the Associative Property. 8 × 5 = 2 x (4 x 5) Multiply. 4 × 5 8 × 5 = 2 x 20 Double the product. 8 × 5 = 20 + 20 8 × 5 = 40.

Question 14. 8 × 8 ——– ___________

Question 15. 9 × 8 ——- ___________

Question 16. 8 × 3 —— ___________

Explanation: 8 × 3 = (2 x 4) x 3 Use the Associative Property. 8 × 3 = 2 x (4 x 3) Multiply. 4 × 3 8 × 3 = 2 x 12 Double the product. 8 × 3 = 12 + 12 8 × 3 = 24.

Question 17. 8 × 1 —— ___________

Multiplication of any number with 1 is the same number. So, 1 x 8 = 8.

Question 18. 4 × 8 —— ___________

Question 19. There are 6 teams in the basketball league. Each team has 8 players. How many players are there in all? ____________ players

Explanation: Multiply 6 x 8 to get the total number of players. 6 x 8 = 48 players are in the basketball league.

Question 20. Lynn has 4 stacks of quarters. There are 8 quarters in each stack. How many quarters does Lynn have in all? ___________ quarters

Explanation: Multiply 4 x 8 to find quarters in stacks. Lynn has 4 x 8 = 32 quarters in total.

Question 21. Tomas is packing 7 baskets for a fair. He is placing 8 apples in each basket. How many apples are there in all? ___________ apples

Explanation: Multiply 7 x 8 to get the total number of apples. Tomas have 7 x 8 = 56 apples.

Question 22. There are 10 pencils in each box. If Jenna buys 8 boxes, how many pencils will she buy? _____________ pencils

Explanation: To get total pencils, if Jenna buys 8 boxes, multiply 10 x 8. So, Jenna buys 10 x 8 = 80 pencils.

Question 1. Find the product. 5 × 8 = ■ Options: a. 30 b. 32 c. 42 d. 40

Answer: d. 40

Explanation: Using Commutative Property of Multiplication, write 5 x 8 = 8 x 5 8 × 5 = (2 x 4) x 5 Use the Associative Property. 8 × 5 = 2 x (4 x 5) Multiply. 4 × 5 8 × 5 = 2 x 20 Double the product. 8 × 5 = 20 + 20 8 × 5 = 40

Question 2. There are 7 tarantulas in the spider exhibit at the zoo. Each tarantula has 8 legs. How many legs do the 7 tarantulas have in all? Options: a. 15 b. 49 c. 56 d. 63

Answer: c. 56

Explanation: Multiply 7 x 8 to find the 7 tarantulas legs. 7 tarantulas have 7 x 8 = 56 legs.

Question 3. Find the difference. 6 5 2 – 9 9 ——— Options: a. 99 b. 552 c. 553 d. 653

Answer: c. 553

Explanation: Subtract the ones. 2<9. so regroup 5 tens 2 ones = 4 tens 3 ones. Now, do 12 – 9 = 3. Then, Subtract the tens. 4 < 9. So, regroup 6 hundred 5 tens = 5 hundred 5 tens. 14 – 9 = 5. Subtract the hundreds and add them to check the answer. 5 – 0 = 5. The final answer is 553.

Division and the Distributive Property Lesson 4.8 Answer Key Question 4. The school library received an order of 232 new books. What is 232 rounded to the nearest ten? Options: a. 200 b. 230 c. 240 d. 300

Answer: b. 230

Explanation: The 232 lies between 230 and 240. But the 232 is closer to 230 than it is to 240. So, 232 is rounded to the 230.

Question 5. Sam’s picture graph shows that 8 students chose pizza as their favorite lunch. This is the key for the graph. Each ☺ smile = 2 students. How many ☺ smile should be next to pizza on Sam’s graph? Options: a. 2 b. 4 c. 6 d. 8

Answer: b. 4

Explanation: Given 1 smile = 2 students. 2 smiles = 4 students 3 smiles = 6 students 4 smiles = 8 students 4 smiles required for Sam for her next pizza on the graph.

Question 6. Tashia buys 5 packages of oranges. Each package has 4 oranges. How many oranges in all does Tashia buy? Options: a. 1 b. 9 c. 20 d. 25

Answer: d. 25

Explanation: To know the total number of oranges, multiply 5 x 5. Tashia buys 5 x 5 = 25 oranges.

Question 1. 10 × 9 = 90

Explanation: The tens digit is 1 less than the factor that is multiplied by 9. So, ten’s digit number is 10 – 1 = 9. The sum of the digits in the product is always 9. So, to multiply 10 × 9, think the tens digit is 9 and the one’s digit is 0. The product is 90.

Question 2. 2 × 9 = ________

Explanation: 9 = 3 + 6 2 × 9 = 2 x (3 + 6) Multiply each addend by 2. 2 × 9 = (2 × 3) + (2 × 6) Add the products. 2 × 9 = 6 + 12 2 × 9 = 18.

Question 3. 9 × 4 = ________

Explanation: 9 = 3 + 6 9 × 4 = (3 + 6) x 4 Multiply each addend by 4. 9 × 4 = (3 x 4) + (6 x 4) Add the products. 9 × 4 = 12 + 24 9 × 4 = 36.

Question 4. 0 × 9 = ________

Multiplication of any number with 0 is 0. So, the answer for 0 x 9 is 0.

Question 5. 1 × 9 = ________

Multiplication of any number with 1 is the same number. So, 1 x 9 = 9.

Question 6. 8 × 9 = ________

Explanation: 9 = 3 + 6 8 × 9 = 8 x (3 + 6) Multiply each addend by 8. 8 × 9 = (8 × 3) + (8 × 6) Add the products. 8 × 9 = 24 + 48 8 × 9 = 72.

Question 7. 9 × 5 = ________

Explanation: 9 = 3 + 6 9 × 5 = (3 + 6) x 5 Multiply each addend by 5. 9 × 5 = (3 x 5) + (6 x 5) Add the products. 9 × 5 = 15 + 30 9 × 5 = 45.

Question 8. 6 × 9 = ________

Explanation: 9 = 3 + 6 6 × 9 = 6 x (3 + 6) Multiply each addend by 6. 6 × 9 = (6 × 3) + (6 × 6) Add the products. 6 × 9 = 18 + 36 6 × 9 = 54.

Question 9. 9 × 4 ——– ________

Question 10. 5 × 9 ——– ________

Explanation: 9 = 3 + 6 5 × 9 = 5 x (3 + 6) Multiply each addend by 5. 5 × 9 = (5 × 3) + (5 × 6) Add the products. 5 × 9 = 15 + 30 5 × 9 = 45.

Question 11. 9 × 7 ——– ________

Explanation: 9 = 3 + 6 9 × 7 = (3 + 6) x 7 Multiply each addend by 7. 9 × 7 = (3 x 7) + (6 x 7) Add the products. 9 × 7 = 21 + 42 9 × 7 = 63.

Question 12. 2 × 9 ——– ________

Question 13. 9 × 9 ——– ________

Explanation: The tens digit is 1 less than the factor that is multiplied by 9. So, ten’s digit number is 9 – 1 = 8. The sum of the digits in the product is always 9. So, add 1 to 8 to get one’s digit 1 + 8 = 9. The product is 81.

Question 14. 10 × 9 ——– ________

Question 15. 3 × 9 ——– ________

Explanation: 9 = 3 + 6 3 × 9 = 3 x (3 + 6) Multiply each addend by 3. 3 × 9 = (3 × 3) + (3 × 6) Add the products. 3 × 9 = 9 + 18 3 × 9 = 27.

Question 16. 9 × 8 ——– ________

Question 17. 6 × 9 ——– ________

Question 18. 9 × 1 ——– ________

Explanation: Multiplication of any number with 1 is the same number. So, 1 x 9 = 9.

Question 19. There are 9 positions on the softball team. Three people are trying out for each position. How many people in all are trying out? ___________ people

Explanation: To find the total number of people trying for a position on the softball team, multiply 9 x 3. 9 x 3 = 27 people are trying for a softball team position.

Question 20. Carlos bought a book for $9. Now he would like to buy 4 other books for the same price. How much will he have to pay in all for the other 4 books? $ _____________

Answer: $36

Explanation: Carlos bought a book for $9. Now he would like to buy 4 other books for the same price. So, to get them all 4 books, he needs to pay 4 x $9 = $36.

Question 1. Find the product. 7 × 9 = ■ Options: a. 63 b. 56 c. 45 d. 36

Answer: a. 63

Question 2. Clare buys 5 tickets for the high school musical. Each ticket costs $9. How much do the tickets cost in all? Options: a. $36 b. $40 c. $45 d. $52

Answer: c. $45

Explanation: Multiply 5 with $9 to get the total number of tickets. Clare buys 5 tickets for 5 x $9 = $45.

Answer: d. 6

Explanation: From the given figure, there are 6 bars available in the Number of Girls for Brown. So, the answer is 6.

Question 4. Miles picked up 9 shirts from the dry cleaners. It costs $4 to clean each shirt. How much did Miles spend to have all the shirts cleaned? Options: a. $13 b. $22 c. $36 d. $45

Answer: c. $36

Explanation: Miles spend 9 x $4 = $36 to have all the shirts cleaned.

Question 5. In a picture graph, each picture of a baseball is equal to 5 games won by a team. The row for the Falcons has 7 baseballs. How many games have the Falcons won? Options: a. 40 b. 35 c. 12 d. 7

Explanation: From given data, 1 baseball = 5 games. The row for the Falcons has 7 baseballs. So, Falcons won 7 x 5 = 35 games.

Question 6. An array has 8 rows with 4 circles in each row. How many circles are in the array? Options: a. 12 b. 24 c. 32 d. 36

Explanation: 8 x 4 = 32 circles are in the array.

Answer: 5 ways

Explanation: Henry can put the cards in 5 ways. They are 1. (1 x 6 cards pages) x (10 x 3 cards pages) = 6 cards + 30 cards = 36 cards. 2. (2 x 6 cards pages) x (8 x 3 cards pages) = 12 cards + 24 cards = 36 cards. 3. (3 x 6 cards pages) x (6 x 3 cards pages) = 18 cards + 18 cards = 36 cards. 4. (4 x 6 cards pages) x (4 x 3 cards pages) = 24 cards + 12 cards = 36 cards. 5. (5 x 6 cards pages) x (2 x 3 cards pages) = 30 cards + 6 cards = 36 cards.

Question 2. Ms. Hernandez has 17 tomato plants that she wants to plant in rows. She will put 2 plants in some rows and 1 plant in the others. How many different ways can she plant the tomato plants? Make a table to solve.

Answer: 8 ways

Explanation: Ms. Hernandez wants to grow 2 tomoto plants in one row and 1 in other row. The total number of plants should be 17. So, 1. (8 rows x 2 plants) x (1 row x 1plant) = 16 plants + 1 plant = 17 plants. 2. (7 rows x 2 plants) x (3 rows x 1plant) = 14 plants + 3 plant = 17 plantst. 3. (6 rows x 2 plants) x (5 rows x 1plant) = 12 plants + 5 plant = 17 plants. 4. (5 rows x 2 plants) x (7 rows x 1plant) = 10 plants + 7 plant = 17 plants. 5. (4 rows x 2 plants) x (9 rows x 1plant) = 8 plants + 9 plant = 17 plants. 6. (3 rows x 2 plants) x (11 rows x 1plant) = 6 plants + 11 plant = 17 plants. 7. (2 rows x 2 plants) x (13 rows x 1plant) = 4 plants + 13 plant = 17 plants. 8. (1 rows x 2 plants) x (15 rows x 1plant) = 2 plants + 15 plant = 17 plants.

Question 3. Bianca has a total of 25¢. She has some nickels and pennies. How many different combinations of nickels and pennies could Bianca have? Make a table to solve.

Answer: 4 ways

Explanation: 1 Nickel = 5 pennies. Bianca can have combinations of nickels and pennies to get 25¢ are 1. 1 Nickel + 20 Pennies = 5 Pennies + 20 Pennies = 25 Pennies = 25¢ 2. 2 Nickels + 15 Pennies = 10 Pennies + 15 Pennies = 25 Pennies = 25¢ 3. 3 Nickels + 10 Pennies = 15 Pennies + 10 Pennies = 25 Pennies = 25¢ 4. 4 Nickels + 5 Pennies = 20 Pennies + 5 Pennies = 25 Pennies = 25¢

Question 1. The table shows different ways that Cameron can display his 12 model cars on shelves. How many shelves will display 2 cars if 8 of the shelves each display 1 car? Options: a. 1 b. 2 c. 3 d. 4

Answer: b. 2

Explanation: 1. (Shelves with 1 car x 2) + (Shelves with 2 cars x 5) = 2 Cars + 10 Cars = 12 Cars 2. (Shelves with 1 car x 4) + (Shelves with 2 cars x 4) = 4 Cars + 8 Cars = 12 Cars 3. (Shelves with 1 car x 6) + (Shelves with 2 cars x 3) = 6 Cars + 6 Cars = 12 Cars 4. (Shelves with 1 car x 8) + (Shelves with 2 cars x 2) = 8 Cars + 4 Cars = 12 Cars 5. (Shelves with 1 car x 10) + (Shelves with 2 cars x 1) = 10 Cars + 2 Cars = 12 Cars Therefore, 2 shelves will display 2 cars if 8 of the shelves each display 1 car.

Question 2. Find the sum. 3 1 7 + 1 5 1 ——– Options: a. 166 b. 268 c. 468 d. 568

Answer: c. 468

Explanation: Add the ones. Add 7 + 1 =8. Then, Add the tens. Add 1 + 5 = 6. Add the hundreds. Add 3 + 1 = 4. Place the one’s, ten’s and hundreds to get the sum. The sum is 468.

Question 3. The school cafeteria has an order for 238 hot lunches. What is 238 rounded to the nearest ten? Options: a. 300 b. 240 c. 230 d. 200

Answer: b. 240

Explanation: The 238 lies between 230 and 240. But the 238 is closer to 240 than it is to 230. So, 238 is rounded to the 240.

Explanation: Each circle = 3 votes. If 12 students voted for green, total votes = 12. Write 12 = 3 + 3 + 3 +3. So, 4 circles represent 12 votes.

Question 5. There are 5 bikes in each bike rack at the school. There are 6 bike racks. How many bikes in all are in the bike racks? Options: a. 11 b. 24 c. 25 d. 30

Explanation: To find the total bikes in the bike rack at the school, multiply 5 bikes x 6 bike racks. 5 x 6 = 30 bikes are available in bike racks.

Question 1. Mrs. Ruiz sorted spools of thread into 4 boxes. Each box holds 5 spools. How many spools of thread does Mrs. Ruiz have? Draw circles to model the problem. Then solve. ________ spools

Answer: 20 spools

Explanation: 4 boxes of spools x 5 spools = 20 spools. Mrs. Ruiz has 20 spools of thread.

Question 2. For numbers 2a–2d, select True or False for each multiplication sentence. a. 2 × 8 = 16 i. True ii. False

Answer: i. True

Explanation: Double 8. 8 + 8 = 16. So, 2 x 8 = 16.

Question 2. b. 5 × 8 = 40 i. True ii. False

Question 2. c. 6 × 8 = 56 i. True ii. False

Answer: ii. False

Use doubles to find the answer of 6 x 8. Firstly, multiply 3 x 8 = 24. Then, double the value of 3 x 8. 24 + 24 = 48. The answer for 6 x 8 is 48. So, 6 × 8 = 56 is false.

Question 2. d. 8 × 8 = 64 i. True ii. False

Question 3. Bella is planning to write in a journal. Some pages will have one journal entry on them, and other pages will have two journal entries on them. If Bella wants to make 10 entries, how many different ways can she write them in her journal? ________ different ways

Explanation: 1. (1 journal entry x 2) + (2 journal entries x 4) = 2 journals + 8 journals = 10 journals. 2. (1 journal entry x 4) + (2 journal entries x 3) = 4 journals + 6 journals = 10 journals. 3. (1 journal entry x 6) + (2 journal entries x 2) = 6 journals + 4 journals = 10 journals. 4. (1 journal entry x 8) + (2 journal entries x 1) = 8 journals + 2 journals = 10 journals.

Bella can use 4 ways to write journals.

Question 4. There are 7 days in 1 week. How many days are there in 4 weeks? _______ days

Answer: 28 days

Explanation: 1 week = 1 x 7 = 7 days. 4 weeks = 4 x 7 = 28 days.

3 × (2 × 3) = 3 x 6 = 18.

Question 6. Dale keeps all of his pairs of shoes in his closet. Select the number of shoes that Dale could have in his closet. Mark all that apply. Options: a. 3 b. 4 c. 6 d. 7 e. 8

Answer: b. 4 c. 6 e. 8

Explanation: Pair of shoes have 2 in number. So, the possible ways are always even. Dale could have 4, 6, 8 in his closet.

Answer: 0, 2, 4, 6, 8

Question 7. Part B Explain how you know that you have selected all of the correct possibilities. Type below: __________

Answer: Given that the product numbers are even. The product of an even number with another number is even. So, we should take the mystery factor as an even number.

Explanation: Kate drew 7 octagons. An octagon has 8 sides. Kate draw 8 x 7 = 56 sides.

Question 9. José buys 6 bags of flour. Each bag weighs 5 pounds. How many pounds of flour did José buy? _________ pounds

Answer: 30 pounds

Explanation: 6 x 5 = 30. José spends 30 pounds to buy flours.

Explanation: Break the array of 4 columns and 6 rows to get the answer.

Answer: <

Explanation: 9 x 6 = 54 3 x 27 = 81 54 < 81. So, 9 x 6 < 3 x (3 x 9)

Question 12. Roberto wants to make $2.00 using dollars, half dollar, and quarters. How many different ways can he make $2.00? __________ different ways

Explanation: 0.25  – 8 |6 |4 |4 |2 |2 |0 |0 |0 0.50 – 0 |1 |2 |0 |3 |1 |2 |4 |0 1        -0 |0 |0 |1 |0 |1 |1 |0 |2

Question 13. A carpenter builds stools that have 3 legs each. How many legs does the carpenter use to build 5 stools? Use the array to explain how you know your answer is correct. _________ legs

Answer: 15 legs

Explanation: Each stool has 3 legs. To build 5 stools, 5 x 3 = 15 legs. 15 legs need to build 5 stools.

Question 14. Etta buys some ribbon and cuts it into 7 pieces that are the same length. Each piece is 9 inches long. How long was the ribbon that Etta bought? _________ inches

Answer: 63 inches

Explanation: The length of the ribbon is 7 x 9 inches = 63 inches.

Question 15. Antoine and 3 friends divide some pennies evenly among themselves. Each friend separates his pennies into 3 equal stacks with 5 pennies in each stack. Write a multiplication sentence that shows the total number of pennies. Type below: _________

Answer: 4 x (5 x 3)

Explanation: 5 pennies into 3 equal stacks = 5 x 3 = 15. 15 stacks shared between 4 friends = 4 x 15 = 4 x (5 x 3).

Question 16. Luke is making 4 first-aid kits. He wants to put 3 large and 4 small bandages in each kit. How many bandages does he need for the kits? Show your work. _________ bandages

Answer: 28 bandages

Explanation: Luke wants to put 3 large and 4 small bandages in each kit. So, total = 3 + 4 = 7 bandages. He is making 4 first-aid kits. So, 4 x 7 bandages = 28 bandages.

Question 17. For numbers 17a–17d, select True or False for each equation. a. 3 × 7 = 21 i. True ii. False

Skip count by 3’s until you say 7 numbers. 3, 6, 9, 12, 15, 18, 21. So, the answer for 3 x 7 is 21. The answer is true.

Question 17. b. 5 × 7 = 28 i. True ii. False

Skip count by 5’s until you say 7 numbers. 5, 10, 15, 20, 25, 30, 35. Now, the count of the number is 7. So, the answer for 5 x 7 is 35. The answer is False.

Question 17. c. 8 × 7 = 49 i. True ii. False

Use Distributive Property to find 8 x 7 = (4 + 4) x 7 = (4 x 7) + (4 x 7) = 28 + 28 = 56 is the correct answer. The answer is False.

Question 17. d. 9 × 7 = 63 i. True ii. False

Explanation: 9 = 3 + 6 9 × 7 = (3 + 6) x 7 Multiply each addend by 7. 9 × 7 = (3 x 7) + (6 x 7) Add the products. 9 × 7 = 21 + 42 9 × 7 = 63. The answer is true.

Explanation: The value of 10 x4 = 40. So, the answer is 4.

Question 19. For numbers 19a–19d, select Yes or No to indicate whether the number sentence has the same value as 8 × 6. a. 8 + (4 × 2) = ■ i. yes ii. no

Answer: ii. no

Explanation: 8 x 6 = 48. 8 + (4 x 2) = 8 + 8 =16. The answer is no.

Question 19. b. (8 × 4) + (8 × 2) = ■ i. yes ii. no

Answer: i. yes

Explanation: 8 x 6 = 48. (8 x 4) + (8 x 2) = 32 + 16 = 48. The answer is yes.

Question 19. c. (6 × 4) + (6 × 2) = ■ i. yes ii. no

Explanation: 8 x 6 = 48. (6 × 4) + (6 × 2) = 24 + 12 = 36. The answer is no.

Question 19. d. 6 × (4 + 4) = ■ i. yes ii. no

Explanation: 8 x 6 = 48. 6 × (4 + 4) = 6 x 8 = 48. The answer is yes.

Question 20. Chloe bought 4 movie tickets. Each ticket cost $6. What was the total cost of the movie tickets? $ _________

Explanation: The total cost of the movie tickets = 4 x $6 = $24.

Answer: 6 x (5 x 2) = 60

Explanation: We can write as 6 x (5 x 2) = 60.

Answer: 12, 15, 18, 21, 24, 27, 30. Add 3 to the product to get the next product.

Explanation: Add 3 to the product to get the next product. 9+3 = 12. 12 + 3 = 15. 15 + 3 = 18. 18 + 3 = 21. 21 + 3 = 24. 24 + 3 = 27. 27 + 3 = 30.

Question 22. Part B If you multiplied 3 × 37, would the product be an even number or an odd number? Use the table to explain your reasoning. __________

Answer: When an even number is multiplied by 3 (an odd number), the product is even. When an odd number is multiplied by 3, the product is odd, so the product of 3 × 37 would be odd.

Explanation: Skip 2 numbers to get the product of 4 multiples. If you skip 2 numbers until you count 8, you can get 32. The answer is 32.

Find Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies along with an explanation for each question. Get third-grade multiplication facts for better practice. All the questions and answers explained with images, graphs for easy understanding. Do all the activities and check your answers.

Your students can strengthen their knowledge by practicing all the multiplications available on this page. Learn multiplication concepts easily in the best way using our Go Math Answer Key for Grade 3 Chapter 4 Multiplication Facts and Strategies. Examples can also include along with the concepts to make your experience better.

Quickly get Go Math Grade 3 Answer Key and know the process of solving every multiplication to grab the knowledge. We support you with our Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Extra Practice PDF every time.

Share this:

Leave a comment cancel reply.

You must be logged in to post a comment.

• Texas Go Math
• Big Ideas Math
• Engageny Math
• McGraw Hill My Math
• enVision Math
• 180 Days of Math
• Math in Focus Answer Key
• Math Expressions Answer Key
• Privacy Policy

HMH Into Math Grade 3 Answer Key PDF | HMH Into Math 3rd Grade Answers

HMH Into Math 3rd Grade Answer Key PDF prevailing here includes questions from the latest edition of textbooks. You can use the HMH Into Math Grade 3 Solutions as a quick guide to resolve any of your doubts and get the proper assistance needed during your homework or class assignments. Our experts tried to design the Houghton Mifflin Harcourt Into Math Third Grade Answers adhering to the Latest K-8 Math Curriculum. Practice consistently using these quick resources for HMH Into Math Answer Key for Grade 3 and stand out from the rest of the crowd in exams.

HMH Into Math Grade 3 Answers | HMH Into Math 3rd Grade Answer Key PDF

Give appropriate attention to the Houghton Mifflin Harcourt Into Math 3rd Grade Solutions and become fluent and proficient in mathematics concepts. All the materials present here HMH Into Math Grade 3 Answer Keys for Volume 1 & Volume 2 are designed carefully so that they meaningfully connect to the Standards of Mathematical Content. You can download the Unitwise Into Math HMH Grade 3 Solutions PDF by simply tapping on the respective links.

HMH Into Math Grade 3 Volume 1 Answer Key PDF

HMH Into Math Grade 3 Answer Key Pdf Unit 1 Understand Multiplication and Area

• Module 1 Understand Multiplication
• Lesson 1 Count Equal Groups
• Lesson 2 Relate Addition and Multiplication
• Lesson 3 Represent Multiplication with Arrays
• Lesson 4 Understand the Commutative Property of Multiplication
• Lesson 5 Represent Multiplication with Number Lines
• Lesson 6 Represent Multiplication with Bar Models
• Into Math Grade 3 Module 1 Review Answer Key
• Module 2 Relate Multiplication and Area
• Lesson 1 Understand Area by Counting Unit Squares
• Lesson 2 Measure Area by Counting Unit Squares
• Lesson 3 Relate Area to Addition and Multiplication
• Lesson 4 Solve Problems with Area
• Lesson 5 Find the Area of Combined Rectangles
• Into Math Grade 3 Module 2 Review Answer Key

HMH Into Math Grade 3 Answer Key Unit 2 Multiplication and Division

• Module 3 Understand Multiplication Strategies
• Lesson 1 Multiply with 2 and 4
• Lesson 2 Multiply with 5 and 10
• Lesson 3 Multiply with 3 and 6
• Into Math Grade 3 Module 3 Review Answer Key
• Module 4 Apply Multiplication Properties as Strategies
• Lesson 1 Understand the Identity and Zero Properties of Multiplication
• Lesson 2 Understand the Distributive Property
• Lesson 3 Understand the Associative Property of Multiplication
• Lesson 4 Multiply with 7
• Lesson 5 Multiply with 8
• Lesson 6 Multiply with 9
• Lesson 7 Identify Number Patterns on the Multiplication Table
• Into Math Grade 3 Module 4 Review Answer Key
• Module 5 Multiplication with Multiples of 10
• Lesson 1 Use the Distributive Property
• Lesson 2 Use the Associative Property of Multiplication
• Lesson 3 Use Place Value Strategies to Multiply with Multiples of 10
• Lesson 4 Multiply Multiples of 10 by 1-Digit Numbers
• Into Math Grade 3 Module 5 Review Answer Key

Into Math Houghton Mifflin Grade 3 Module 6 Understand Division

• Module 6 Understand Division
• Lesson 1 Represent Division
• Lesson 2 Separate Objects into Equal Groups
• Lesson 3 Find the Number of Equal Groups
• Lesson 4 Relate Subtraction and Division
• Lesson 5 Represent Division with Arrays
• Lesson 6 Represent Division with Bar Models
• Lesson 7 Apply Division Rules for 1 and 0
• Into Math Grade 3 Module 6 Review Answer Key
• Module 7 Relate Multiplication and Division
• Lesson 1 Relate Multiplication and Division
• Lesson 2 Write Related Facts
• Lesson 3 Multiply and Divide with 2, 4, and 8
• Lesson 4 Multiply and Divide with 5 and 10
• Lesson 5 Multiply and Divide with 3 and 6
• Lesson 6 Multiply and Divide with 7 and 9
• Lesson 7 Build Fluency with Multiplication and Division
• Into Math Grade 3 Module 7 Review Answer Key
• Module 8 Apply Multiplication and Division
• Lesson 1 Identify and Extend Patterns
• Lesson 2 Find Unknown Factors and Numbers
• Lesson 3 Use Multiplication and Division to Solve Problem Situations
• Lesson 4 Solve Two-Step Problems
• Lesson 5 Practice with One- and Two-Step Problems
• Into Math Grade 3 Module 8 Review Answer Key

Into Math Grade 3 Answer Key Unit 3 Addition and Subtraction Strategies and Applications

• Module 9 Addition and Subtraction Strategies
• Lesson 1 Identify Number Patterns on the Addition Table
• Lesson 2 Use Mental Math Strategies for Addition and Subtraction
• Lesson 3 Use Properties to Add
• Lesson 4 Use Mental Math to Assess Reasonableness
• Lesson 5 Round to the Nearest Ten or Hundred
• Lesson 6 Use Estimation with Sums and Differences
• Into Math Grade 3 Module 9 Review Answer Key
• Module 10 Addition and Subtraction Within 1,000
• Lesson 1 Use Expanded Form to Add
• Lesson 2 Use Place Value to Add
• Lesson 3 Combine Place Values to Subtract
• Lesson 4 Use Place Value to Subtract
• Lesson 5 Choose a Strategy to Add or Subtract
• Lesson 6 Model and Solve Two-Step Problems
• Into Math Grade 3 Module 10 Review Answer Key

Into Math Textbook Grade 3 Module 11 Understand Perimeter

• Module 11 Understand Perimeter
• Lesson 1 Describe Perimeter
• Lesson 2 Find Perimeter
• Lesson 3 Find Unknown Side Lengths
• Lesson 4 Represent Rectangles with the Same Area and Different Perimeters
• Lesson 5 Represent Rectangles with the Same Perimeter and Different Areas
• Into Math Grade 3 Module 11 Review Answer Key
• Module 12 Time Measurement and Intervals
• Lesson 1 Tell and Write Time to the Minute
• Lesson 2 Use a.m. and p.m. to Describe Time
• Lesson 3 Measure Time Intervals
• Lesson 4 Find Start and End Times
• Lesson 5 Solve Time Interval Problems
• Into Math Grade 3 Module 12 Review Answer Key

HMH Into Math Grade 3 Volume 2 Answer Key PDF

HMH Into Math Answers Grade 3 Unit 4 Fractions

• Module 13 Understand Fractions as Numbers
• Lesson 1 Describe Equal Parts of a Whole
• Lesson 2 Represent and Name Unit Fractions
• Lesson 3 Represent and Name Fractions of a Whole
• Lesson 4 Represent and Name Fractions on a Number Line
• Lesson 5 Express Whole Numbers as Fractions
• Lesson 6 Represent and Name Fractions Greater Than 1
• Lesson 7 Use Fractions to Measure Lengths
• Into Math Grade 3 Module 13 Review Answer Key
• Module 14 Relate Shapes, Fractions, and Area
• Lesson 1 Relate Fractions and Area
• Lesson 2 Partition Shapes into Equal Areas
• Lesson 3 Use Unit Fractions to Describe Area
• Into Math Grade 3 Module 14 Review Answer Key

Into Math HMH Grade 3 Module 15 Compare Fractions

• Module 15 Compare Fractions
• Lesson 1 Compare Fractions Using Concrete and Visual Models
• Lesson 2 Compare Fractions with the Same Denominator
• Lesson 3 Compare Fractions with the Same Numerator
• Lesson 4 Use Reasoning Strategies to Compare Fractions
• Into Math Grade 3 Module 15 Review Answer Key
• Module 16 Understand Equivalent Fractions
• Lesson 1 Represent Equivalent Fractions with Smaller Parts
• Lesson 2 Represent Equivalent Fractions with Larger Parts
• Lesson 3 Recognize and Generate Equivalent Fractions
• Into Math Grade 3 Module 16 Review Answer Key

Into Math Book Answers Grade 3 Unit 5 Measurement and Data

• Module 17 Liquid Volume and Mass
• Lesson 1 Estimate and Measure Liquid Volume
• Lesson 2 Estimate and Measure Mass
• Lesson 3 Solve Problems About Liquid Volume and Mass
• Into Math Grade 3 Module 17 Review Answer Key

HMH Into Math Grade 3 Module 18 Represent and Interpret Data

• Module 18 Represent and Interpret Data
• Lesson 1 Use Picture Graphs
• Lesson 2 Make Picture Graphs
• Lesson 3 Use Bar Graphs
• Lesson 4 Make Bar Graphs
• Lesson 5 Use Line Plots to Display Measurement Data
• Lesson 6 Make Line Plots to Display Measurement Data
• Lesson 7 Solve One- and Two-Step Problems Using Data
• Into Math Grade 3 Module 18 Review Answer Key

Houghton Mifflin Into Math Grade 3 Unit 6 Geometry

• Module 19 Define Two-Dimensional Shapes
• Lesson 1 Describe Shapes
• Lesson 2 Describe Angles in Shapes
• Lesson 3 Describe Sides of Shapes
• Lesson 4 Define Quadrilaterals
• Into Math Grade 3 Module 19 Review Answer Key

HMH Into Math Grade 3 Teacher Edition Module 20 Categorize Two-Dimensional Shapes

• Module 20 Categorize Two-Dimensional Shapes
• Lesson 1 Draw Quadrilaterals
• Lesson 2 Categorize Quadrilaterals
• Lesson 3 Categorize Plane Shapes
• Into Math Grade 3 Module 20 Review Answer Key

Key Features of K-8 Math Curriculum HMH Into Math Grade 3 Solution Key

There are several advantages of going through our HMH Into Math Third Grade Answer Key and we have listed few of them for your reference. They are as follows

• Into Math HMH Grade 3 Answer Key can be a great aid in your exam preparation as well as clear your ambiguities in the subject.
• Assess your preparation levels by attempting the questions in the Houghton Mifflin Harcourt Into Math Grade 3 Answer Key and understand your weak and strong areas.
• Excel in your academics by making the most out of the Into Math HMH 3rd Grade Answer Keys PDF existing.
• All the Solutions in the HMH Into Math Answers for Third Grade are in accordance with the Common Core State Standards and give you a clear idea of the concepts.
• HMH Into Math 3rd Grade Answers PDF is accessible round the clock and you can download it for free.

Wrapping Up

Hope the information prevailing here with regards to HMH Into Math Grade 3 Answer Key PDF has enlightened you in some or the other way possible. If you have any questions unanswered and need help feel free to drop us your comments so that we can look into them. Stay connected to our site to avail latest updates on Gradewise HMH Into Math Answer Keys in no time.

Leave a Comment Cancel Reply

You must be logged in to post a comment.

Latest Searches

Top searches, most popular exams.

• For Parents
• For Teachers
• Teaching Topics

• Kindergarten
• EM3/CCSS at Home
• Family Letters
• Student Gallery
• Understanding EM
• Algorithms/ Computation
• Student Links

EM4 at Home

Multidigit multiplication.

Everyday Mathematics for Parents: What You Need to Know to Help Your Child Succeed

The University of Chicago School Mathematics Project

University of Chicago Press

Learn more >>

Related Links

Help with algorithms.

Access video tutorials, practice exercises, and information on the research basis and development of various algorithms.

Everyday Mathematics Online

With a login provided by your child's teacher, access resources to help your child with homework or brush up on your math skills.

Parent Connections on Publisher's site

McGraw-Hill Education offers many resources for parents, including tips, activities, and helpful links.

Parent Resources on EverydayMath.com

EverydayMath.com features activity ideas, literature lists, and family resources for the EM curriculum.

Understanding Everyday Mathematics for Parents

Learn more about the EM curriculum and how to assist your child.

4.10 Problem Solving Multiplication

By alisa olsen on jan 02, 2014.

About FAQ Contact Terms Privacy © 2024 Educreations, Inc.

enVision Math Common Core Grade 3 Answer Key Topic 4 Use Multiplication to Divide: Division Facts

Go through the  enVision Math Common Core Grade 3 Answer Key  Topic 4 Use Multiplication to Divide: Division Facts  regularly and improve your accuracy in solving questions.

enVision Math Common Core 3rd Grade Answers Key Topic 4 Use Multiplication to Divide: Division Facts

enVision STEM Project: Testing Models Do Research Tests can be done to see if a model works or if a change makes it better. Use the Internet or other sources to find information about a model or prototype that was tested. Identify how the testing was done.

Journal: Write a Report Include what you found. Also in your report:

• Make a chart that includes the model, what changed in the test, and what stayed the same.
• Explain the results of the test.
• Write an equation to show one of the relationships in the test. Explain what the numbers represent.

Review What You Know

Vocabulary Choose the best term from the box. Write it on the blank.

• multiplication

Question 1. _________ are multiplied together to give a product. Answer: __Factors _______ are multiplied together to give a product.

Question 2. Use _________ to find how many equal groups or how many are in each group. Answer: Use __division_______ to find how many equal groups or how many are in each group.

Question 3. ___________ is an operation that gives the total number when you put together equal groups. Answer: __Multiplication_________ is an operation that gives the total number when you put together equal groups.

Question 5. There are 32 muffins. Eight people share them equally. How many muffins does each person get? Answer: Number of muffins each person get = 4.

Explanation: Number of muffins = 32. Number of people share them equally = 8. Number of muffins each person get = Number of muffins ÷ Number of people share them equally = 32 ÷ 8 = 4.

Question 6. Suzy has 12 granola bars. There are 2 granola bars in each package. How many packages of granola bars are there? Answer: Number of packages of granola bars there = 6.

Explanation: Number of granola bars Suzy has = 12. Number of granola bars in each package = 2. Number of packages of granola bars there = Number of granola bars Suzy has ÷ Number of granola bars in each package = 12 ÷ 2 = 6.

Equations Question 7. Brian has 5 boxes. He puts 8 markers in each box. Which equation shows the total number of markers? A. 5 + 8 = 13 B. 5 × 8 = 40 C. 40 ÷ 5 = 8 D. 40 ÷ 8 = 5 Answer: Total number of markers = 40. B. 5 × 8 = 40.

Explanation: Number of boxes Brian has = 5. Number of markers in each box = 8. Total number of markers = Number of boxes Brian has × Number of markers in each box = 5 × 8 = 40.

Pick a Project

Lesson 4.1 Relate Multiplication and Division

Look Back! What relationships do you see between the multiplication and division equations for each of your arrays? Answer: The relationships  between the multiplication and division equations for each of the arrays may be different in process yet the result value is same.

Explanation: Process different to multiplication and division equations yet both are done to find the solution to the problem.

Essential Question How Can Multiplication Question Facts Help You Divide? Answer: In multiplication, we find the product of two factors. In division, we find the missing factor if the other factor and the product are known.

Explanation: In multiplication, we find the product of two factors. In division, we find the missing factor if the other factor and the product are known. This is how Multiplication Question Facts Helps in Divide.

Explanation:

Guided Practice Do You Understand? Question 1. Look at the fact family for 3, 10, and 30 on the previous page. What do you notice about the products and the dividends? Answer: It is noticed that the product in mathematics means that the two factors should be multiplied together. In division, the amount or number to be divided is called the dividend.

Explanation: Multiplication 3 rows of 10 drums 3 × 10 = 30 drums. Division 30 drums in 3 equal rows 30 ÷ 3 = 10 drums in each row. It is noticed that the product in mathematics means that the two factors should be multiplied together. In division, the amount or number to be divided is called the dividend. Dividend is the whole that is to be divided into parts.

Question 2. Is 4 × 6 = 24 part of the fact family for 3, 8, and 24? Explain. Answer: Yes, 4 × 6 = 24 is a part of the fact family for 3, 8, and 24.

Explanation: Is 4 × 6 = 24 part of the fact family for 3, 8, and 24. 4 × 6 = 24. 24 ÷ 4 = 6. Dividend = 24. Divisor = 4 Quotient = 6 . 3 × 8 = 24. 24 ÷ 3 = 8. Dividend = 24. Divisor = 3 Quotient = 8.

Do You Know How? In 3-5, use the relationship between multiplication and division to complete each equation. Question 3. 3 × 7 = 21 21 ÷ 3 = ________ Answer: 3 × 7 = 21. 21 ÷ 3 = __7__.

Explanation: 3 × 7 = 21. 21 ÷ 3 = 7. Dividend ÷ Quotient = Divisor.

Question 4. 18 ÷ 2 = 9 2 × ______ = 18 Answer: 18 ÷ 2 = 9. 2 × __9____ = 18.

Explanation: 18 ÷ 2 = 9. 2 × 9 = 18. Quotient × divisor = dividend.

Question 5. 2 × 10 = 20 20 ÷ 2 = _________ Answer: 2 × 10 = 20. 20 ÷ 2 = ____10_____.

Explanation: 2 × 10 = 20. 20 ÷ 2 = 10. Dividend ÷ quotient = Divisor.

Explanation: 2 × 8 = 16 16 ÷ 2 = 8. Dividend ÷ quotient = Divisor.

Question 7. 56 ÷ 8 = 7 8 × _____ = 56 Answer: 56 ÷ 8 = 7. 8 × __7___ = 56.

Explanation: 56 ÷ 8 = 7. 8 × 7 = 56. Dividend = Divisor ÷ quotient.

In 8-13, write the fact family. Question 8. Write the fact family for 6, 7, and 42. Answer: 6 × 7 = 42. 42 ÷ 6 = 7.

Explanation: 6 × 7 = 42. 42 ÷ 6 = 7. Dividend ÷ quotient = Divisor.

Question 9. Write the fact family for 9, 10, and 90. Answer: 9 × 10 = 90. 90 ÷ 9 = 10.

Explanation: 9 × 10 = 90. 90 ÷ 9 = 10. Dividend ÷ quotient = Divisor.

Question 10. Write the fact family for 2, 3, and 6. Answer: 2 × 3 = 6. 6 ÷ 2 = 3.

Explanation: 2 × 3 = 6. 6 ÷ 2 = 3. Dividend ÷ quotient = Divisor.

Question 11. Write the fact family for 1, 5, and 5. Answer: 1 × 5 = 5. 5 ÷ 1 = 5.

Explanation: 1 × 5 = 5. 5 ÷ 1 = 5. Dividend ÷ quotient = Divisor.

Question 12. Write the fact family for 3, 8, and 24. Answer: 3 × 8 = 24. 24 ÷ 3 = 8.

Explanation: 3 × 8 = 24. 24 ÷ 3 = 8. Dividend ÷ quotient = Divisor.

Question 13. Write the fact family for 5, 6, and 30. Answer: 5 × 6 = 30. 30 ÷ 5 = 6.

Explanation: 5 × 6 = 30. 30 ÷ 5 = 6. Dividend ÷ quotient = Divisor.

Explanation: 4 × 5 = 20. 20 ÷ 4 = 5. Dividend ÷ quotient = Divisor.

Explanation: Length of the red fabric = 72 inches. Length of the green fabric = 36 inches. Length of the yellow fabric = 54 inches. Length of  the red fabric shorter than the green and yellow fabrics combined = (Length of the green fabric + Length of the yellow fabric) – Length of the red fabric = (36 + 54) – 72 = 90 – 72 = 18 inches.

Question 16. Higher Order Thinking Anya says that with 24 counters she can make only 6 possible arrays. Todd says he can make 8 arrays. Who is correct? Explain. Answer: Anya says with 24 counters she can make only 6 possible arrays is incorrect because we can make 8 arrays out of 24 counters as Todd says.

Explanation: Anya says that with 24 counters she can make only 6 possible arrays. => 24 ÷ 6 = 4.

Todd says that with 24 counters he can make 8 arrays. => 24 ÷ 8 = 3.

Question 17. Algebra Carla picked 9 apples a day for three days. Which number tells you how many apples she picked in three days and makes this equation true? ☐ ÷ 3 = 9 Answer: Number of apples she picked in three days = 27. Equation: 27 ÷ 3 = 9.

Explanation: Number of apples Algebra Carla picked a day = 9. Number of days Algebra Carla picked  apples = 3. Number of apples she picked in three days = Number of apples Algebra Carla picked a day  × Number of days Algebra Carla picked  apples = 9 × 3 = 27.

Question 18. Vocabulary Can you write a fact family for 3, 5, and 7? Explain. Answer: 3, 5 , and 7 are nor fact family because there is no product number among this three numbers.

Explanation: No, you cannot write a fact family for 3, 5 , and 7 because they are odd numbers and there is no product among these three numbers.

Question 19. Lisa, Bret, and Gary harvested apples. Lisa filled 3 carts with apples. Bret also filled 3 carts with apples. Gary filled another 3 carts with apples. Write a multiplication equation and a division equation for this story. Answer: Number of carts each person filled with apples = 9 ÷ 3 = 3. Total number of carts of apples these three filled = 3 × 3 = 9.

Explanation: Number of carts Lisa filled with apples = 3. Number of carts Bret filled with apples = 3. Number of carts Gary filled with apples = 3. Total number of carts these three filled = Number of carts Lisa filled with apples + Number of carts Bret filled with apples + Number of carts Gary filled with apples = 3 + 3 + 3 = 6 + 3 = 9. Number of people filled carts with apples = 3. Number of carts each person filled with apples = Total number of carts of apples these three filled ÷ Number of people filled carts with apples = 9 ÷ 3 = 3. Total number of carts of apples these three filled = Number of people filled carts with apples × Number of carts each person filled with apples = 3 × 3 = 9.

Explanation: Numbers to create a multiplication equation that could be used to solve 20 ÷ 5 = ☐. 20 ÷ 5 = 4. 5 × 4 = 20. 4 × 5 = 20.

Explanation: Numbers to create a multiplication equation that could be used to solve 24 ÷ 8 = ☐. 24 ÷ 8 = 3. 8 × 3 = 24. 3 × 8 = 24.

Lesson 4.2 Use Multiplication to Divide with 2, 3, 4, and 5

Look Back! Show two pictures you might draw to represent 30 ÷ 5. Answer: Number of toys are in each bag = 6. 30 ÷ 5 = 6. 5 × 6 = 30. 6 × 5 = 30.

Explanation: Number of toys Kara has = 30. Number of party bags Kara has = 5. Number of toys are in each bag = Number of toys Kara has ÷ Number of party bags Kara has = 30 ÷ 5 = 6. 5 × 6 = 30. 6 × 5 = 30.

Essentials Question What Multiplication Fact Can You Use? Answer: Some basic multiplication facts are needed to follow for multiplying numbers. The repeated addition of the same number is expressed by multiplication in short.

Explanation: Multiplication facts which we commonly use is multiplying two numbers together to get the product.

What You Write 40 ÷ 5 = 8 Dee can decorate 8 bags. You can use multiplication to help divide.

What You Write 15 ÷ 3 = 5 Dee will put 5 cups in each stack. Multiplication and division facts form relationships.

Convince Me! Reasoning How can you use multiplication to help solve 20 ÷ 4? Write the related multiplication fact you use to help solve the problem. Answer: 20 ÷ 4 = 5. 5 × 4 = 20.

Explanation: Dee wants to put 20cups in 4 equal stacks on the table. How many cups will Dee put in each stack? 20 ÷ 4 = 5. 5 × 4 = 20. 4 × 5 = 20.

Guided Practice Do You Understand? Question 1. How can 5 × 3 = 15 help you divide 15 by 3? Answer: 5 × 3 = 15. 15 ÷ 3 = 5.

Explanation: 5 × 3 = 15. 15 ÷ 3 = 5.

Question 2. Mr. Dean has 3 children. He buys 30 pencils to share equally among his children for the school year. How many pencils will each child get? Write the answer and the fact family you used. Answer: Number of pencils each child gets = 10.

Explanation: Number of children Mr. Dean has = 3. Number of pencils he buys to share equally among his children for the school year = 30. Number of pencils each child gets = Number of pencils he buys to share equally among his children for the school year ÷ Number of children Mr. Dean has = 30 ÷ 3 = 10.

Do You Know How? In 3 and 4, complete each fact family. Question 3. 3 × 6 = 18 _________ 18 ÷ 3 = 6 _________ Answer: 3 × 6 = 18 __Dividend_______. 18 ÷ 3 = 6 ____quotient___.

Explanation: 3 × 6 = 18 (Dividend) 18 ÷ 3 = 6 (quotient).

Question 4. 9 × 4 = 36 _________ 36 ÷ 4 = 9 _________ Answer: 9 × 4 = 36 __Dividend_______. 36 ÷ 4 = 9 ___quotient______.

Explanation: 9 × 4 = 36 (Dividend). 36 ÷ 4 = 9 (quotient).

In 5-8, find each quotient. Question 5. 36 ÷ 4 = ________ Answer: 36 ÷ 4 = ____9____.

Explanation: 36 ÷ 4 = ___9_____.

Question 6. _______ = 15 ÷ 5 Answer: ___3____ = 15 ÷ 5.

Explanation: ___3____ = 15 ÷ 5.

Independent Practice In 9-20, find each quotient. Question 9. 12 ÷ 2 = _______ Answer: 12 ÷ 2 = __6_____.

Explanation: 12 ÷ 2 = 6.

Question 10. _______ = 12 ÷ 3 Answer: ___4____ = 12 ÷ 3.

Explanation: 4 = 12 ÷ 3.

Question 11. 16 ÷ 4 = _______ Answer: 16 ÷ 4 = ___4____.

Explanation: 16 ÷ 4 = 4.

Question 12. 35 ÷ 5 = _______ Answer: 35 ÷ 5 = ___7____.

Explanation: 35 ÷ 5 = 7.

Question 13. 14 ÷ 2 = _______ Answer: 14 ÷ 2 = ___7___.

Explanation: 14 ÷ 2 = 7.

Question 14. 20 ÷ 4 = ______ Answer: 20 ÷ 4 = __5____.

Explanation: 20 ÷ 4 = 5.

Question 15. _______ = 24 ÷ 4 Answer: ___6____ = 24 ÷ 4.

Explanation: 6= 24 ÷ 4.

Question 16. 45 ÷ 5 = ______ Answer: 45 ÷ 5 = ___9___.

Explanation: 45 ÷ 5 = 9.

Explanation: Number of squares rows = 5. Number of squares columns = 4. Total number of squares in the rectangle = Number of squares rows × Number of squares columns = 5 × 4 = 20. Division Equation: Total number of squares in the rectangle ÷ Number of squares columns = Number of squares rows. 20 ÷ 4 = 5.

Question 22. Make Sense and Persevere If Anna arranges the squares into an array with 2 columns, how many rows will there be? Answer: Number of rows = 10.

Explanation: Number of squares = 20. Number of columns = 2 Number of rows = Number of squares ÷ Number of columns = 20 ÷ 2 = 10.

Question 23. Number Sense Joey says, “I cannot solve 8 ÷ 2 by using the fact 2 × 8 = 16.” Do you agree or disagree? Explain. Answer: Yes, I agree with Joey. We cannot solve 8 ÷ 2 by using the fact 2 × 8 = 16.

Explanation: 2 × 8 = 16. => 16 ÷ 8 = 2. => 16 ÷ 2 = 8. 8 ÷ 2 = 4.

Question 24. Miko has 8 counters to arrange in an array. Write multiplication and division equations to represent all the ways Miko might arrange her counters. Answer: Way:1:  Total number of counters = Number of rows × Number of columns = 4 × 2 = 8. Way:2: Total number of counters = Number of rows × Number of columns = 2 × 4 = 8. Way:3: Total number of counters = Number of rows × Number of columns = 8 × 1 = 8. Way:4: Total number of counters = Number of rows × Number of columns = 1 × 8 = 8.

Explanation: Number of counters Miko has = 8. Way:1: Number of rows = 4. Number of columns = 2. Total number of counters = Number of rows × Number of columns = 4 × 2 = 8.

Way:2: Number of rows = 2. Number of columns = 4. Total number of counters = Number of rows × Number of columns = 2 × 4 = 8.

Way:3: Number of rows = 8. Number of columns = 1. Total number of counters = Number of rows × Number of columns = 8 × 1 = 8.

Way:4: Number of rows = 1. Number of columns = 8. Total number of counters = Number of rows × Number of columns = 1 × 8 = 8.

Question 25. Vocabulary Write a division equation. Tell which number is the quotient, the dividend, and the divisor. Answer: Division Equation: Total number of counters ÷ Number of columns = Number of rows 8 ÷ 8 = 1. Dividend = 8. Divisor = 8. Quotient = 1.

Explanation: Number of rows = 1. Number of columns = 8. Total number of counters = Number of rows × Number of columns = 1 × 8 = 8. Division Equation: Total number of counters ÷ Number of columns = Number of rows 8 ÷ 8 = 1. Dividend = 8. Divisor = 8. Quotient = 1.

Question 26. Higher Order Thinking Chris gives 18 pretzels equally to 3 friends. Martha gives 20 pretzels equally to 4 friends. Whose friends got more pretzels? Use equations to justify your answer. Answer: Chris’s friends gets each 6 pretzels more than Martha’s friends.

Explanation: Number of pretzels Chris gives = 18. Number of friends Chris gives equally = 3. Number of pretzels Chris’s friends gets each = Number of pretzels Chris gives ÷ Number of friends Chris gives equally = 18 ÷ 3 = 6.

Number of pretzels Martha gives = 20. Number of friends Martha gives equally = 4. Number of pretzels Martha’s friends gets each = Number of pretzels Martha gives ÷ Number of friends Martha gives equally = 20 ÷ 4 = 5.

Assessment Practice Question 27. Which expression can help you divide 12 ÷ 3? A. 2 × 3 B. 3 × 3 C. 4 × 3 D. 5 × 3 Answer: C. 4 × 3 is the expression which helps to divide 12 ÷ 3 = ??.

Explanation: Expression can help you divide 12 ÷ 3 = ?? 12 ÷ 3 = 4. => 4 × 3 = 12.

Question 28. Which expression can help you divide 28 ÷ 4? A. 7 × 4 B. 6 × 4 C. 5 × 4 D. 4 × 4 Answer: A. 7 × 4 is the expression which helps to divide 28 ÷ 4 = ??.

Explanation: Expression can help you divide 28 ÷ 4 = ?? 28 ÷ 4 = 7. => 7 × 4 = 28.

Lesson 4.3 Use Multiplication to Divide with 6 and 7

Look Back! Draw a bar diagram to represent the problem. Answer: Number of children in each row = 3.

Explanation: Number of children in a ballet class = 18 Number of rows children are standing for a dance recital = 6. Number of children in each row = Number of children in a ballet class ÷ Number of rows children are standing for a dance recital = 18 ÷ 6 = 3.

Essential Question How Do You Divide with 6 and 7? Answer: The dividend to be divided with the number 6 or 7 to get the answer which is called quotient.

Explanation: What is being divided is called the dividend, which is divided by the divisor, and the result is called the quotient. In the example, 24 is the dividend, 6 is the divisor, and 4 is the quotient

Find 48 ÷ 6. What You Think What number times 6 is 48? 8 × 6 = 48

What You Write 48 ÷ 6 = 8 There will be 8 groups. Use a multiplication problem to make sense of a division problem.

Another dog was entered in the show. There will now be 7 dogs in each group. How many groups will there be? Find 49 ÷ 7. What You Think What number times 7 is 49? 7 × 7 = 49

What You Write 49 ÷ 7 = 7 There will be 7 groups.

Convince Me! Model with Math Draw a bar diagram using the numbers 36, 6, and 6. Write the division fact and the related multiplication fact that your bar diagram shows. Answer: 36 ÷ 6 = 6. 6 × 6 = 36.

Explanation: Division Equation: 36 ÷ 6 = 6. Multiplication Equation: 6 × 6 = 36.

Guided Practice Do You Understand? Question 1. How can you tell without dividing that 42 ÷ 6 will be greater than 42 ÷ 7? Answer: If the divisor is small, the quotient in division is going to be greater number and vice versa.

Explanation: 42 ÷ 6  will be greater than 42 ÷ 7  you can say without doing division by seeing the divisor. If the divisor is small the quotient in division is going to be greater number and vice versa.

Question 2. How can 8 × 6 = 48 help you divide 48 by 6? Answer: 8 × 6 = 48 helps in dividing 48 by 6. 48 ÷ 6 = 8.

Explanation: 8 × 6 = 48 helps in dividing 48 by 6. 48 ÷ 6 = 8.

Do You Know How? In 3-8, write the related multiplication fact, and then find each quotient. Question 3. 36 ÷ 6 = ________ Answer: 36 ÷ 6 = ____6____.

Explanation: 36 ÷ 6 = 6 (quotient). 6 × 6 = 36.

Question 4. ______ = 42 ÷ 6 Answer: ___7___ = 42 ÷ 6.

Explanation: 42 ÷ 6 = 7 (quotient). 6 × 7 = 42.

Question 5. 42 ÷ 7 = _______ Answer: 42 ÷ 7 = __6_____.

Explanation: 42 ÷ 7 = 6 (quotient). 7 × 6 = 42.

Question 6. ______ = 18 ÷ 6 Answer: __3____ = 18 ÷ 6.

Explanation: 18 ÷ 6 = 3 (quotient). 6 × 3 = 18.

Independent Practice Leveled Practice In 9-20, use related multiplication and division facts to find the quotient. Question 9. 12 ÷ 6 = ? What number times 6 is 12? 6 × ☐ = 12 12 ÷ 6 = ☐ Answer: 12 ÷ 6 = 2.

Explanation: 12 ÷ 6 = ?? 6 × 2 = 12. 12 ÷ 6 = 2.

Question 10. 21 ÷ 3 = ? What number times 3 is 21? 3 × ☐ = 21 21 ÷ 3 = ☐ Answer: 21 ÷ 3 = 7.

Explanation: 21 ÷ 3 = ?? 3 × 7 = 21. 21 ÷ 3 = 7.

Question 11. 30 ÷ 6 = ? What number times 6 is 30? 6 × ☐ = 30 30 ÷ 6 = ☐ Answer: 30 ÷ 6 = 5.

Explanation: 30 ÷ 6 = ?? 6 × 5 = 30. 30 ÷ 6 = 5.

Question 18. Find 49 divided by 7.

Answer: 49 ÷ 7 = 7.

Explanation: 49 ÷ 7 = 7. 7 × 7 = 49.

Question 19. Divide 54 by 6. Answer: 54 ÷ 6 = 9.

Explanation: 54 ÷ 6 = 9. 6 × 9 = 54.

Question 20. Find 35 divided by 7. Answer: 35 ÷ 7 = 5.

Explanation: 35 ÷ 7 = 5. 7 × 5 = 35.

Problem Solving Question 21. A pizza parlor made 88 deep-dish pizzas. It made 10 more thin-crust pizzas than deep-dish pizzas. How many thin-crust pizzas did the parlor make? Answer: 10 more thin-crust pizzas the parlor makes than deep-dish pizzas.

Explanation: Number of deep-dish pizzas pizza parlor made = 88. It made 10 more thin-crust pizzas than deep-dish pizzas. => Number of thin-crust pizzas pizza parlor made = 88 + 10 = 98. Difference: Number of thin-crust pizzas pizza parlor made – Number of deep-dish pizzas pizza parlor made = 98 – 88 = 10.

Question 22. Higher Order Thinking There are 35 new tires. Each truck will get 6 tires plus 1 tire for a spare. How many trucks will get new tires? Answer: Number of trucks gets new tires = 5.

Explanation: Number of new tires = 35. Each truck will get 6 tires plus 1 tire for a spare. => Number of tires each truck gets = 6 + 1 = 7. Number of trucks gets new tires = Number of new tires ÷ Number of tires each truck gets = 35 ÷ 7 = 5.

Question 23. Make Sense and Persevere Explain the mistake in the fact family below. Give the correct fact. 4 × 7 = 28 7 × 4 = 28 7 ÷ 4= 28 28 ÷ 7 = 4 Answer: 4 × 7 = 28. Correct. 7 × 4 = 28. Correct. 7 ÷ 4= 28. Incorrect. 28 ÷ 7 = 4. Correct.

Explanation: 4 × 7 = 28. Correct. 7 × 4 = 28. Correct. 7 ÷ 4 = 28. Division is not correct. Incorrect. 28 ÷ 7 = 4. Correct.

Question 24. Gloria mowed 7 lawns and earned $56. She was paid the same amount for each lawn. How much money did Gloria earn for mowing each lawn? Write an equation to represent this problem. Answer: Amount Gloria earn for mowing each lawn = $392.

Explanation: Number of lawns Gloria mowed = 7. Money Gloria earned = $56. She was paid the same amount for each lawn. Amount Gloria earn for mowing each lawn = Number of lawns Gloria mowed × Money Gloria earned = 7 × $56. = $392.

Question 25. Andy bought 35 beads. He bought only one color of beads. Which beads could Andy have bought? How many packages of that color bead did he buy? Answer: Andy would have bought red or gold beads. Number of packets red beads Andy bought = 5. Number of packets gold beads Andy bought = 7.

Explanation: Number of beads Andy bought = 35. Number of beads in green package = 6. Number of beads in red package = 7. Number of beads in gold package = 5. Number of packets red beads Andy bought = Number of beads Andy bought ÷ Number of beads in red package = 35 ÷ 7 = 5. Number of packets gold beads Andy bought = Number of beads Andy bought ÷ Number of beads in gold package = 35 ÷ 5 = 7.

Question 26. Cassidy bought 48 beads. She bought only one color of beads. Which beads could Cassidy have bought? How many packages of that color bead did she buy? Answer: Number of packets green beads Cassidy bought = 8.

Explanation: Number of beads Cassidy bought = 48. Number of beads in green package = 6. Number of beads in red package = 7. Number of beads in gold package = 5 Number of packets green beads Cassidy bought = Number of beads Cassidy bought ÷ Number of beads in green package = 48 ÷ 6 = 8.

Assessment Practice Question 27. Which multiplication fact can you use to help find the value of the unknown number in the equation 42 ÷ 7 = ☐? A. 5 × 7 B. 6 × 7 C. 7 × 7 D. 8 × 7 Answer: Equation 42 ÷ 7 = ☐? B. 6 × 7 multiplication fact can be used to help, find the value of the unknown number in the equation 42 ÷ 7 = ??.

Explanation: Equation 42 ÷ 7 = ☐? 42 ÷ 7 = 6. 7 × 6 = 42. 6 × 7 = 42.

Question 28. Which multiplication fact can you use to help find the value of the unknown number in the equation 36 ÷ 6 = ☐? A. 5 × 6 B. 6 × 6 C. 7 × 6 D. 8 × 6 Answer: Equation 36 ÷ 6 = ☐? B. 6 × 6 multiplication fact can be used to help, find the value of the unknown number in the equation 36 ÷ 6 = ☐?

Explanation: Equation 36 ÷ 6 = ☐? 36 ÷ 6 = 6. 6 × 6 = 36.

Lesson‌ ‌4.4‌ ‌Use‌ ‌Multiplication‌ ‌to‌ ‌Divide‌ ‌with‌ ‌8‌ ‌and‌ ‌9‌ ‌

Look‌ ‌Back!‌ ‌Draw‌ ‌a‌ ‌picture‌ ‌you‌ ‌could‌ ‌use‌ ‌to‌ ‌help‌ ‌solve‌ ‌the‌ ‌problem‌ ‌above.‌ ‌

Answer: Number of boxes crayons are there = 9.

Essential Question What Multiplication Fact Can You Use?

Answer: Some basic multiplication facts are needed to follow for multiplying numbers. The repeated addition of the same number is expressed by multiplication in short.

Explanation: Basic multiplication facts are needed to follow for multiplying numbers. The repeated addition of the same number is expressed by multiplication in short. For example: 36 ÷ 6 = 6. 6 × 6 = 36.

What You Write 54 ÷ 9 = 6 Luz used 6 straws for each animal.

Answer: Division Fact    Related Multiplication Fact. 72 ÷ 8 = 9.               9 × 8 = 72. 48 ÷ 8 = 6.               8 × 6 = 48. 63 ÷ 9 = 7.               9 × 7 = 63.

Explanation: Related multiplication fact that can be used to complete each division fact is as below: Division Fact    Related Multiplication Fact. 72 ÷ 8 = 9.               9 × 8 = 72. 48 ÷ 8 = 6.               8 × 6 = 48. 63 ÷ 9 = 7.               9 × 7 = 63.

Guided Practice

Do You Understand? Question 1. What multiplication fact can you use to find 18 ÷ 9? Answer: 2 × 9 = 18 multiplication fact can be used to find 18 ÷ 9.

Explanation: 18 ÷ 9 = ?? 18 ÷ 9 = 2. 2 × 9 = 18.

Question 2. Carla and Jeff each use 72 straws. Carla makes animals with 9 legs. Jeff makes animals with 8 legs. Who makes more animals? Explain.

Answer: Jeff makes 1 more animal with legs than Carla makes.

Explanation: Number of straws Carla and Jeff each use = 72 Number of animals with legs Carla makes = 9. Number of animals with legs Jeff makes = 8. Total number of animals with legs Carla makes = Number of straws Carla and Jeff each use ÷ Number of animals with legs Carla makes = 72 ÷ 9 = 8. Total number of animals with legs Jeff makes = Number of straws Carla and Jeff each use ÷ Number of animals with legs Jeff makes = 72 ÷ 8 = 9.

Do You Know How? In 3 and 4, use the multiplication equation to help find each quotient. Question 3. 16 ÷ 8 = ? What number times 8 is 16? ______ × 8 = 16 So, 16 ÷ 8 = _______

Answer: 16 ÷ 8 = 2. ___2___ × 8 = 16. So, 16 ÷ 8 = __2_____.

Explanation: 16 ÷ 8 = ? 16 ÷ 8 = 2. => 2 × 8 = 16. So, 16 ÷ 8 =2.

Question 4. 64 ÷ 8 = ? What number times 8 is 64? ______ × 8 = 64 So, 64 ÷ 8 = _______

Answer: 64 ÷ 8 = 8. __8____ × 8 = 64. So, 64 ÷ 8 = __8_____.

Explanation: 64 ÷ 8 = ? 64 ÷ 8 = 8. 8 × 8 = 64 So, 64 ÷ 8 = 8.

Independent Practice Leveled Practice In 5-7, use the multiplication equation to help find each quotient.

Question 5. 24 ÷ 8= ? What number times 8 is 24? ______ × 8 = 24 24 ÷ 8 = ______

Answer: 24 ÷ 8= 3. ___3___ × 8 = 24. 24 ÷ 8 = ___3___.

Explanation: 24 ÷ 8= ? 24 ÷ 8= 3. 3 × 8 = 24. 24 ÷ 8 = 3.

Question 6. 45 ÷ 9 = ? What number times 9 is 45? ______ × 9 = 45 45 ÷ 9 = ______ Answer: 45 ÷ 9 = 5. ___5___ × 9 = 45. 45 ÷ 9 = ___5___.

Explanation: 45 ÷ 9 = ? 45 ÷ 9 = 5. 5 × 9 = 45. 45 ÷ 9 = 5.

Question 7. 27 ÷ 9 = ? What number times 9 is 27? ______ × 9 = 27 27 ÷ 9 = _______

Answer: 27 ÷ 9 = 3. ___3___ × 9 = 27. 27 ÷ 9 = ___3____.

Explanation: 27 ÷ 9 = ? 27 ÷ 9 = 3. 3 × 9 = 27. 27 ÷ 9 = 3.

In 8-16, find each quotient. Question 8. 48 ÷ 8 = _______

Answer: 48 ÷ 8 = 8.

Explanation: 48 ÷ 8 = 8. (quotient)

Question 9. 72 ÷ 9 = ______

Answer: 72 ÷ 9 = ___8___.

Explanation: 72 ÷ 9 = 8. (quotient)

Question 10. ______ = 8 ÷ 8

Answer: __1____ = 8 ÷ 8.

Explanation: 8 ÷ 8 = 1. (quotient)

Question 11. _____ = 54 ÷ 9

Answer: __6___ = 54 ÷ 9.

Explanation: 54 ÷ 9 = 6. (quotient)

Question 12. 72 ÷ 8 = ______

Answer: 72 ÷ 8 = ___9___.

Explanation: 72 ÷ 8 = 9. (quotient)

Question 13. 90 ÷ 9 = ________

Answer: 90 ÷ 9 = __10______.

Explanation: 90 ÷ 9 = 10. (quotient)

Problem Solving Question 17. Callie biked 27 miles on Saturday. She biked 9 miles every hour. How many hours did Callie bike? Draw a picture to represent the problem.

Answer: Total number of hours she biked = 3.

Explanation: Number of miles Callie biked  on Saturday = 27. Number of miles Callie biked  every hour = 9. Total number of hours she biked = Number of miles Callie biked  on Saturday ÷ Number of miles Callie biked  every hour = 27 ÷ 9 = 3.

Question 18. en Vision® STEM Eight friends decide to test how far 40 paper airplanes with different shapes will fly. If each friend tests the same number of airplanes, how many airplanes does each friend test?

Answer: Number of airplanes each friend gets to test = 5.

Explanation: Number of friends of Stem = 8. Number of paper airplanes with different shapes  = 40. Number of airplanes each friend gets to test = Number of paper airplanes with different shapes ÷ Number of friends of Stem = 40 ÷ 8 = 5.

Question 19. Reasoning What other equations are in the same fact family as 18 ÷ 9 = 2?

Answer: Other equations which are in the same fact family as 18 ÷ 9 = 2: 18 ÷ 2 = 9. 2 × 8 = 18. 9 × 2 = 18.

Explanation: 18 ÷ 9 = 2. Other equations which are in the same fact family as 18 ÷ 9 = 2: 18 ÷ 2 = 9. 2 × 8 = 18. 9 × 2 = 18.

Question 20. Higher Order Thinking Jeremy had 30 gummy bears. He ate 6, and then gave the rest to 8 friends. Each friend got the same number of gummy bears. How many did each friend get?

Answer: Number of gummy bears each friend gets = 3.

Explanation: Number of gummy bears Jeremy had = 30. Number of gummy bears Jeremy ate = 6. Number of friends he gave the rest gummy bears = 8. Number of gummy bears each friend gets = (Number of gummy bears Jeremy had – Number of gummy bears Jeremy ate) ÷ Number of friends he gave the rest gummy bears = (30 – 6) ÷ 8 = 24 ÷ 8 = 3.

Explanation: Mr. Stern spends $36 on tickets. Cost of the child ticket = $4 Amount Mr. Stern spends on child tickets = $36 Number of child tickets he buys = Amount Mr. Stern spends on child tickets ÷ Cost of the child ticket = $36 ÷ $4 = 9.

Cost of the adult ticket = $9. Amount Mr. Stern spends on adult tickets = $36 Number of adult tickets he buys = Amount Mr. Stern spends on adult tickets ÷ Cost of the adult ticket = $36 ÷ $9 = 4.

b. Which type of ticket could Mr. Stern NOT buy? Explain why not. Answer: Cost the youth ticket = $8 because the amount cannot be divided exactly by the amount he spent on tickets purchase.

Explanation: Cost the youth ticket = $8. This ticket may not be purchased by Mr. Stern because the amount cannot be divided exactly by the amount he spent on tickets purchase.

Assessment Practice

Answer: 8 × 9 = 32. 32 ÷ 8 = 4.

Explanation: 32 ÷ 8 = 4. 8 × 9 = 32. Number 4 is selected from the given numbers to complete the following equations.

Answer: 9 × 6 = 54. 54 ÷ 9 = 6.

Explanation: 54 ÷ 9 = 6. 9 × 6 = 54. 6 number is selected from the given numbers to complete the following equations.

Lesson 4.5 Multiplication Patterns: Even and Odd Numbers

Look Back! What do you notice about the numbers for the prizes that can be packaged in 2s with none left over? What do you notice about the numbers for the other prizes?

Answer: The prizes listed can be packaged with none left over are: car prizes, boats prizes and books prizes. It is noticed about the numbers for the prizes that can be packaged in 2s with none left over that they are the multiples of 2. It is noticed about the numbers for the other prizes that they are prime numbers and are not multiples of 2.

Explanation: Number of car prizes = 6. Number of hats prizes = 15. Number of balls prizes = 23. Number of boats prizes = 18. Number of books prizes = 36. Number of groups the prizes are packed = 2. Numbers for the prizes that can be packaged in 2s with none left over: = Number of car prizes ÷ Number of groups the prizes are packed = 6 ÷ 2 = 3. Number of boats prizes ÷ Number of groups the prizes are packed = 18 ÷ 2 = 9. Number of books prizes ÷ Number of groups the prizes are packed = 18 ÷ 2 = 9.

Essential Question How Can You Explain Multiplication Question Patterns for Even and Odd Numbers? Answer: An  even number can only be formed by multiplication in three ways: even × odd, odd × even and even × even. An odd number can only be formed by multiplication in one way: odd × odd = odd.

Explanation: Multiplication Question Patterns for Even and Odd Numbers can be explained as below: An  even number can only be formed by multiplication in three ways: even × odd, odd × even and even × even. An odd number can only be formed by multiplication in one way: odd × odd = odd.

Even numbers greater than 0 can be shown as two equal groups. Think about 2 × 3 and 2 × 5. 2 is an even number. 2 × 3 means 2 equal groups of 3. 2 × 3 = 6 2 × 5 means 2 equal groups of 5. 2 × 5 = 10 There are always 2 equal groups, so the product of 2 times any number is even.

You can generalize. All even numbers are multiples of 2. Think about 4 × 3. You can think of 4 as 2 groups of 2. Using properties you can write 4 × 3 = (2 × 2) > 3 as 4 × 3 = 2 × (2 × 3). So, 4 × 3 = 2 × 6. There are 2 equal groups of 6. So, the product will be even.

You can write any even number as 2 equal groups. So, Nita is correct: me even X odd = even.

Convince Me! Generalize Does multiplying by 8 also always result in an even product? Explain.

Answer: Multiplying by 8 also always result in an even product is true because even numbers are whole numbers that can be divided by 2 with none left over. Odd numbers are whole numbers that cannot be divided by 2 with none left over.

Explanation: Multiplying by 8 also always result in an even product is true because even numbers are whole numbers that can be divided by 2 with none left over. Odd numbers are whole numbers that cannot be divided by 2 with none left over. 2 × 8 = 16. 3 × 8 = 24.

Guided Practice Do You Understand? Question 1. If you multiply two even numbers, will the product be even or odd? Explain with an example.

Answer: If you multiply two even numbers, will the product be even not odd.

Explanation: If you multiply two even numbers, will the product be even not odd. For example: 2 × 6 = 12.

Do You Know How? Write or circle to complete the sentences. Then solve. Question 2. 4 × 6 = ? Can 4 be divided by 2? _______ Can 6 be divided by 2? _______ So 4 × 6 is even, odd 4 × 6 = _______

Answer: 4 × 6 = 24. Can 4 be divided by 2? __Yes_____. Can 6 be divided by 2? ____Yes___. So 4 × 6 is even. 4 × 6 = _24______.

Explanation: 4 × 6 = 24. Can 4 be divided by 2? 4 ÷ 2 = 2 yes. Can 6 be divided by 2? 6 ÷ 2 = 3 yes. So 4 × 6 is even. 4 × 6 = 24.

Independent Practice In 3-5, circle the factors that can be divided by 2. Then write even or odd to describe the product and solve the equation. Question 3. 9 × 5 = ? 9 × 5 is _______ 9 × 5 = _______

Answer: 9 × 5 = ? 9 × 5 is __odd_____. 9 × 5 = __45_____.

Explanation: 9 × 5 = ?? 9 × 5 is odd. 9 × 5 = 45.

Question 4. 8 × 7 = ? 8 × 7 is ______ 8 × 7 = ______

Answer: 8 × 7 = ? 8 × 7 is __even____. 8 × 7 = __56____.

Explanation: 8 × 7 = ? 8 × 7 is even. 8 × 7 = 56.

Question 5. 4 × 8 =? 4 × 8 is ______ 4 × 8 = ______

Answer: 4 × 8 =? 4 × 8 is _Even_____. 4 × 8 = __32____.

Answer: Number of miles Joseph bicycled in 6 days = 18. The product is ___18(Even)_____.

Explanation: Number of miles Joseph bicycled per day = 3. Number of miles Joseph bicycled in 6 days = Number of miles Joseph bicycled per day  × 6 = 3 × 6 = 18.

Question 7. How many miles did Caitlin bicycle in 8 days? The product is ________.

Answer: Number of miles Caitlin bicycled in 8 days = 48. The product is ___48 (Even)_____.

Explanation: Number of miles Caitlin bicycled per day = 6. Number of miles Caitlin bicycled in 8 days = Number of miles Caitlin bicycled per day  × 8 = 6 × 8 = 48.

Question 8. How many miles did Maria and Riaz bicycle in 3 days? The total is _________

Answer: Total number of miles Maria and Riaz bicycled in 3 days = 27. The total is ___27 (Odd)______.

Explanation: Number of miles Maria bicycled per day = 4. Number of miles Maria bicycled in 3 days = Number of miles Maria bicycled per day  × 3 = 4 × 3 = 12. Number of miles Riaz bicycled per day = 5. Number of miles Riaz bicycled in 3 days = Number of miles Riaz bicycled per day  × 3 = 5 × 3 = 15.

Total number of miles Maria and Riaz bicycled in 3 days = Number of miles Maria bicycled in 3 days + Number of miles Riaz bicycled in 3 days = 12 + 15 = 27.

Question 9. Critique Reasoning Ryan says that the following patterns are true: even × odd = even odd × even = odd Is he correct? Explain.

Answer: (even × odd = even) pattern Ryan’s says is correct yet not odd × even = odd pattern.

Explanation: even × odd = even. => 2 × 5 = 10. odd × even = odd => 5 × 4 = 20.

Question 10. Draw a shape with an odd number of sides. Then write the name of the shape.

Question 11. Higher Order Thinking The bakery had 84 muffins. Ms. Craig bought 5 packs of 6 muffins. Did she purchase an even or an odd number of muffins? Is the number of muffins left even or odd? Explain.

Answer: Total number of muffins Ms. Craig bought = 30. (Even) Number of muffins left = 54. (Even)

Explanation: Number of muffins bakery had = 84. Number of muffins Ms. Craig bought = 6. Number of packs Ms. Craig bought = 5. Total number of muffins Ms. Craig bought = Number of muffins Ms. Craig bought  × Number of packs Ms. Craig bought = 6 × 5 = 30. (Even) Number of muffins left = Number of muffins bakery had – Total number of muffins Ms. Craig bought = 84 – 30 = 54. (Even)

Assessment Practice Question 12. Select all of the equations where you can use properties of operations to show that the product will be even. ☐ 7 × 9 = ? ☐ 9 × 2 = ? ☐ 5 × 3 = ? ☐ 1 × 6 = ? ☐ 7 × 5 = ?

Answer: 9 × 2 = 18. => odd × even = even. 1 × 6 = 6. => odd × even = even.

Explanation: ☐ 7 × 9 = 63. => odd × odd = odd. ☐ 9 × 2 = 18. => odd × even = even. ☐ 5 × 3 = 15. => odd × odd = odd. ☐ 1 × 6 = 6. => odd × even = even. ☐ 7 × 5 = 35. => odd × odd = odd.

Question 13. Select all of the equations that do NOT have even products. ☐ 5 × 1 = ? ☐ 2 × 7 = ? ☐ 3 × 9 = ? ☐ 8 × 8 = ? ☐ 6 × 4 = ?

Answer: 5 × 1 = 5. => odd × odd = odd. 3 × 9 = 27. => odd × odd = odd.

Explanation: ☐ 5 × 1 = 5. => odd × odd = odd. ☐ 2 × 7 = 14. => even × odd = even. ☐ 3 × 9 = 27. => odd × odd = odd. ☐ 8 × 8 = 64. => even × even = even. ☐ 6 × 4 = 24. => even × even = even.

Lesson 4.6 Division Involving 0 and 1

Look Back! Use your understanding of multiplying by 0 to find 0 ÷ 7,0 ÷ 4, and 0 ÷ 10. Describe the patterns you see.

Answer: 0 ÷ 4 = 0. 0 ÷ 7 = 0. 0 ÷ 10 = 0. It is observed that any number multiplied to zero or zero divided by any number the product of it is same that is zero.

Explanation: 0 × 4 = 0. 0 ÷ 4 = 0. 0 × 7 = 0. 0 ÷ 7 = 0. 0 × 10 = 0. 0 ÷ 10 = 0.

Essential Question How Do You Divide with 1 or 0? Answer: Any number divided by the given number to be divided. 2 ÷ 1 = 2. 2 ÷ 0 = 0.

Explanation: We divided the number with one or 0 by the following: 2 ÷ 1 = 2. 2 ÷ 0 = 0.

1 as a Quotient Find 3 ÷ 3. 3 times what number equals 3? 3 × 1 = 3 S0, 3 ÷ 3 = 1. Rule: Any number (except 0) divided by itself is 1.

Dividing O by a Number Find 0 ÷ 3. 3 times what number equals 0? 3 × 0 = 0 So, 0 ÷ 3 = 0. Rule: 0 divided by any number (except 0) is 0.

Dividing by 0 Find 3 ÷ 0. 0 times what number equals 3? There is no such number. So, 3 ÷ 0 can’t be done. Rule: You cannot divide any number by 0.

Convince Me! Be Precise Sue wrote 9 invitations. She put 1 invitation in each mailbox on her street. How many mailboxes got invitations? Which equation shows the problem and the solution? Explain your thinking. 0 ÷ 9 = 0 9 ÷ 1 = 9

Answer: Number of mailboxes got invitations = Number of invitations Sue wrote ÷ Number of invitation she puts in each mailbox on her street = 9 ÷ 1 = 9.

Explanation: Number of invitations Sue wrote = 9. Number of invitation she puts in each mailbox on her street = 1. Number of mailboxes got invitations = Number of invitations Sue wrote ÷ Number of invitation she puts in each mailbox on her street = 9 ÷ 1 = 9.

Guided Practice Do You Understand? Question 1. How can you tell, without dividing, that 375 ÷ 375 = 1?

Answer: Any number divided by itself, the product is always 1. 375 ÷ 375 = 1

Explanation: We can tell without dividing, that 375 ÷ 375 = 1 because any number divided by itself, the product is always 1.

Answer: 8 × __1___ = 8 So, 8 ÷ 8 = ___1____. (quotient)

Explanation: 8 × 1 = 8 So, 8 ÷ 8 = 1.

Question 4. Find 0 ÷ 9. 9 × ______ = 0 So, 0 ÷ 9 = ______

Answer: 9 × __0____ = 0 So, 0 ÷ 9 = __0____. (quotient)

Explanation: 9 × 0 = 0 So, 0 ÷ 9 = 0.

Independent Practice Leveled Practice In 5-7, solve the multiplication equation to find each quotient. Question 5. Find 0 ÷ 7. 7 × _______ = 0 So, 0 ÷ 7 = _______

Answer: 7 × ___0____ = 0. So, 0 ÷ 7 = ___0____. (quotient)

Explanation: 7 × 0 = 0 So, 0 ÷ 7 = 0.

Question 6. Find 4 ÷ 4. 4 × _______ = 4 So, 4 ÷ 4 = ________

Answer: 4 × ___1____ = 4 So, 4 ÷ 4 = ___1_____. (quotient)

Explanation: 4 × 1 = 4 So, 4 ÷ 4 = 1.

Question 7. Find 6 ÷ 1. 1 × _______ = 6 So, 6 ÷ 1 = _______

Answer: 1 × ___6____ = 6 So, 6 ÷ 1 = ___6____. (quotient)

Explanation: 1 × 6 = 6 So, 6 ÷ 1 = 6.

In 8-18, find each quotient. Question 8. 3 ÷ 3 = __________

Answer: 3 ÷ 3 = ____1______.(quotient)

Explanation: 3 ÷ 3 = 1.

Question 9. ______ = 0 ÷ 8

Answer: ___0___ = 0 ÷ 8. (quotient)

Explanation: 0 = 0 ÷ 8.

Question 10. ______ = 5 ÷ 5

Answer: ___1___ = 5 ÷ 5. (quotient)

Explanation: 1 = 5 ÷ 5.

Question 11. 7 ÷ 1 = _______

Answer: 7 ÷ 1 = __7_____. (quotient)

Explanation: 7 ÷ 1 = 7.

Question 16. Find 0 divided by 8.

Answer: 0 ÷ 8 = 0.

Explanation: 0 divided by 8. => 0 ÷ 8 = 0.

Question 17. Find 9 divided by 1. Answer: 9 ÷ 1 = 9.

Explanation: 9 divided by 1. 9 ÷ 1 = 9.

Question 18. Find 10 divided by 10.

Answer: 10 ÷ 10 = 1.

Explanation: 10 divided by 10. => 10 ÷ 10 = 1.

Explanation: Number of miles of Blue hike = 3. Number of miles of White hike = 5. Number of miles of Red hike = 2. Number of miles of Green hike = 4. Number of different trails Addie hiked = 3. Number of total miles distance Addie hiked = 11. Trails Addie hiked = Number of miles of White hike + Number of miles of Red hike + Number of miles of Green hike = 5 + 2 + 4 = 7 + 4 = 11.

Question 20. Marty hikes one of the trails 4 times. In all, he hikes more than 10 miles but less than 16 miles. Which trail does Marty hike? Explain your answer. Answer: Blue Trail Marty hiked 4times hiking of 12 miles.

Explanation: Number of different trails Marty hiked = 1. Number of times Marty hiked same trail = 4. Number of miles of Blue hike = 3. Trail Marty hiked = Number of miles of Blue hike  × 4 = 3 × 4 = 12 > 10 < 16.

Question 21. Four teams are tidying the Green trail. They will each tidy an equal distance. How many miles does each team tidy? Answer: Miles each team tidy = 1.

Explanation: Number of miles of Green hike = 4. Number of teams hiking the green trial = 4. Miles each team tidy = Number of miles of Green hike  ÷ Number of teams hiking the green trial = 4 ÷ 4 = 1.

Question 22. Fiona hiked on Wednesday and Sunday. Each day she hiked all of the trails. How many miles did Fiona hike? Answer: Total number of Miles Fiona hiked = 28.

Explanation: Number of miles of Blue hike = 3. Number of miles of White hike = 5. Number of miles of Red hike = 2. Number of miles of Green hike = 4. Fiona hiked on Wednesday and Sunday. => Number of days Fiona hiked  = 2. Total number of Miles Fiona hiked = Number of miles of Blue hike + Number of miles of White hike + Number of miles of Red hike + Number of miles of Green hike × Number of days Fiona hiked = (3 + 5 + 2 + 4) × 2 = ( 8 + 2 + 4) = ( 10 + 4) = 14 × 2 = 28.

Question 23. Model with Math Use a representation to explain why any number divided by 1 is itself. Answer: Same number divided by itself, always gives the product of 1.

Explanation: 1 ÷ 1 = 1 because same number divided by itself, always gives the product of 1. 2 ÷ 2 = 1.

Question 24. Higher Order Thinking Yvonne says that 0 ÷ 21 and 21 ÷ 0 both have a quotient of 0. Is Yvonne correct? Explain.

Answer: Yes, Yvonne is correct 0 ÷ 21 and 21 ÷ 0 both have a quotient of 0 because any number divided by zero or zero divided by any number the quotient is always zero.

Explanation: 0 ÷ 21 = 0. 21 ÷ 0 = 0.

Explanation: 8 ÷ 8 = 1. Any number divided by itself, quotient is always 1. 0 ÷ 4 = 0. Zero divided by any number, quotient is always 0. 3 ÷ 3 = 1. Any number divided by itself, quotient is always 1.

Explanation: 4 ÷ 4 = 1. Any number divided by itself, quotient is always 1. 0 ÷ 5 = 0. Zero divided by any number, quotient is always 0. 0 ÷ 7 = 0. Zero divided by any number, quotient is always 0.

Lesson 4.7 Practice Multiplication and Division Facts

Look Back! How can 7 × ? = 56 help you find 56 ÷ 7 = ? Answer: Number of people in each tour group = 8. Amount of each tour guide collects = $16.

Explanation: Number of people A tour bus to a national park holds = 56. Number of tour guides at the park to lead equal groups of people from the bus = 7. Number of people in each tour group = Number of people A tour bus to a national park holds ÷ Number of tour guides at the park to lead equal groups of people from the bus = 56 ÷ 7 = 8. Amount of entrance fee each person in a group to pay tour guide = $2. Amount of each tour guide collects = Number of people in each tour group × Amount of entrance fee each person in a group to pay tour guide = 8 × $2 = $16.

Essential Question What Fact Can You Use? Answer: To solve the problem we can use multiplication facts or division facts according to the requirment of the question asked.

Explanation: We can use multiplication facts 1s, 2s, 3s, 4s, 5s…… and division facts to solve the problems to find the asked solution.

Another Way What number times 4 equals 28? You can use multiplication facts to help solve the problem. 28 quarters ? × 4 = 28 7 × 4= 28 Sabrina can trade 28 quarters for 7 one-dollar bills.

Convince Me! Construct Arguments Why can both 28 ÷ 7 = ? and ? × 7 = 28 be used to solve the problem above? Answer: Number of one-dollar bills Sabrina gets = 7. 4 × 7 = 28. 28 ÷ 7 = 4. We can use both 28 ÷ 7 = ? and ? × 7 = 28  to solve the problem above explained as below: Number of quarters in one dollar × Number of one-dollar bills Sabrina gets = Number of quarters Sabrina has in her bank. => 4 × 7 = 28. Number of quarters Sabrina has in her bank ÷ Number of one-dollar bills Sabrina gets = Number of quarters in one dollar. 28 ÷ 7 = 4.

Explanation: There are 4 quarters in one dollar. Number of quarters Sabrina has in her bank = 28. Number of quarters in one dollar = 4. Number of one-dollar bills Sabrina gets = Number of quarters Sabrina has in her bank  ÷ Number of quarters in one dollar = 28 ÷ 4 = 7. We can use both 28 ÷ 7 = ? and ? × 7 = 28  to solve the problem above explained as below: Number of quarters in one dollar × Number of one-dollar bills Sabrina gets = Number of quarters Sabrina has in her bank. => 4 × 7 = 28. Number of quarters Sabrina has in her bank ÷ Number of one-dollar bills Sabrina gets = Number of quarters in one dollar. => 28 ÷ 7 = 4.

Guided Practice Do You Understand? Question 1. Look back at the problem on the previous page. Suppose Sabrina put 8 more quarters in her bank. How many one-dollar bills can she trade for the quarters in her bank now? Answer: Number of one-dollar bills Sabrina gets = 10.

Explanation: There are 4 quarters in one dollar. Number of quarters Sabrina has in her bank = 28 + 12 = 40. Number of quarters in one dollar = 4. Number of one-dollar bills Sabrina gets = Number of quarters Sabrina has in her bank  ÷ Number of quarters in one dollar = 40 ÷ 4 = 10.

Question 2. Calvin solves the equation 49 ÷ 7 = ☐. How does this help him complete the equation 7 × ☐ = 49? Answer: Yes, this helps Calvin to complete the equation 7 × ☐ = 49.

Explanation: Equation: 49 ÷ 7 = ☐. 49 ÷ 7 = 7. => 7 × 7= 49.

Do You Know How? In 3-7, use a multiplication or a division fact to complete the equations. You can use multiplication to help divide. Question 3. ______ = 45 ÷ 5 45 = 5 × ______ Answer: ___9___ = 45 ÷ 5. 45 = 5 × ___9___.

Explanation: 9 = 45 ÷ 5 45 = 5 × 9.

Question 4. _____ × 7 = 21 21 ÷ ______ = 7 Answer: __3___ × 7 = 21. 21 ÷ __3____ = 7.

Explanation: 3 × 7 = 21. 21 ÷ 3 = 7.

Question 5. 6 × _____ = 30 30 ÷ 6 = ______ Answer: 6 × __5___ = 30. 30 ÷ 6 = ___5___.

Explanation: 6 × 5 = 30. 30 ÷ 6 = 5.

Question 6. 4 = 24 ÷ _______ 24 = ______ × 4 Answer: 4 = 24 ÷ ___6____. 24 = __6____ × 4.

Explanation: 4 = 24 ÷ 6. 24 = 6 × 4.

Question 7. 6 × _____ = 12 12 ÷ 6 = _______ Answer: 6 × __2___ = 12. 12 ÷ 6 = __2_____.

Explanation: 6 × 2 = 12. 12 ÷ 6 = 2.

Independent Practice Leveled Practice In 8-10, use fact families to complete the equations. Question 8. 42 ÷ 7 = ______ 7 × _____ = 42 Answer: 42 ÷ 7 = ___6___. 7 × __6___ = 42.

Explanation: 42 ÷ 7 = 6. 7 × 6 = 42.

Question 9. 18 = 6 × ______ _____ = 18 ÷ 6 Answer: 18 = 6 × ___3___. __3___ = 18 ÷ 6.

Explanation: 18 = 6 × 3. 3 = 18 ÷ 6.

Question 10. 9 = _____ ÷ 8 9 × 8 = ______ Answer: 9 = __2___ ÷ 8. 9 × 8 = ___2___.

Explanation: 9 = 2 ÷ 8. 9 × 8 = 2.

In 11-19, find the product or quotient. Question 11. 36 ÷ 4 = ______ Answer: 36 ÷ 4 = __9____.

Explanation: 36 ÷ 4 = 9. (quotient)

Question 12. _____ = 8 × 8 Answer: __1___ = 8 × 8.

Explanation: 1= 8 × 8. (quotient)

Question 13. 15 ÷ 3 = ________ Answer: 15 ÷ 3 = ___5_____.

Explanation: 15 ÷ 3 = 5. (quotient)

Question 17. Multiply 8 times 5. Answer: 8 × 5 = 40.

Explanation: Multiply 8 times 5. 8 × 5 = 40. (product)

Question 18. Divide 18 by 9. Answer: 18 ÷ 9 = 2.

Explanation: 18 ÷ 9 = 2. (product)

Question 19. Divide 27 by 3. Answer: 27 ÷ 3 = 9.

Explanation: Divide 27 by 3. 27 ÷ 3 = 9.(product)

Explanation: Number of cups of peanuts would Eric need to make of trail mix = 4. Number of batches to make trail mix = 5. Number of cups of peanuts would Eric need to make of 5 batches trail mix = Number of cups of peanuts would Eric need to make of trail mix × Number of batches to make trail mix = 5 × 4 = 20.

Question 21. How many batches of trail mix can Eric make with 16 cups of peanuts, 15 cups of raisins, and 8 cups of walnuts? Answer: Number of batches of trail mix can Eric make with 16 cups of peanuts = 16 ÷ 4 = 4. Number of batches of trail mix can Eric make with 8 cups of walnuts = 8 ÷ 2 = 4. Number of batches of trail mix can Eric make with 15 cups of raisins = 15 ÷ 3 = 5.

Explanation: Number of cups of peanuts would Eric need to make of trail mix = 4. Number of cups of peanuts Eric want the trail mix = 16 Number of batches of trail mix can Eric make with 16 cups of peanuts = Number of cups of peanuts Eric want the trail mix ÷ Number of cups of peanuts would Eric need to make of trail mix = 16 ÷ 4 = 4. Number of  cups of raisins would Eric need to make of trail mix = 3. Number of  cups of raisins Eric want the trail mix = 15. Number of batches of trail mix can Eric make with 15 cups of raisins = Number of cups of raisins Eric want the trail mix ÷ Number of cups of raisins would Eric need to make of trail mix = 15 ÷ 3 = 5. Number of cups of walnuts would Eric need to make of trail mix = 2. Number of cups of walnuts Eric want the trail mix = 8. Number of batches of trail mix can Eric make with 8 cups of walnuts = Number of cups of walnuts Eric want the trail mix ÷ Number of cups of walnuts would Eric need to make of trail mix = 8 ÷ 2 = 4.

Question 22. Reasoning Eric spends $30 to buy the ingredients for 5 batches of trail mix. Find the cost of the ingredients Eric needs for one batch. How much would Eric need for 2 batches? Answer: Cost of the ingredients Eric needs for one batch = $6. Amount of money Eric need for buying 2 batches = $12.

Explanation: Amount of money Eric spends to buy the ingredients for 5 batches of trail mix = $30. Number of batches of trail mix Eric buys = 5. Cost of the ingredients Eric needs for one batch = Amount of money Eric spends to buy the ingredients for 5 batches of trail mix ÷ Number of batches of trail mix Eric buys = $30 ÷ 5 = $6. Amount of money Eric need for buying 2 batches = Cost of the ingredients Eric needs for one batch × 2 = $6 × 2 = $12.

Explanation: one way to name these parts: Square. Triangle.

Question 24. Higher Order Thinking Wilson is thinking of 2 one-digit numbers. When he multiplies them, the product is 27. What is the sum of the two numbers? Explain your answer. Answer: 2 one-digit numbers: 3 and 9. Product: 3 × 9 = 27. or 9 × 3 = 27. Sum: 3 + 9 = 12. or 9 + 3 = 12.

Explanation: 2 one-digit numbers: 3 and 9. Product: 3 × 9 = 27. or 9 × 3 = 27. Sum: 3 + 9 = 12. or 9 + 3 = 12.

Explanation: 8 ÷ 1 = ?    => 8 ÷ 1 = 8. ? = 9 ÷ 9.    =>1 = 9 ÷ 9. ? = 0 ÷ 3.    => 0 = 0 ÷ 3. 6 × 0 = ?     => 6 × 0 = 0.

Lesson 4.8 Solve Multiplication and Division Equations

Look Back! Would the problem 1 × 3 × 2 × 1 keep the pans above balanced? Explain. Answer: Yes, the problem 1 × 3 × 2 × 1 keep the pans above balanced because 24 ÷ 4 = 6. (1 × 3) × (2 × 1) = 3 × (2 × 1) = 3 × 2 = 6.

Explanation: Problem 1 × 3 × 2 × 1 keep the pans above balanced. 24 ÷ 4 = 6. (1 × 3) × (2 × 1) = 3 × (2 × 1) = 3 × 2 = 6.

Essential Question How Do Multiplication and Division Equations Work? Answer: Multiplication works by multiplying the numbers to find the answers and Division works by dividing the numbers to find the answers.

Explanation: Multiplication is the process of multiplying the numbers and Division  means the process of divinding the numbers to find the answers.

Frank has some tubes of tennis balls. Each tube has 4 tennis balls. Frank has 8 tennis balls in all. How many tubes of tennis balls does he have? You can write an equation to represent the problem. 8 = ? × 4

Convince Me! Reasoning Use the value of ? in the multiplication equation to write and solve two division equations. 7 × ? = 42 42 ÷ ? = ☐ 42 ÷ ☐ = ? Answer: 7 × ? = 42     => 7 × 6 = 42. 42 ÷ ? = ☐    => 42 ÷ 6 = 7. 42 ÷ ☐ = ?    => 42 ÷ 7 = 6.

Explanation: 7 × 6 = 42. 42 ÷ 6 = 7. 42 ÷ 7 = 6.

Guided Practice Do You Understand? Question 1. Write an equation that represents the following problem: Walt makes some sandwiches. Each sandwich uses 2 slices of bread. He uses 16 slices of bread. How many sandwiches does Walt make? Use ? to represent the number of sandwiches. Answer: Number of sandwiches Walt makes = 8.

Explanation: Number of slices of bread each sandwich uses = 2. Number of slices of bread Walt uses = 16. Number of sandwiches Walt makes = ?? => Number of slices of bread Walt uses ÷ Number of slices of bread each sandwich uses => 16 ÷ 2 => 8.

Do You Know How? In 2-5, find the value for ? that makes the equation true. Question 2. 9 × ? = 27 Answer: 9 × 3 = 27.

Explanation: 9 × ? = 27. 9 × 3 = 27.

Question 3. 8 = 40 ÷ ? Answer: 8 = 40 ÷ 5.

Explanation: 8 = 40 ÷ ? 8 = 40 ÷ 5.

Question 4. 32 = ? × 8 Answer: 32 = 4 × 8.

Explanation: 32 = ? × 8. 32 = 4 × 8.

Question 5. ? ÷ 3 = 6 Answer: 18 ÷ 3 = 6.

Explanation: ? ÷ 3 = 6. 18 ÷ 3 = 6.

Independent Practice In 6-9, find the value for ? that makes the equation true. Question 6. ? ÷ 4 = 7 Answer: 28 ÷ 4 = 7.

Explanation: ? ÷ 4 = 7. 28 ÷ 4 = 7.

Question 7. 25 = 5 × ? Answer: 25 = 5 × 5.

Explanation: 25 = 5 × ? 25 = 5 × 5.

Question 8. 72 = ? × 9 Answer: 72 = 8 × 9.

Explanation: 72 = ? × 9. 72 = 8 × 9.

Question 9. 4 = 20 ÷ ? Answer: 4 = 20 ÷ 5.

Explanation: 4 = 20 ÷ ?. 4 = 20 ÷ 5.

In 10-13, write and solve an equation that represents the problem. Question 10. Sasha has 21 dimes. She puts them in stacks with the same number of dimes in each stack. In all, she has 3 stacks. How many dimes are in each stack? Use? to represent the number of dimes in each stack. Answer: Number of dimes in each stack = 7.

Explanation: Number of dimes Sasha has = 21. She puts them in stacks with the same number of dimes in each stack. Number of stacks Sasha has = 3. Number of dimes in each stack = Number of dimes Sasha has ÷ Number of stacks Sasha has = 21 ÷ 3 = 7.

Question 11. There were some sheep in a barnyard. Each sheep had 4 legs. There were 24 legs in the barnyard. How many sheep were in the barnyard? Use ? to represent the number of sheep in the barnyard. Answer: Number of sheep in the barnyard = 6.

Explanation: Number of legs each sheep has = 4. Total number of legs in the barnyard = 24. Number of sheep in the barnyard = ?? => Total number of legs in the barnyard  ÷ Number of legs each sheep has => 24 ÷ 4 => 6.

Question 12. A football team scored 48 points. The team only scored on touchdowns, worth 6 points each. How many touchdowns did the team score? Use ? to represent the number of touchdowns. Answer: Number of touchdowns the team scored = 8.

Explanation: Number of points football team scored = 48. Number of points team scored on touchdowns each = 6. Number of touchdowns the team scored = ?? => Number of points football team scored ÷ Number of points team scored on touchdowns each => 48 ÷ 6 => 8.

Question 13. There were 6 ladybugs on a leaf. Each ladybug had the same number of spots. There were 36 spots. How many spots were on each ladybug? Use ? to represent the number of spots on each ladybug. Answer: Number of spots on each ladybug = 6.

Explanation: Number of ladybugs on a leaf = 6. Each ladybug had the same number of spots. Total number of spots = 36. Number of spots on each ladybug =?? => Total number of spots ÷ Number of ladybugs on a leaf => 36 ÷ 6 => 6.

Question 16. Higher Order Thinking A building has more than 2 stories but fewer than 10 stories. Each story of the building has the same number of windows. The building has 25 windows. Complete the sentence. Then explain how you found your answer. The building has each story has ________stories, and each story has ______ windows. Answer: The building has each story has ___25_____stories, and each story has ___25___ windows.

Explanation: A building has more than 2 stories but fewer than 10 stories. Number of windows building has = 25. Each story of the building has the same number of windows. => Number of stories each building has = 25.

Question 17. Rosi and Karen are trying to solve 4= ? ÷ 8. Rosi says the value of the unknown is 32. Karen says the value of the unknown is 2. Is Rosi or Karen correct? Explain. Answer: Rosi is correct because 32 ÷ 8 = 4 not 2 ÷ 8 = 4.

Explanation: Equation: 4 = ? ÷ 8. => 4 = 32 ÷ 8.

Assessment Practice Question 18. What is the value of the unknown in the equation 30 ÷ ? = 6? A. 4 B. 5 C. 6 D. 7 Answer: 30 ÷ 5 = 6. C. 6

Explanation: Equation : 30 ÷ ? = 6 => 30 ÷ 5 = 6.

Question 19. What is the value of the unknown in the equation 8 × ? = 64? A. 5 B. 6 C. 7 D. 8 Answer: 8 × 8 = 64. D. 8

Explanation: Equation: 8 × ? = 64 8 × 8 = 64.

Lesson 4.9 Problem Solving

Make Sense and Persevere Solve & Share Natalie prepared a crate of oranges for shipment. She packed the oranges in 2 layers. In each layer, she packed 6 rows with 7 oranges in each row. How many oranges did Natalie pack? Use equations to represent your work. I can… make sense of problems and keep working if I get stuck.

Thinking Habits Be a good thinker! These questions can help you.

• What do I need to find?
• What do I know?
• What’s my plan for solving the problem?
• What else can I try if get stuck?

Look Back! Make Sense and Persevere How did you find how many oranges Natalie packed in each layer? How did this plan help you solve the problem? Answer: Total number of oranges Natalie packed = 84. This plan helped to solve the problem by step by step process and its easy to understand.

Explanation: Natalie prepared a crate of oranges for shipment. She packed the oranges in 2 layers. In each layer, she packed 6 rows with 7 oranges in each row. How many oranges did Natalie pack? Number of layers of oranges she packed = 2. Number of rows of oranges she packed = 6. Number of oranges in each row she kept = 7. Total number of oranges Natalie packed = ?? => Number of layers of oranges she packed ( Number of rows of oranges she packed × Number of oranges in each row she kept ) => 2 ( 6 × 7) => 2 × 42 => 84.

Essential Question How Can You Make Sense of a Problem and Persevere in Solving It? Answer: According to the  Common Core State Standards, mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. You should understand the problem step by step then should try to find out the solve the problem.

Explanation: According to the  Common Core State Standards, mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals.

How can I make sense of and solve this problem? I can

• identify what is known from the problem.
• look for and answer hidden questions in the problem.
• make a plan to solve the problem.
• check to make sure my work and answer make sense.

Here’s my thinking…

I know a box costs $54. There are 2 rows of 3 games in a box. First, I need to find the total number of games in a box. I will multiply the number of rows by the number of games in each row. 2 × 3 = 6 6 games are in a box. Then I will divide the cost of a box by the total number of games to find the cost of each game. $54 ÷ 6 = $ 9 Each game costs $9.

Convince Me! Make Sense and Persevere How can you check to make sure the work and answer given above make sense? Answer: CHECK: Cost of video game box = Total number of video games in a box × Cost of each game = 6 × $9 = $54.

Explanation: Number of rows of video games = 2. Number of video games in each row = 3. Cost of video game box= $54. Total number of video games in a box = Number of rows of video games × Number of video games in each row = 2 × 3 = 6. Cost of each game = Cost of video game box ÷ Total number of video games in a box = $54 ÷ 6 = $9.

Explanation: Number of friends went camping = 12. All except 4 of them went on a hike. => Number of friends went on a hike = 12 – 4 = 8. Number of water bottles the hikers carried = 32. Number of water bottles each hiker carried = Number of water bottles the hikers carried  ÷ Number of friends went on a hike = 32 ÷ 8 = 4.

Question 2. Tell which operations you will use. Then solve the problem. Answer: Multiplication and Division are the operations used and solved the problem.

Explanation: The operations used re multiplication and division to solve the problem.

Independent Practice Make Sense and Persevere Four students went bowling. They bowled 2 games each. The cost was $5 per game. How much money did the students spend on bowling? Explain. Question 3. Tell what you know. Then explain what you need to find first to solve the problem. Answer: Amount of money the students spend on bowling = $40.

Explanation: Number of students went for bowling = 4. Number of games they bowled each = 2. Cost of each game = $5. Amount of money the students spend on bowling = ( Number of students went for bowling × Number of games they bowled each ) Cost of each game = (4 × 2) × $5 = 8 × $5 = $40.

Question 4. Tell which operations you will use. Then solve the problem.

Answer: Multiplication and Division are the operations used and solved the problem.

Question 5. How can you check that your work is correct? Answer: CHECK: Number of students went for bowling × Number of games they bowled each = Amount of money the students spend on bowling ÷ Cost of each game => 4 × 2 =  $40 ÷ $5 = 8.

Explanation: CHECK: Number of students went for bowling × Number of games they bowled each = Amount of money the students spend on bowling ÷ Cost of each game => 4 × 2 =  $40 ÷ $5 = 8.

Question 6. Make Sense and Persevere What do you know? What are you asked to find? Answer: Number of children in his group = 4.

Explanation: Amount spent on admission tickets for himself and the children in his group = $24. Amount for admission ticket for adult = $8. Amount for admission ticket for child = $4. Amount for boat ride ticket for adult = $2. Amount for boat ride ticket for child = $1. Number of children in his group = (Amount spent on admission tickets for himself and the children in his group – Amount for admission ticket for adult) ÷ Amount for admission ticket for child = ($24 – $8) ÷ $4. = $16 ÷ $4. = 4.

Explanation: Mr. Casey buys the tickets to go country fair he needs to know which kind of tickets he purchased.

Question 8. Critique Reasoning Dan says there are 6 children in Mr. Casey’s group because $24 ÷ $4 = 6. Does Dan’s reasoning make sense? Explain. Answer: Yes, Dan does not make sense because $24 ÷ $4 = 6 because total amount spent divided by amount for admission ticket for child.

Explanation: Dan equation is correct because total amount spent divided by amount for admission ticket for child.

Question 9. Reasoning Solve the problem. Write an equation for each step and explain. Answer: Number of children took the admission tickets = 6.

Explanation: Amount spent on admission tickets for himself and the children in his group = $24. Amount for admission ticket for adult = $8. Amount for admission ticket for child = $4. Amount for boat ride ticket for adult = $2. Amount for boat ride ticket for child = $1. Number of children in his group = 4. Number of children took the admission tickets = Amount spent on admission tickets for himself and the children in his group ÷ Amount for admission ticket for child = $24 ÷ $4. = 6.

Topic 7 Fluency Review Activity

Find a Match Work with a partner. Point to a clue. Read the clue. Look below the clues to find a match. Write the clue letter in the box next to the match. Find a match for every clue. I can … add and subtract within 100. man

Explanation: 73 – 64 = 9. 37 + 14 = 51. 47 + 39 = 86. 48 + 25 = 73. 24 + 26 = 50. 56 – 8 = 48. 92 – 11 = 81. 65 – 43 = 22. 19 – 12 = 7. 52 + 26 = 78. 72 + 26 = 98. 66 – 27 = 39.

A. is equal to 59 + 19 = 78. B. is equal to 13 – 6 = 7. C. is equal to 48 + 38 = 86. D. is equal to 57 – 18 = 39. E. Is equal to 72 – 24 = 48. F. is equal to 35 + 15 = 50. G. is equal to 100 – 19 = 81. H. is equal to 65 + 33 = 98. I. Is equal to 39 – 17 = 22. J. is equal to 29 +44 = 73. K. is equal to 56 – 47 = 9. L. is equal to 16 + 35 = 51.

Topic 4 Vocabulary Review Understand Vocabulary Word List

• even number
• fact family
• odd number product

Explanation: 30 ÷ 6 = 5.   Divisor – 6. 24 ÷ 3 = 8.      Divisor – 3. 14 ÷ 2 =7.    Divisor – 2. 45 ÷ 5 = 9.    Divisor – 5.

Explanation: 63 ÷ 7 = 9.    Dividend – 63. 4 ÷ 1 = 4.      Dividend –  4. 0 ÷ 5 = 0.     Dividend – 0. 8 ÷ 4 = 2.    Dividend –  8.

Explanation: 21 ÷ 3 = 7.      quotient – 7. 54 ÷ 9 = 6.      quotient – 54. 15 ÷ 5 = 3.    quotient – 15. 16 ÷ 8 = 2.    quotient – 16.

Explanation: 24 and 68 are even numbers.

Explanation: 21, 13, 47 are odd numbers.

Question 6. Look at the equations below. Write Y if the product is 6. Write N if the product is NOT 6. 4 × 6 = 24 _______ 2 × 3 = 6 _______ 6 = 3 × 2 ________ Answer: 4 × 6 = 24 ___N____. 2 × 3 = 6 ____Y___. 6 = 3 × 2 ____Y____.

Explanation: 4 × 6 = 24.   N 2 × 3 = 6.     Y 6 = 3 × 2.     Y

Question 7. Look at the equations below. Write Y if the group shows a fact family. Write N if the group does NOT show a fact family. 3 × 9 = 27 _______ 27 ÷ 9 = 3 9 × 3 = 27 27 ÷ 3 = 9

12 ÷ 6 = 2 ________ 2 × 6 = 12 12 ÷ 3 = 4 6 × 2 = 12

56 ÷ 8 = 7 _________ 56 ÷ 7 = 8 8 × 7 = 56 7 × 8 = 56 Answer:

3 × 9 = 27 ___Y____ 27 ÷ 9 = 3 9 × 3 = 27 27 ÷ 3 = 9

12 ÷ 6 = 2 ___N_____ 2 × 6 = 12 12 ÷ 3 = 4 6 × 2 = 12

56 ÷ 8 = 7 _____Y____ 56 ÷ 7 = 8 8 × 7 = 56 7 × 8 = 56

3 × 9 = 27       Y 27 ÷ 9 = 3 9 × 3 = 27 27 ÷ 3 = 9

12 ÷ 6 = 2         N 2 × 6 = 12 12 ÷ 3 = 4 6 × 2 = 12

56 ÷ 8 = 7          Y 56 ÷ 7 = 8 8 × 7 = 56 7 × 8 = 56

Use Vocabulary in Writing Question 8. Explain how to find the fact family for 2, 4, and 8. Use at least 2 terms from the Word List in your explanation. Answer: 2, 4, 8. 2 × 4 = 8. 4 × 2 = 8. 8 ÷ 2 = 4. 8 ÷ 4 = 2.

Explanation: In math, a fact family can be defined as a group of math facts or equations created using the same set of numbers. The fact family shows the relationships between the three numbers involved. 2, 4, 8. 2 × 4 = 8. 4 × 2 = 8. 8 ÷ 2 = 4. 8 ÷ 4 = 2.

Topic 4 Reteaching Set A pages 117-120

Remember that a fact family is a group of related facts using the same numbers.

In 1-4, write the other three facts in the fact family Question 1. 3 × 7 = 21 Answer: 3 × 7 = 21. 7 × 3 = 21. 21 ÷ 7 = 3. 21 ÷ 3 = 7.

Explanation: Other three facts in the fact family of 3 × 7 = 21: 7 × 3 = 21. 21 ÷ 7 = 3. 21 ÷ 3 = 7.

Question 2. 5 × 3 = 15 Answer: 3 × 5 = 15. 15 ÷ 5 = 3. 15 ÷ 3 = 5.

Explanation: Other three facts in the fact family of 5 × 3 = 15: 3 × 5 = 15. 15 ÷ 5 = 3. 15 ÷ 3 = 5.

Question 3. 8 × 6 = 48 Answer: 6 × 8 = 48. 48 ÷ 8 = 6. 48 ÷ 6 = 8.

Explanation: Other three facts in the fact family of 8 × 6 = 48: 6 × 8 = 48. 48 ÷ 8 = 6. 48 ÷ 6 = 8.

Question 4. 4 × 5 = 20 Answer: 5 × 4 = 20. 20 ÷ 5 = 4. 20 ÷ 4 = 5.

Explanation: Other three facts in the fact family of 4 × 5 = 20: 5 × 4 = 20. 20 ÷ 5 = 4. 20 ÷ 4 = 5.

Remember that you can use multiplication to help divide. In 1 and 2, solve each problem. Write the multiplication fact and division fact you use to solve the problem. Question 1. Sally has 32 flowers. She puts 8 flowers in each vase. How many vases does Sally need for all the flowers? Answer: Number of vases Sally needs for all the flowers = 4. Division fact: 32 ÷ 8 = 4. 32 ÷ 4 = 8.

Explanation: Number of flowers Sally has = 32. Number of flowers she puts in each vase = 8. Number of vases Sally needs for all the flowers = Number of flowers Sally has ÷ Number of flowers she puts in each vase = 32 ÷ 8 = 4. Division fact: 32 ÷ 8 = 4. 32 ÷ 4 = 8.

Question 2. Jon has 18 peaches. He uses 3 peaches to make a peach tart. How many peach tarts does Jon make if he uses all the peaches? Answer: Number of peach tarts Jon makes if he uses all the peaches = 6. Division fact: 18 ÷ 3 = 6. 18 ÷ 6 = 3.

Explanation: Number of peaches Jon has = 18. Number of peaches he uses to make a peach tart = 3. Number of peach tarts Jon makes if he uses all the peaches = Number of peaches Jon has ÷ Number of peaches he uses to make a peach tart = 18 ÷ 3 = 6. Division fact: 18 ÷ 3 = 6. 18 ÷ 6 = 3.

Remember that you can use multiplication facts for 6s and 7s to help you divide by 6s and 7s.

In 1-3, solve each problem. Write the multiplication fact and division fact you use to solve the problem. Question 1. There are 36 runners entered in a marathon. They run in groups of 6. How many groups are there? Answer: Number of groups = 6. Division fact: 36 ÷ 6 = 6.

Explanation: Number of runners entered in a marathon = 36. Number of runners run in groups = 6. Number of groups = Number of runners entered in a marathon ÷ Number of runners run in groups = 36 ÷ 6 = 6.

Question 2. Lani has 35 bird stickers. There are 5 stickers on each sheet. How many sheets of bird stickers does she have? Answer: Number of sheets of bird stickers she has = 7. Division fact: 35÷ 7 = 5.

Explanation: Number of bird stickers Lani has = 35. Number of stickers on each sheet = 5. Number of sheets of bird stickers she has = Number of bird stickers Lani has ÷ Number of stickers on each sheet = 35 ÷ 5 = 7. Division fact: 35÷ 7 = 5.

Question 3. Jake has 18 remote-controlled boats for 6 friends to share equally. How many boats will each friend get? Answer: Number of boats each friend gets = 3. Division fact: 18÷ 3 = 6.

Explanation: Number of remote-controlled boats Jake has =18. Number of friends he shares them equally = 6. Number of boats each friend gets = Number of remote-controlled boats Jake has ÷ Number of friends he shares them equally = 18 ÷ 6 = 3. Division fact: 18÷ 3 = 6.

Remember that you can use multiplication facts for 8s and 9s to help divide by 8s and 9s.

In 1-5, write the related multiplication fact that can be used to complete each division fact. Then find the quotient. Question 1. 54 ÷ 9 = ______ _____ × ______ = _______ Answer: 54 ÷ 9 = __6____ __9___ × __6____ = ___54____.

Explanation: 54 ÷ 9 = 6. 9 × 6 = 54.

Question 2. 64 ÷ 8 = ______ _____ × ______ = _______ Answer: 64 ÷ 8 = __8____ __8___ × ___8___ = __64_____.

Explanation: 64 ÷ 8 = 8. 8 × 8 = 64.

Question 3. 36 ÷ 9 = ______ _____ × ______ = _______ Answer: 36 ÷ 9 = __4____ __9___ × ___4___ = __36_____.

Explanation: 36 ÷ 9 = 4. 9 × 4 = 36.

Question 4. 56 ÷ 8 = ______ _____ × ______ = _______ Answer: 56 ÷ 8 = __7____ __8___ × ___7___ = ___56____.

Explanation: 56 ÷ 8 = 7. 8 × 7 = 56.

Question 5. 72 ÷ 8 = ______ _____ × ______ = _______ Answer: 72 ÷ 8 = ___9___ __8__ × ___9___ = __72_____.

Explanation: 72 ÷ 8 = 9. 8 × 9 = 72.

Set E pages 133-136 A whole number is even if it can be divided by 2 with none left over. A whole number is odd if it cannot be divided by 2 with none left over. Which product is even? Which is odd? 3 × 7 = odd product 5 × 8 = even product All even numbers can be thought of as 2 equal groups. When at least one factor is even, the product is even.

Remember that you can think about dividing by 2 to tell whether a number is even or odd.

Explanation: Even factors: 6 and 4 both. Product 6 × 4 = 24 is also even number.

Explanation: Odd factors: 9 and 1 both. Product 9 × 1 = 9 is also odd number.

Explanation: Even factors: 8 is even number. Product 8 × 7 =  56 is even number.

Remember that any number divided by 1 is itself. Any number (except 0) divided by itself is 1. Zero divided by any number (except 0) is 0.

In 1-3, use division to solve. Question 1. 0 ÷ 16 = ______ Answer: 0 ÷ 16 = __0____.

Explanation: 0 ÷ 16 = 0.

Question 2. 10 ÷ 10 = _______ Answer: 10 ÷ 10 = ___1____.

Explanation: 10 ÷ 10 = 1.

Question 3. Leroy had 4 oranges. He gave one orange to each of his 4 friends. How many oranges did each friend get? Write an equation to show your answer. Answer: Number of oranges each friend gets = 1.

Explanation: Number of oranges Leroy had = 4. Number of friends he gave one orange each = 4. Number of oranges each friend gets = Number of oranges Leroy had  ÷ Number of friends he gave one orange each = 4 ÷ 4 = 1.

Remember that you can use bar diagrams or multiplication facts to help solve a division problem.

In 1 and 2, use related multiplication and division facts to solve. Question 1. 21 ÷ 7 = _____ 7 × ______ = 21 Answer: 21 ÷ 7 = _3___. 7 × __3____ = 21.

Explanation: 21 ÷ 7 = 3. 7 × 3 = 21.

Question 2. 5 × __ = 45 45 ÷ 5 = ______ Answer: 5 × __9__ = 45. 45 ÷ 5 = __9____.

Explanation: 5 × 9 = 45 45 ÷ 5 = 9.

Remember that you can use multiplication and division facts to find the value of an unknown.

In 1-6, find the value of the unknown. Question 1. ? ÷ 2 = 6 Answer: 12 ÷ 2 = 6., so the unknown number is 12.

Explanation: “Divide by 2 number. The result is 6.” ? ÷ 2 = 6 => 12 ÷ 2 = 6.

Question 2. 7 × ? = 42 Answer: 7 × 6 = 42., so the unknown number is 42.

Explanation: “Multiply 7 by a number. The result is 42.” 7 × ? = 42 => 7 × 6 = 42.

Question 3. 20 = 4 × ? Answer: 20 = 4 × 5., so the unknown number is 5.

Explanation: “Multiply 4 by a number. The result is 20.” 20 = 4 × ? => 20 = 4 × 5.

Question 4. 9 = ? ÷ 3 Answer: 9 = 27 ÷ 3., so the unknown number is 27.

Explanation: “Divide by 3 number. The result is 9.” 9 = ? ÷ 3 => 9 = 27 ÷ 3.

Question 5. 16 ÷ ? = 2 Answer: 16 ÷ 8 = 2., so the unknown number is 8.

Explanation: “16 Divide by. The result is 2.” 16 ÷ ? = 2 => 16 ÷ 8 = 2.

Question 6. 24 ÷ ? = 6 Answer: 24 ÷ 4 = 6., so the unknown number is 4.

Explanation: “24 Divide by. The result is 6.” 24 ÷ ? = 6 => 24 ÷ 4 = 6.

Set I pages 149-152 Think about these questions to help you make sense of problems and persevere in solving them. Thinking Habits

• What else can I try if I get stuck?

Remember to use the information in each step to solve the problem.

In 1 and 2, answer to solve a two-step problem. Fourteen friends went to the county fair. All except 6 of them bought a hot dog. Each hot dog costs $3. How much did the friends spend on hot dogs?

Question 1. Tell what you know. Then explain what you need to find first to solve the problem. Answer: Number of friends went to the county fair = 14. All except 6 of them bought a hot dog. => Number of friends bought a hot dog = 14 – 6 = 8. Each hot dog costs $3. => Cost of each hot dog = $3. We need to find amount of money the friends spend on hot dogs = ?? Amount of money the friends spend on hot dogs = $24.

Explanation: Number of friends went to the county fair = 14. All except 6 of them bought a hot dog. => Number of friends bought a hot dog = 14 – 6 = 8. Each hot dog costs $3. => Cost of each hot dog = $3. We need to find amount of money the friends spend on hot dogs = ?? Amount of money the friends spend on hot dogs = Number of friends bought a hot dog  × Cost of each hot dog = 8 × $3 = $24.

Question 2. Tell which operations you will use. Then solve the problem. Answer: Multiplication and Division operations  we use to solve the problem.

Explanation: The operations used here are multiplication and division to solve the problem to find the answer. Number of friends went to the county fair = 14. Number of friends bought a hot dog = 14 – 6 = 8. Cost of each hot dog = $3. Amount of money the friends spend on hot dogs = Number of friends bought a hot dog  × Cost of each hot dog = 8 × $3 = $24.

Topic 4 Assessment Practice

Explanation: Number of rows = 9. Number of columns = 5. Heather wrote a multiplication fact and a division fact for the array below: Multiplication fact: 9 × 5 = 45. 5 × 9 = 45. Division fact: 45 ÷ 9 = 5. 45 ÷ 5 = 9.

B. Look at the multiplication fact you selected in Part A. Which of these is a way to rewrite the product in it? ☐ (5 × 3) + (5 × 4) ☐ (5 × 5) + (5 × 4) ☐ (5 × 5) + (5 × 2) ☐ 5 × 5 × 4 Answer: Multiplication fact you selected in Part A: 5 × 9 = (5 × 4) + (5 × 5) = 45.

Explanation: Multiplication fact you selected in Part A: 5 × 9 = 45. = (5 × 4) + (5 × 5) = 20 + 25 = 45.

Question 2. Colin wrote three equations. What number will make all of Colin’s equations true? 14 = ? × 2 56 ÷ 8 = ? ? × ? = 49 Answer: 7 number will make all of Colin’s equations true.

Explanation: 14 = ? × 2 => 14 = 7 × 2. 56 ÷ 8 = ? => 56 ÷ 8 = 7. ? × ? = 49 7 × 7 = 49.

Question 3. If a group of objects is divided into 2 equal groups, 1 object is left over. Is the total number of objects even or odd? What could the total number of objects be? Use a drawing to explain. Answer: If a group of objects is divided into 2 equal groups, 1 object is left over then the total number of objects going to be odd not even.

Question 4. Mrs. Raspa wrote the expression 6 × 3 on the board. Which of the following expressions has the same value? A. (3 × 3) + (3 × 1) B. (6 × 2) + (6 × 1) C. (6 × 0) + (6 × 4) D. (4 × 3) + (5 × 3) Answer: B. (6 × 2) + (6 × 1)  has the same value of the expression 6 × 3.

Explanation: Expression 6 × 3 = 18. A. (3 × 3) + (3 × 1) = 9 + 3 = 12. B. (6 × 2) + (6 × 1) = 12 + 6 = 18. C. (6 × 0) + (6 × 4) = 0 + 24 = 24. D. (4 × 3) + (5 × 3) = 12 + 15 = 27.

Question 5. A. Mr. Vargas is buying used computer equipment. He buys 3 keyboards and 4 mice. He spends $42. If the items are all the same price, how much does each item cost? Answer: Cost of each item = $6.

Explanation: Number of keyboards Mr. Vargas buys = 3. Number of mice Mr. Vargas buys = 4. Amount he spends = $42. Total number of items he bought = Number of keyboards Mr. Vargas buys + Number of mice Mr. Vargas buys = 3 + 4 = 7. Cost of each item = Amount he spends  ÷ Total number of items he bought = $42 ÷ 7 = $6.

B. Mr. Vargas decides to buy more keyboards that cost another $12 in all. How many more keyboards does Mr. Vargas buy? Answer: Number of more keyboards Mr. Vargas buy = 9.

Explanation: Amount he spends to buy more keyboards in all = $12. Number of keyboards Mr. Vargas buys = 3. Amount he spends = $42. Amount he spends more = $12. Amount he spends now = Amount he spends + Amount he spends more = $42 + $12 = $54. Cost of each keyboard = $6. Number of more keyboards Mr. Vargas buy = Amount he spends now ÷ Cost of each keyboard = $54 ÷ $6 = 9.

Explanation: 12 ÷ 6 = 2.

B. Write a multiplication fact related to the drawing you completed in Part A. Answer: 6 × 2 = 12. 2 × 6 = 12.

Explanation: Multiplication fact related to the drawing you completed in Part A: 6 × 2 = 12. 2 × 6 = 12.

Explanation: 9 ÷ 1 = 9. 3 ÷ 3 = 0. 1 × 6 = 6. 7 ÷ 7 = 1. 8 ÷ 8 = 1. 0 × 7 = 0. 24 ÷ 4 = 6. 27 ÷ 3 = 9.

Question 8. A. Peter wrote five numbers. Which of Peter’s numbers can be divided into 7 equal groups with 0 left over? Select all that apply. ☐ 56 ☐ 35 ☐ 52 ☐ 27 ☐ 42 Answer: Peter’s numbers can be divided into 7 equal groups with 0 left over are as below: 56, 35, 42.

Explanation: Peter’s numbers can be divided into 7 equal groups with 0 left over: ☐ 56 ÷ 7 = 8. ☐ 35 ÷ 7 = 5. ☐ 52 ÷ 7 = 7.4. ☐ 27 ÷ 7 = 3.8. ☐ 42 ÷ 7 = 6.

B. How can you check to make sure the numbers you chose are divisible by 7? A. Check that each number is even. B. Check that each number is odd. C. Use multiplication to multiply 0 by a number to determine if it is equal to the number you chose. D. Use multiplication to multiply 7 by a number to determine if it is equal to the number you chose. Answer: D. Use multiplication to multiply 7 by a number to determine if it is equal to the number you chose.

Explanation: To make sure the numbers choosed are divisible by 7, use multiplication facts to determine if it is equal to the number you chose.

Explanation: Total count given = 35. Number of boxes divided = 5. Number value used to divided = Total count given ÷ Number of boxes divided = 35 ÷ 5 = 7. Multiplication Equation: 5 × 7 = 35. 7 × 5 = 35.

Question 10. A. Xavier divided his action figure collection into 2 equal groups. Which describes the number of action figures Xavier has? A. It is an even number. B. It is an odd number. Answer: The number of action figures Xavier has is an even number because to divide into anything into 2 groups equally it has to be even.

Explanation: To divide anything into two groups equally means, it has to be even not odd because odd number cannot be divided into two parts.

B. Xavier finds 2 more action figures. Select all statements that are true. ☐ Including the action figures he found, Xavier has an even number of action figures. ☐ Including the action figures he found, Xavier has an odd number of action figures. ☐ Xavier can divide all of the action figures into 2 equal groups. ☐ Xavier could now have a total of 6 action figures in his collection. ☐ Xavier could now have a total of 8 action figures in his collection. Answer: All statements that are true are below: Including the action figures he found, Xavier has an even number of action figures. Xavier can divide all of the action figures into 2 equal groups. Xavier could now have a total of 6 action figures in his collection. Xavier could now have a total of 8 action figures in his collection.

Explanation: ☐ Including the action figures he found, Xavier has an even number of action figures. ☐ Xavier can divide all of the action figures into 2 equal groups. ☐ Xavier could now have a total of 6 action figures in his collection. ☐ Xavier could now have a total of 8 action figures in his collection.

Question 11. Mandy is trying to find 6 ÷ 0. She says the answer is 6 because 6 × 0 = 6. Is Mandy correct? Explain. Answer: Mandy is incorrect because 6 × 0 = 0 not 6 × 0 = 6.

Explanation: 6 ÷ 0 = 0. 6 × 0 = 0.

Question 12. Luz has 36 pencil toppers. She sorts her pencil toppers into 6 equal groups. A. Write an expression that represents how many pencil toppers are in each group. Answer: Number of pencil toppers are in each group = 36 ÷ 6 = 6.

Explanation: Number of pencil toppers Luz has = 36. Number of equal groups She sorts her pencil toppers = 6. Number of pencil toppers are in each group = Number of pencil toppers Luz has  ÷ Number of equal groups She sorts her pencil toppers = 36 ÷ 6 = 6.

B. How many are in each group? Answer: There are 6 in each group.

Explanation: Number of pencil toppers are in each group = 6.

Question 14. Jules has 4 classes. For each class, he needs 3 folders. Find how many folders he needs in all. Then write the fact family related to this situation. Answer: Number of folders he needs in all = 12.

Explanation: Number of classes Jules has = 4. Number of folders he needs for each class = 3. Number of folders he needs in all = Number of classes Jules has × Number of folders he needs for each class = 4 × 3 = 12. Fact family: 4 × 3 = 12. 3 × 4 = 12. 12 ÷ 3 = 4. 12 ÷ 4 = 3.

Question 15. A. Gennaro wrote 4 true statements about even and odd products. Select all of the true statements. ☐ An even number times an even number has an even product. ☐ An even number times an odd number has an even product. ☐ An odd number times an odd number has an odd product. ☐ An odd number times an even number has an odd product. ☐ If one factor is even, then the product is even. Answer: All of the true statements are: An even number times an even number has an even product. An even number times an odd number has an even product. An odd number times an odd number has an odd product. If one factor is even, then the product is even.

Explanation: All of the true statements are: ☐ An even number times an even number has an even product. ☐ An even number times an odd number has an even product. ☐ An odd number times an odd number has an odd product. ☐ If one factor is even, then the product is even.

B. Look at the statement you did NOT select in Part A. Give an example of why it is not true. Answer: An odd number times an even number has an odd product. For an example: 3 × 4 = 12.

Explanation: The statement which is NOT selected in Part A is as below: An odd number times an even number has an odd product. For an example: 3 × 4 = 12.

Question 16. Which number makes both equations true? 18 ÷ 9 = ? ? × 9 = 18 Answer: 2 number makes both equations true.

Explanation: 18 ÷ 9 = ? => 18 ÷ 9 = 2. ? × 9 = 18 => 2 × 9 = 18.

Explanation: Way:1: Total number given = 18. Number of sectors divided given = 3. Value of sector divided = Total number given ÷ Number of sectors divided given = 18 ÷ 3 = 6. Way:2: Total number given = 18. Number of sectors divided given = 3. Value of sector divided = ?? Total number given = Number of sectors divided given × Value of sector divided => 18 = 3 × ?? => 18 ÷ 3 = ?? => 6 = ??.

Question 18. A balloon artist wants to make 6 different kinds of balloon animals. She needs 4 balloons to make each animal. How many balloons will she need to buy? Tell which operations you will use. Then solve the problem. Answer: We are going to use multiplication operations  to solve the problem. Number of balloons she needs to buy = 24.

Explanation: We are going to use multiplication operations  to solve the problem. Number of different kinds of balloon animals a balloon artist wants to make = 6. Number of balloons she needs to make each animal = 4. Number of balloons she needs to buy = Number of different kinds of balloon animals a balloon artist wants to make × Number of balloons she needs to make each animal = 6 × 4 = 24.

Topic 4 Performance Task

Relay Race Mrs. Achilles teaches Physical Education. She is planning a relay race for her school. Each grade forms teams. Each student is on 1 team.

Race Details

• The field is 40 feet wide.
• Each runner gets 1 lane.
• Mrs. Achilles has 7 trophies.

Use the Race Details list to answer the following question. Question 1. Each lane must be an equal width. Mrs. Achilles wants to use the entire width of the field for lanes. How wide will each lane be if Mrs. Achilles sets out 10 lanes? 5 lanes? Use multiplication facts to help you. Answer: IF, Number of lanes set out = 10. Width of the each lane = 4. IF, Number of lanes set out = 5. Width of the each lane = 8.

Explanation: Number of lanes each runner gets = 1. Number of trophies Mrs. Achilles has = 7. Number of students in each team = 1. IF, Number of lanes set out = 10. Width of the field = 40 feet. Width of the each lane = Width of the field ÷ Number of lanes set out = 40 ÷ 10 = 4. IF, Number of lanes set out = 5. Width of the field = 40 feet. Width of the each lane = Width of the field ÷ Number of lanes set out = 40 ÷ 5 = 8.

Use the Race Details list and Grade Size table to answer the following question. Question 2. Each grade gets an equal number of trophies. How many trophies does each grade get? Write a division fact and a related multiplication fact you can use to solve this problem. Answer: Number of trophies each grade gets = 1.

Explanation: Number of trophies Mrs. Achilles has = 7. Number of grades = 7. Number of trophies each grade gets = Number of trophies Mrs. Achilles has ÷ Number of grades = 7 ÷ 7 = 1. Division fact: = 7 ÷ 7 = 1. Multiplication fact: = 1 × 7 = 7.

Explanation: Yes, its possible to have 2 people in each team if the students strength is even. if the strength of students is odd, then its not possible to have 2 people in each team.

Question 4. Mrs. Achilles puts more than 2 students on each team. Each team must have an equal number of students.

Part A Complete the table to show the 4 different ways Mrs. Achilles can form teams for Grade 3. Answer: Way:1: = 24 ÷ 3 = 8. Way:2: = 3 × 8 = 24. Way:3: = 8 × 3 = 24. Way:4: = 24 ÷ 8 = 3.

Explanation: Total number of students in grade 3 = 24. Way:1: Number of people in each team = 3. Team 1 form =  Total number of students in grade 3 ÷ Number of people in each team = 24 ÷ 3 = 8. Way:2: Number of people in each team × Team 1 form = Total number of students in grade 3. = 3 × 8 = 24. Way:3: Team 1 form × Number of people in each team = Total number of students in grade 3. = 8 × 3 = 24. Way:4: Total number of students in grade 3 ÷ Team 1 form = Number of people in each team. = 24 ÷ 8 = 3.

Explanation: Grade: K and 3: Number of students = 24. Number of people in team = 4. Number of teams = Number of students ÷ Number of people in team = 24 ÷ 4 = 6. Grade: 1: Number of students = 28. Number of people in team = 4. Number of teams = Number of students ÷ Number of people in team = 28 ÷ 4 = 7. Grade: 2 , 4 , 5: Number of students number is not the multiple of 4 , so they cannot be having 4 people in each team. Grade: 6: Number of students = 32. Number of people in team = 4. Number of teams = Number of students ÷ Number of people in team = 32÷ 4 = 8.

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

• Kindergarten
• DMPS Grading Website
• Fast Assessments
• Student Resources

Grade 4 GO Math! Resources