Learn about the distributive property

1. Distributive Property
BY: DEBBY CHAMBERLAIN

2. Content Standard and Learning
Expectations
 7.EE.1 - Apply properties of operations as strategies to add, subtract,
factor, and expand linear expressions with rational coefficients.
 7.EE.2 - Understand that rewriting an expression in different forms in a
problem context can shed light on the problem and how the quantities in
it are related.
 Students will learn how to apply the distributive property to factor out the
greatest common factor from and algebraic expression, such as 2 + 4x.

3. If you don’t know the rules you can’t play the game
What’s the game? Solving math problems
What are the rules? Properties of operations
In this lesson we will apply properties of operations as strategies to:
add, subtract, and factor expressions

4. The Properties of Operations
are the Foundation of
Arithmetic
We will use these properties when performing
computations in this lesson:
 Addition property of operations
 Subtraction property of operations
 Commutative property
 Distributive property

5. Combine like Terms Review
STOP! Simplify these expressions on your
guided notes before moving on
1. 9y + 3 – 4x – 2y – 3x – 5
2. 4c – 1a + 7b – 2c + 8b
3. c – 3 + 4ax – 7a + 2a – 6ax – 5

6. Answer #1
9y + 3 – 4x – 2y – 3x – 5
Step 1: Commutative Property
9y – 2y – 4x – 3x + 3 – 5
Step 2: Addition and Subtraction Properties of Operations
7y – 7x – 2

7. Answer #2
4c – 1a + 7b – 2c + 8b
Step 1: Commutative Property
–1a + 7b + 8b + 4c – 2c
Step 2: Addition and Subtraction Properties of Operations
–a + 15b – 2c

8. Answer #3
c – 3 + 4ax – 7a + 2a – 6ax – 5
Step 1: Commutative Property
4ax – 6ax – 7a + 2a + c – 3 – 5
Step 2: Addition and Subtraction Properties of Operations
– 2ax – 5a + c – 8

9. Distributive Property
 Use the Distributive Property to simplify the product of a
number and a sum and difference.
 Let a, b, and c be real numbers
Algebra Examples
 a(b + c) = ab + ac 4(50 + 7) = 4(50) + 4(7)
 (b + c)a = ba + ca (50 + 7)4 = 50(4) + (7)4
 a(b – c) = ab + ac 6(40 – 9) = 6(40) - 6(9)
 (b - c)a = ba - ca (40 – 9)6 = 40(6) - 9(6)

10. Practice the Distributive Property
STOP! Simplify these expressions on your guided notes before
moving on. Show your work
1. 5(x + 15)
2. (x + 27)4
3. 8(x – 19)
4. (x – 12)6

11. Answer #1
5(x + 15)
Step 1: Distributive Property
5(x + 15)
5x + 75

12. Answer #2
(x + 27)4
Step 1: Distributive Property
(x + 27)4
4x + 108

13. Answer #3
8(x – 19)
Step 1: Distributive Property
8(x – 19)
8x – 152

14. Answer #4
(x – 12)6
Step 1: Distributive Property
(x – 12)6
6x - 72

15. How can we use the distributive
property to factor expressions?
Students learn to apply the distributive property when an
expression can be factored. Start with finding the greatest
common factor (GCF).
30b + 45
5 * 6 * b + 5 * 9
Factor out the GCF 5 to rewrite the expression
5(6b + 9)

16. Video on Distributive Property
Factor algebraic expressions using the distributive property
Learn how to apply the distributive property to factor out the
greatest common factor from an algebraic expression.
Khan Academy

17. Your Turn
 Factor out the GCF of each term and apply the distributive
property to determine an equivalent expression
1. 24 + 48x
2. 35x + 49
3. 200x – 150

18. Answer #1
24 + 48x
Step 1: Factor out the GCF
24
Step 2: Apply the Distributive property
24(1 + 3x)

19. Answer #2
35x + 49
Step 1: Factor out the GCF
7
Step 2: Apply the Distributive property
7(5x + 7)

20. Answer #3
200x - 150
Step 1: Factor out the GCF
50
Step 2: Apply the Distributive property
50(4x - 3)

21. Culminating activity
Part 1
Explain the
distributive property in your own
words on your notes.

22. Culminating activity
Part 2
 Write four problems involving the
distributive property
 Solve the problems
 Show your work
 Check your answer