lesson 6 homework practice distributive property answer key

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6th Grade Distributive Property

Welcome to our 6th Grade Distributive Property Worksheets.

Here you will find a range of algebra worksheets to help you learn how to use the distributive property to expand and factorize a range of expressions.

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Distributive Property Support

Evaluate the expression worksheets, expand the expression worksheets, factorize the expression worksheets.

• Distributive Property Mixed Worksheets
• More recommended resources

6th Grade Distributive Property Online Quiz

This page is all about using the distributive property to expand and factorize a range of expressions.

We have split the worksheets up into 4 different sections:

• Evaluate the expression - work out the value of different algabraic expressions;
• Expand the expression - use the distributive property to multiply out the brackets;
• Factorize the expression - use the distributive property to factorize different expressions.
• Mixed questions involving all 3 of the above.

By splitting the algebra up into sections, you only need to concentrate on one aspect at a time!

Each question sheet comes with its own separate answer sheet.

Want to test yourself to see how well you have understood this skill?.

• Try our NEW quick quiz at the bottom of this page.

What is an algebraic expression?

An expression is a mathematical statement where variables and operations are combined.

• 2a + 5 is an expression involving the variable a
• 5(y 2 - 6) is another expression

How to Evaluate an Expression

When we are evaluating the value of an expression, we work out the value of the expression when we give a value to the variable.

• 2(p + 5) has a value of 22 when p = 6 because 2(6 + 5) = 2 x 11 = 22
• 3(12 - q) has a value of 21 when q = 5 because 3(12 - 5) = 3 x 7 = 21
• 8(n - 2) has a value of 64 when n = 10 because 8 (10 - 2) = 8 x 8 = 64
• 8(n - 2) has a value of 0 when n = 2 because 8 (0 ) = 8 x 0 = 0

How to Expand an Expression

When we are expanding an expression, we multiply out the factors.

• 2(p + 5) = 2 x p + 2 x 5 = 2p + 10
• 3(12 - q) = 3 x 12 - 3 x q = 36 - 3q
• 8(n - 2) = 8 x n - 8 x 2 = 8n - 16
• 5(y + 3z) = 5 x y + 5 x 3z = 5y + 15z

How to Factorize an Expression

When we are factorizing an expression, we try to find the greatest common factor of all the numbers and take it out as a factor.

• 3n + 15 = 3(n + 5) - greatest common factor of 3 and 15 is 3.
• 4p + 32 = 4(p + 8) - the greatest common factor of 4 and 32 is 8.
• 20 - 8y = 4(5 - 2y) - the greatest common factor of 20 and 8 is 4.
• 4a - 10b + 6c = 2(2a - 5b + 3c) - the greatest common factor of 4, 10 and 6 is 2.
• 35d + 42 = 7(5d + 6) - the greatest common factor of 35 and 42 is 7.

6th Grade Distributive Property Worksheets

These sheets involve working out the value of the expression using PEMDAS and order of operations.

The first sheets is a multiple choice sheet with only numbers in the expressions.

The second sheet involves finding the value of the expression with only numbers in the expression.

The third sheet involves finding the value of the expression with numbers and variables in the expression.

• Evaluate the Expression Sheet 6:1
• PDF version
• Evaluate the Expression Sheet 6:2
• Evaluate the Expression Sheet 6:3

Sheet 1 is a multiple choice sheet where you match the factorized expression with the correct expanded expression.

Sheet 2 involes writing the factorized expression as an expanded expression.

• Expand the Expression Sheet 6:1
• Expand the Expression Sheet 6:2

Expand the Expression Walkthrough Video

This short video walkthrough shows several problems from our Expand the Expression Worksheet 6:1 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, please check out the video below!

Sheet 1 is a multiple choice sheet where you match the expression with the correct factorized expression.

Sheet 2 involes writing the expression as a factorized expression.

• Factorize the Expression Sheet 6:1
• Factorize the Expression Sheet 6:2

6th Grade Distributive Property Mixed Worksheets

These questions involve expanding, factorizing and evaluating different expressions..

They are a combination of questions from all the above categories.

• 6th Grade Distributive Property Sheet 6:1
• 6th Grade Distributive Property Sheet 6:2

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

More 6th Grade Algebra Worksheets

If you are looking for some basic algebra worksheets to use with your child to help them understand simple equations then try our selection of basic algebra worksheets.

There are a range of 6th grade math worksheets covering the following concepts:

• Generate the algebra - and write your own algebraic expressions;
• Calculate the algebra - work out the value of different expressions;
• Solve the algebra - find the value of the term in the equation.
• Expressions and Equations 6th Grade
• Basic Algebra Worksheets (6th & 7th Grade)

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PEMDAS Worksheets

The sheets in this section involve using parentheses and exponents in simple calculations.

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Interactive Equality Explorer

This interactive equality explorer has been produced by PhET Interactive Simulations at the University of Colorado.

It is a useful tool for exploring different ideas including negative numbers and algebra equations and equality.

Probably the most useful part of the app is to use the 'Solve It' section once you are confident how it works.

You can then select your level of difficulty and start solving some algebraic equations by getting your variables onto one side of the equation and the numerical values on the other, and then multiplying or dividing the equation until you find the value of the required variable.

• Interactive Equality Explorer by PhET

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This quick expressions and equations 6th grade quiz tests your knowledge and skill at generating and calculating expressions, as well as solving equations.

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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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• Burger Junior High School
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6.EE.3 - Distributive Property

• See the left menu for Video Tutorials, Online Practice Resources, Class Notes, and Homework and Extra Practice Worksheets with ANSWERS. Use these resources to help reinforce the following 6th Grade Common Core Learning Standard and "I Can Statement(s)." 6.EE.3 Apply the properties of operations to generate equivalent expressions "I Can Apply the Distributive Property to Generate an Equivalent Expression."
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• Grade 6 McGraw Hill Glencoe - Answer Keys

Explanation:

• \(\large 4\times5\frac{1}{8}=\)

Use the Distributive Property to rewrite each algebraic expression.

Identify Repeated Reasoning A coyote can run up to 43 miles per hour while a rabbit can run up to 35 miles per hour. Write two equivalent expressions and then find how many more miles a coyote can run in six hours than a rabbit at these rates.

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McGraw Hill My Math Grade 5 Chapter 2 Lesson 6 Answer Key Use Partial Products and the Distributive Property

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 2 Lesson 6 Use Partial Products and the Distributive Property  will give you a clear idea of the concepts.

McGraw-Hill My Math Grade 5 Answer Key Chapter 2 Lesson 6 Use Partial Products and the Distributive Property

Darnel and his four friends went to an ice skating rink and bought sandwiches. They divided the total cost and found that each person needs to pay $17. What was the total cost for ice skating and sandwiches?

Find 5 × 17 using an area model.

When you use partial products, you are using a property. A property is a rule in mathematics that can be applied to all numbers. The property that you applied above is called the Distributive Property. You will learn more about this property in the next lesson.

Find 7 × 56 using an area model.

Explanation: 7 × 56 = (7 × 50) + (7 × 6) = 350 + 42 = 392 So, 7 × 56 = ____ 392

Talk About It

Question 1. Mathematical PRACTICE 3 Draw a Conclusion How do area models show partial products? Answer:

Question 2. In finding 7 × 56 above, why does the area model separate 56 into 50 and 6? Answer: The area model separates 56 into 50 and 6 to calculate the multiplication easily.

Practice It

Multiply using the area model. Label each model.

Question 8. Ronnie swims 4 laps each day at the pool. How many laps does he swim in 28 days? Use an area model to solve. Answer: 4 × 28 = 112

Question 9. Mathematical PRACTICE Model Math Yoshi saved $5 each week for 23 weeks. What is the total amount of money he saved? Use an area model to solve. Answer: 5 × 23 = 115

Question 10. Thirty-eight fish are in each aquarium at a fish store. How many fish are there in five aquariums? Use an area model to solve. Answer: 38 × 5 = 190

Question 11. Mathematical PRACTICE Find the Error Omar was using an area model to find 4 × 61. Find his mistake and correct it. (4 × 60) + (4 × 10) = 240 + 40 = 280 Answer: The answer is 244, not 280.

Write About It

Question 12. How can area models be used to solve multiplication problems? Answer:

McGraw Hill My Math Grade 5 Chapter 2 Lesson 6 My Homework Answer Key

Problem Solving

Question 4. Mathematical PRACTICE 4 Model Math Brandon packs his lunch 4 days each week. How many days does he pack his lunch for 36 weeks? Use an area model to solve. Answer: Bradon packs 144 days in 36 weeks.

Question 5. Ricarda earns a $25 allowance each week. How much allowance will she earn after 7 weeks? Use an area model to solve. Answer: $175

Question 6. Write an expression that uses partial products to multiply 8 × 64. Answer: (80 × 6) + (8 × 4)

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