lesson 4 homework practice distributive property answer key

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 .

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• Distributive Property Quiz

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1-7 The Distributive Property

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The Distributive Property - Word Docs & PowerPoint

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The Distributive Property - PDFs

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Distributive Property Practice Problems

Hopefully you've read and understood the distributive property lesson. If you are ready, let's move on and practice our skill!

Directions: Use the distributive property to simplify each expression.

NOTE: The answers are down below the practice problems. Make sure you check your answers carefully!

1. 5(x+6) =

2. 3(2x+1) =

3. 2(2x-3) =

4. 6(x-4) =

5. 8(2x-3) =

6.    -3(x + 4)=

7.    -2(3x - 1)=

8.    -10(2x + 1/5 )=

9.    -18(x - 2/3)=

10.    1/2(x -4) =

1.  5x + 30

2.  6x +3

3.  4x - 6

4.  6x - 24

5.  16x - 24

6.  -3x - 12

7.  -6x +2

8.  -20x - 2

9.  -18x + 12

10.  1/2x - 2

Ok... The distributive property isn't so bad is it? If you're ready, you can move onto simplifying algebraic expressions!

If you didn't do so well on the distributive property, you may need to go back and review Adding Integers , Subtracting Integers , or Multiplying and Dividing Integers.

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Distributive Property Worksheets

The sums given on the below free and printable worksheets test you on your knowledge of distribute property as you perform basic mathematical operations like multiplication and addition.

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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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• Grade 7 McGraw Hill Glencoe - Answer Keys

Explanation:

Identify Structure Use the Distributive Property to rewrite each expression.

3(-4x + 8) =

• Type below:

4(x - 6y) =

\(\frac{1}{2}(c - 8) =\)

-3(5 - b) =

(d + 2)(-7) =

Amelia bought roast beef for $6.85 per pound. Find the total cost if Amelia bought 4 pounds of roast beef. Justify your answer by using the Distributive Property.

The table shows the different prices of items at a movie theater. a. Suppose Mina and two of her friends go to the movies. Write an expression that could be used to find the total cost for them to go to the movies and buy one of each item.

b. What is the total cost for all three people?

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Unit 1 – The Building Blocks of Algebra

This unit revolves around the concept of equivalency.  Within this larger framework, we review and develop the real number properties and use them to justify equivalency amongst algebraic expressions.  Students get work in mindful manipulation of algebraic expressions and actively seek structure within expressions to understand equivalency.

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Variables and Expressions

The Commutative and Associative Properties

The Distributive Property

Equivalent Expressions

Seeing Structure in Expressions

Exponents as Repeated Multiplication

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McGraw Hill My Math Grade 4 Chapter 4 Lesson 7 Answer Key The Distributive Property

All the solutions provided in McGraw Hill Math Grade 4 Answer Key PDF Chapter 4 Lesson 7 The Distributive Property  will give you a clear idea of the concepts.

McGraw-Hill My Math Grade 4 Answer Key Chapter 4 Lesson 7 The Distributive Property

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Guided Practice

Use the Distributive Property to multiply. Draw an area model.

Independent Practice :

Algebra Find each unknown number.

Question 9. 37 × 5 = s s = ____ Answer: Multiplication of 37 with 5 then you get 185. 37 x 5 = 185. s = 185. Therefore the unknown is 185.

Question 10. 99 × 9 = t t = ____ Answer: Multiplication of 99 with 9 then you get 891. 99 x 9 = 891. t = 891. Therefore the unknown is 891.

Question 11. 85 × 5 = v v = ____ Answer: Multiplication of 85 with 5 then you get 425. 85 x 5 = 425. v = 425. Therefore the unknown is 425.

Problem Solving

Question 13. Mr. Kline bought 4 sheets of postage stamps. Each sheet had 16 stamps. What is the total number of postage stamps Mr. Kline bought? Write an equation to solve. s = ___ × ____ s = _____ Mr. Kline bought ____ stamps. Answer: Given that, Mr. Kline bought 4 sheets of postage stamps. Each sheet had 16 stamps. s = 4 x 16 s = 64. Mr. Kline bought 64 stamps.

Question 14. The World of Maps store displays its maps on 3 shelves. There are 26 world maps on each shelf. How many world maps does the store have to sell? Write an equation to solve. m = ___ × ____ m = ____ The store has ____ world maps. Answer: Given that, The World of Maps store displays its maps on 3 shelves. There are 26 world maps on each shelf. m = 3 x 26 m = 78. The store has 78 world maps.

HOT Problems

Question 15. Mathematical PRACTICE 3 Find the Error Candace is finding 67 × 2. She thinks the product is 124. Find and correct her mistake. Answer: Multiplication of 67 with 2 then you get 134. 67 x 2 = 134. She thinks the product is 124 is her mistake. The correct product is 134.

Question 16. ? Building on the Essential Question How can the Distributive Property help when you are multiplying by a two-digit number? Answer: Distributive property of multiplication says that when the number is multiplied by the two digits number the first number can be distributed to the both of two numbers and multiplied by each separately. Then add the both products to get the real product.

McGraw Hill My Math Grade 4 Chapter 4 Lesson 7 My Homework Answer Key

Multiply. Use the Distributive Property.

Question 4. 75 × 6 = ___ Answer: Distributive property of 75 x 6 is 75 x 6 = (70 x 6) + (5 x 6) 75 x 6 = 420 + 30. 75 x 6 = 450.

Question 5. 4 × 52 = ___ Answer: Distributive property of 4 x 52 is 4 x 52 = (4 x 50) x (4 x 2) 4 x 52 = 200 + 8. 4 x 52 = 208.

Question 6. 8 × 38 = ____ Answer: Distributive property of 8 x 32 is 8 x 32 = (8 x 30) + (8 x 2) 8 x 32 = 240 + 16. 8 x 32 = 256.

Question 7. 97 × 2 = ___ Answer: Distributive property of 97 x 2 is 97 x 2 = (90 x 2) + (7 x 2) 97 x 2 = 180 + 14. 97 x 2 = 194.

Question 8. 7 × 63 = ____ Answer: Distributive property of 7 x 63 is 7 x 63 = (7 x 60) + (7 x 3) 7 x 63 = 420 + 21. 7 x 63 = 441.

Question 9. 6 × 33 = ____ Answer: Distributive property of 6 x 33 is 6 x 33 = (6 x 30) + (6 x 3) 6 x 33 = 180 + 18. 6 x 33 = 198.

Question 10. Mathematical PRACTICE 3 Justify Conclusions Paula can make 14 beaded bracelets in an hour. Tina can make 13 bracelets in an hour. In one week, Paula made bracelets for 6 hours, and Tina made bracelets for 8 hours. Who made more bracelets that week? Explain. Answer: Given that, Paula can make 14 beaded bracelets in an hour. Tina can make 13 bracelets in an hour. In one week, Paula made bracelets for 6 hours In one week, Tina made bracelets for 8 hours. Paula made bracelets in all is 14 x 6 = 84. Tina made bracelets in all is 13 x 8 = 104. Therefore Tina made more bracelets than Paula.

Question 11. Alejandro owns 3 sets of trains. Each set has 18 cars. How many train cars does Alejandro have altogether? Answer: Given that, Alejandro owns 3 sets of trains. Each set has 18 cars. So, 3 x 18 = 54. Therefore there are 54 train cars does Alejandro have altogether.

Vocabulary Check

Write Distributive Property or decompose on each line.

Question 12. To ____ a number means to break it into parts. Answer: To decompose a number means to break it into parts.

Question 13. The ____ states that you can multiply addends of a number, then add the products. Answer: The distributive property states that you can multiply addends of a number, then add the products.

Test Practice

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Chapter 1, Lesson 4: The Distributive Property

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Chapter 1, Lesson 4: The Distributive Property

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