my homework lesson 7 the distributive property

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McGraw Hill My Math Grade 5 Chapter 2 Lesson 7 Answer Key The Distributive Property

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 2 Lesson 7 The Distributive Property  will give you a clear idea of the concepts.

McGraw-Hill My Math Grade 5 Answer Key Chapter 2 Lesson 7 The Distributive Property

Example 2 Find 7 × 26 mentally using the Distributive Property. Show the steps that you used.

Guided Practice

Find each product mentally using the Distributive Property. Show the steps that you used.

Question 1. 5 × 18 5 × 18 = 5 × (___ + 8) = (5 × ___) + (5 × ___) = ____ + ____ = _____ So, 5 × 18 = ____ Answer: 90

Explanation: 5 × 18 5 × 18 = 5 × (10 + 8) = (5 × 10) + (5 × 8) = 50 + 40 = 90 So, 5 × 18 = 90

Question 2. 2 × 21 2 × 21 = 2 × (___ + ___) = (2 × ___) + (2 × ___) = ____ + ____ = _____ So, 2 × 21 = ____ Answer: 42

Explanation: 2 × 21 2 × 21 = 2 × (20 + 1) = (2 × 20) + (2 × 1) = 40 + 2 = 42 So, 2 × 21 = 42

Independent Practice

Question 3. 6 × 13 = ___ Answer: 78

Explanation: Given multiplicand is 6 and the multiplier is 13. By multiplying both multiplicand 6 and multiplier 13, we get the value 78 The multiplication of the given number 6 × 13 = 78

Question 4. 3 × 52 = ____ Answer: 156

Explanation: Given multiplicand is 3 and the multiplier is 52. By multiplying both multiplicand 3 and multiplier 52, we get the value 156. The multiplication of the given number 3 × 52 = 156

Question 5. 5 × 26 = ___ Answer: 130

Explanation: Given multiplicand is 5 and the multiplier is 26. By multiplying both multiplicand 5 and multiplier 26, we get the value 130. The multiplication of the given number 5 × 26 = 130

Question 6. 4 × 69 = ___ Answer: 276

Explanation: Given multiplicand is 4 and the multiplier is 69. By multiplying both multiplicand 4 and multiplier 69, we get the value 276. The multiplication of the given number 4 × 69 = 276

Question 7. 2 × 49 = ___ Answer: 98

Explanation: Given multiplicand is 2 and the multiplier is 49. By multiplying both multiplicand 2 and multiplier 49, we get the value 98. The multiplication of the given number 2 × 49 = 98

Question 8. 7 × 23 = ___ Answer: 161

Explanation: Given multiplicand is 7 and the multiplier is 23. By multiplying both multiplicand 7 and multiplier 23, we get the value as 161. The multiplication of the given number 7 × 23 = 161

Question 9. 26 × 6 = ___ Answer: 156

Explanation: Given multiplicand is 26 and the multiplier is 6. By multiplying both multiplicand 26 and multiplier 6, we get the value as 156. The multiplication of the given number 26 × 6 = 156.

Question 10. 55 × 4 = ___ Answer: 220

Explanation: Given multiplicand is 55 and the multiplier is 4. By multiplying both multiplicand 55 and multiplier 4, we get the value as 220. The multiplication of the given number 55 × 4 = 220.

Problem Solving

Question 11. A horse is 17 hands tall. If a hand equals 4 inches, how tall is the horse in inches? Use the Distributive Property to solve. Answer: 68 inches.

Explanation: A horse is 17 hands tall. If a hand equals 4 inches 17 × 4 = 68 inches.

Question 12. Mr. Collins is buying 5 train tickets for $36 each. What is the total cost of the tickets? Use the Distributive Property to solve. Answer: $180

Explanation: From the given question find 36 × 5 = 180 The total cost of the ticket is $180

Question 13. Melanie runs 23 miles each week. How many miles does she run in 9 weeks? Use the Distributive Property to solve. Answer: 207 miles

Explanation: 23 × 9 The distributive property is as follows (20 + 3) × 9 20 × 9 + 3 × 9 180 + 27 207 miles

Hot Problems

Question 14. Mathematical PRACTICE Find the Error Dylan is using the Distributive Property to simplify 6 × (9 + 4). Find his mistake and correct it. 6 × (9 + 4) = 54 + 4 = 58 Answer: 6 × (9 + 4) = 6 × 13 = 78

Explanation: Dylan didn’t follow the arithmetic rule. He doesn’t do the parentheses first. 6 × (9 + 4) = 6 × 13 = 78

Question 15. ? Building on the Essential Question How can the Distributive Property be used to multiply numbers? Explain. Answer: You can use the distributive property to multiply numbers by changing the order of the numbers you’re multiplying and still achieve the same correct answer.

McGraw Hill My Math Grade 5 Chapter 2 Lesson 7 My Homework Answer Key

Question 1. 4 × 48 = ___ Answer: 192

Explanation: Given multiplicand is 4 and the multiplier is 48. By multiplying both multiplicand 4 and multiplier 48, we get the value as 192. The multiplication of the given number 4 × 48 is 192.

Question 2. 3 × 67 = ____ Answer: 201

Explanation: Given multiplicand is 3 and the multiplier is 67. By multiplying both multiplicand 3 and multiplier 67, we get the value as 201. The multiplication of the given number 3 × 67 is 201.

Question 3. 6 × 18 = ____ Answer: 108

Explanation: Given multiplicand is 6 and the multiplier is 108. By multiplying both multiplicand 6 and multiplier 108, we get the value as 108. The multiplication of the given number 6 × 18 = 108.

Question 4. 8 × 74 = ___ Answer: 592

Explanation: Given multiplicand is 8 and the multiplier is 74. By multiplying both multiplicand 8 and multiplier 74, we get the value as 592. The multiplication of the given number 8 × 74 = 592.

Explanation: From the given question find 4 × 12 48 Hence there are 48 books are on the bookshelf altogether.

Question 6. Jorge is collecting baseball cards. He has 29 stacks of cards with 4 in each stack. How many cards does he have altogether? Answer: 116

Explanation: From the given question find = 29 × 4 = 116

Question 7. Mathematical PRACTICE 3 Justify Conclusions The Distributive Property also combines subtraction and multiplication. For example, 3 × (5 – 2) = (3 × 5) – (3 × 2). Explain how you could use the Distributive Property and mental math to find 5 × 198. Answer: The value of 5 × 198 is 990.

Explanation: The distributive property is a(b + c) = ab + ac The given expression is 5 × 198. 5 × (100 + 90 + 8) 5 × 100 + 5 × 90 + 5 × 8 500 + 450 + 40 990.

Vocabulary Check

Fill in each blank with the correct term or number to complete the sentence.

Question 8. The Distributive Property combines ____ and ____ to make multiplying whole numbers simpler. Answer: Addition and multiplication

Explanation: The Distributive Property combines addition and multiplication to make multiplying whole numbers simpler.

Test Practice

Question 9. Susana collected 5 cents at the recycling plant for each of her 78 cans. How much money did she collect altogether? A. $0.39 B. $3.50 C. $3.90 D. $39.00 Answer: $3.90

Explanation: Susana collected 5 cents at the recycling plant for each of her 78 cans 5 × 78 = 390 1 dollar = 100 cents 390 ÷ 100 = $3.90

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1-7 The Distributive Property

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Distributive Property Worksheet (pdf) and Answer Key

Students will practice applying the distributive property of multiplication over addition.

This worksheet has 23 problems.

This is a 4 part worksheet

• Part I. Model Problems
• Part II. Practice
• Part III. Challenge Problems
• Part IV. Answer Key

Example Worksheet Questions

Directions: Simplify by applying the distributive property .

Visual Aids

• Distributive Property Quiz

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Student-Centered Math Lessons

The Distributive Property

The distributive property is an important building block for algebraic concepts such as multiplying polynomials, recognizing equivalent expressions, and factoring polynomials. Since it starts as early as 6th grade, let’s talk about how to make this as concrete as possible for students. If you haven’t already, go back and read last week’s post on simplifying expressions by combining like terms .

Sidenote: I have to admit that when I first taught the distributive property, I focused solely on the procedure. I had students draw two arrows from the term outside of the parentheses to the two terms inside and called it a day. This is how I was taught. I tell you this to remind you that there are more ways to teach a skill than the way you may have learned it. 

Let’s get to it!

Introducing the Distributive Property

By the time you are teaching the distributive property, students are familiar with order of operations. If you give them a problem like 3(8+2), they will jump at the chance to solve. Students will add 8+2 to get 3(10) and then multiply to get 30. 

You can have students discover that the distributive property allows for another way to solve.  3(8+2) = 3(8) + 3(2) = 24+6 = 30. Proving to students that a property works instead of just telling them a property works will always earn a thumbs up from me.

Introduce Variables

Students may be wondering, “Why can’t I just keep following the order of operations? Why do I need to use the distributive property?” This is a fair question, and a perfect opportunity to introduce the distributive property using variables.

Let’s look at: 3(2x+4).

Ask students if 2x+4 can be combined or added together. No, they do not have the same variable.

Combining like terms only applies to addition and subtraction. You can multiply and divide terms that do not have the same variable or exponent, so you can use the distributive property to simplify this expression further. 

3(2x+4) is like having 3 groups of (2x+4). I encourage you to use Algebra tiles as every possible opportunity, so here is a beautiful visual.

Use the CRA Method

Just like I explained in the previous post, Simplifying Expressions by Combining Like Terms , the Concrete, Representational, and Abstract Framework will help your students develop a solid understanding of the distributive property. 

Area Models with the Distributive Property

As you can see in the “representation” column above, teaching and requiring students to use an area model for distribution, especially when you are teaching the distributive property in Algebra 1 can be extremely helpful. An area model will set them up for success when they are multiplying polynomials and factoring trinomials. 

Distributing with a Negative

T he most common error you will see regarding the distributive property will be related to signs. Those sneaky little negatives can get lost pretty easily. I have some ideas that I have not used in my classroom (in full transparency), but came to mind when writing this blog post. 

Since multiplying by a negative, always results in the opposite, you can teach students that if there is a negative outside the parentheses, then it will always change the inside signs to the opposite. (Reviewing integer rules will reinforce this, but sometimes economy of language wins). 

I actually think that this is best introduced using a visual. Here is how I would show it and ask students to show their work using this method too.

There are so many ways to introduce this topic! Here is another idea from our Student Handouts below.

 Saying “I want one drink, 2 slices of pizza, and one ice cream cone” 4 separate times isn’t efficient.  “I want 4 drinks, 8 slices of pizza, and 4 ice cream cones” makes a lot more sense.

Angie, our amazing editor (and so much more), found this test problem on a New York 7th grade state assessment . This problem could definitely benefit from sketching a square and labeling each side. This would be an excellent problem to talk about why the wrong answers are wrong.

That about covers it! How do you teach the distributive property?

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Related Topics: Lesson Plans and Worksheets for Grade 3 Lesson Plans and Worksheets for all Grades More Lessons for Grade 3 Common Core For Grade 3

Videos, examples, solutions, and lessons to help Grade 3 students learn how to use the distributive property as a strategy to multiply and divide.

Common Core Standards: 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.OA.1, 3.OA.2, 3.OA.6, 3.OA.8

New York State Common Core Math Grade 3, Module 3, Lesson 10 Worksheets for Grade 3

Application Problem

Use the 5 plus something break apart and distribute strategy to solve 6 × 8. Model with a tape diagram.

Note: This problem reviews modeling the break apart and distribute strategy using a tape diagram from Lesson 6. Until today’s lesson students have learned to break apart the first factor and distribute the second factor. Today’s Concept Development reverses the order using the fact in this Application Problem.

Concept Development

Problem 1: Multiply. Problem 2: Divide.

Use the break apart and distribute strategy to solve 6 × 8. 6 × 8 = 6 × (5 + 3)

Use the break apart and distribute strategy to solve 64 ÷ 8. 64 ÷ 8 = (40 ÷ 8) + 24 ÷ 8

Lesson 10 Homework

• Label the array. Then fill in the blanks to make the statements true. a) 8 × 7 = 7 × 8 =_____ 8 × 7 = 7 × (5 + _____) = (7 × 5) + (7 × ___ ) = __ 35 + ______ = ______
• Break apart and distribute to solve 72 ÷ 8. 72 ÷ 8 = (40 ÷ 8) + (_____÷ 8) = 5 + ________ = ________
• Count by 8. Then match each multiplication problem with its value.

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Using area models and the distributive property to find the area: 3.md.7c, distributive property and area, 6.ee.3 / 7.ee.1 / 8.ee.2.b - distributive property, (algebra 1) polynomials - distributive property question #5, 3.oa.5 / 6.ee.3 / 7.ee.1 / 8.ee.2.b - distributive property, understanding the distributive property: 3.oa.5, factoring (reverse distributive property), area of rectangles and the distributive property | measurement | pre-algebra | khan academy.

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Homework Helper Lesson 7 The Distributive Property

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November 23, 2016

Astronomy: Class Sequence, Lessons, and Activities

Text : Exploring Creation with Astronomy . We found the text to be adequate, a bit redundant and simplistic at times, but overall a good start for children ages 8-12. Please always remember to take our age recommendations with a grain of salt as you know your children better than we do. We also used the companion notebooking journal. It is good for building vocabulary and to reinforce key facts. Not essential if you won’t be providing weekly homework.

Companion text: Along Came Galileo .  This is a fun, easy little read that brings an engaging story of one of our most famous astronomers of the past to life. We read a chapter or two a week.  

Other Necessary Resources: A planisphere corresponding to your latitude and a red-filtered flashlight so you can view your planisphere without hindering your night vision while looking at the night sky.

Apps/Programs: There are also a ton of planetarium/night-sky apps and programs for download. Here are two excellent programs that can be installed on your desktop to easily locate stars and to even travel throughout the solar system and beyond!

http://celestiaproject.net/ http://www.stellarium.org/

And a recent review on star-gazing apps .

AstronomyCourseExpectations

We’ll be filling in the week’s activities bit by bit so please come back and visit often. Homework assignments will be  listed in the syllabus below.

Syllabus: to be added soon

Week 1: Lesson Plan, Activities – Introduction to studying the night sky, establishing cardinal directions

Week 2: Lesson Plan, Activities  – The solar and lunar calendars, the Nile calendar, introduction to planisphere

Week 3: Lesson Plan, Activities, Homework

Week 4: Lesson Plan, Activities, Homework

Week 5: Lesson Plan, Activities, Homework

Week 6: Lesson Plan, Activities, Homework

Week 7: Lesson Plan, Activities, Homework

Week 8: Lesson Plan, Activities, Homework

Week 9: Lesson Plan, Activities, Homework

Week 10: Lesson Plan, Activities, Homework

Week 11: Lesson Plan, Activities, Homework

Week 12: Lesson Plan, Activities, Homework

Week 13: Lesson Plan, Activities, Homework

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Week 15: Lesson Plan, Activities, Homework

Week 16: Lesson Plan, Activities, Homework

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