(7) Lesson 5.4 - The Distributive Property

1. Name the property shown by each statement.
1. a + (b + c) = (a + b) + c 2. 3(ab) = (ab)3
3. z + y + 0 = z + y 4. 7 • h • 0 = 0
5. Dance lessons cost $100 per couple per half hour.
Assume 3 couples want to take dance lessons for an
hour. Use mental math to find the total cost of the dance
lessons for the couples.
Course 2, Lesson 5-4

2. Answers
1. Associative (+)
2. Commutative (x)
3. Identity (+)
4. Multiplicative (0)
5. $600
Course 2, Lesson 5-4

3. HOW can you use numbers and
symbols to represent mathematical
ideas?
Expressions and Equations
Course 2, Lesson 5-4

4. • 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.
Course 2, Lesson 5-4 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Expressions and Equations

5. Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
5 Use appropriate tools strategically.
7 Look for and make use of structure.
Course 2, Lesson 5-4 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Expressions and Equations

6. • To model the Distributive Property
using algebra tiles
• To use the Distributive Property to
evaluate numerical expressions
Course 2, Lesson 5-4
Expressions and Equations

7. Course 2, Lesson 5-4
Expressions and Equations
• Distributive Property
• equivalent expressions

8. Course 2, Lesson 5-4
Expressions and Equations
Words The Distributive Property states that to multiply a sum or
difference by a number, multiply each term inside the
parenthesis by the number outside the parenthesis.
Symbols a(b + c) = ab + ac a(b – c) = ab – ac
Examples 4(6 + 2) = 4 • 6 + 4 • 2 3(7 – 5) = 3 • 7 – 3 • 5

9. 1
Need Another Example?
2
Step-by-Step Example
1. Use the Distributive Property to evaluate 8(–9 + 4).
Expand using the Distributive Property.
Multiply. Then add.
8(–9 + 4) = 8(–9) + 8(4)
= –72 + 32 or –40

10. Answer
Need Another Example?
Use the Distributive Property to evaluate
7(3 + 12)
7 • 3 + 7 • 12; 105

11. 1
Need Another Example?
2
Step-by-Step Example
2. Use the Distributive Property to rewrite 4(x + 7).
Expand using the Distributive Property.
Simplify.
4(x + 7) = 4(x) + 4(7)
= 4x + 28

12. Answer
Need Another Example?
Use the Distributive Property to rewrite
11(x + 5).
11x + 55

13. 1
Need Another Example?
2
3
4
Step-by-Step Example
3. Use the Distributive Property to rewrite 6(p – 5).
Rewrite p – 5 as p + (–5).
Expand using the Distributive Property.
6(p – 5) = 6[p + (–5)]
= 6(p) + 6(–5)
Simplify.= 6p + (–30)
Definition of subtraction= 6p – 30

14. Answer
Need Another Example?
Use the Distributive Property to rewrite
5(p – 8).
5p – 40

15. 1
Need Another Example?
2
3
Step-by-Step Example
4. Use the Distributive Property to rewrite –2(x – 8).
Rewrite x – 8 as x + (–8).
Expand using the Distributive Property.
–2(x – 8) = –2[x + (–8)]
= –2(x) + –2(–8)
Simplify.= –2x + 16

16. Answer
Need Another Example?
Use the Distributive Property to rewrite
–3(x – 2).
–3x + 6

17. 1
Need Another Example?
2
Step-by-Step Example
5. Use the Distributive Property to rewrite 5(–3x + 7y).
Expand using the Distributive Property.
Simplify.
5(–3x + 7y) = 5(–3x) + 5(7y)
= –15x + 35y

18. Answer
Need Another Example?
Use the Distributive Property to rewrite
4(–9x + 1).
–36x + 4

19. 1
Need Another Example?
2
3
4
Step-by-Step Example
6. Use the Distributive Property to rewrite (x – 6).
Rewrite x – 6 as x + (–6).
Expand using the Distributive Property.
(x – 6) = [x + (–6)]
= x + (–2) Simplify.
= x – 2 Definition of subtraction

20. Answer
Need Another Example?
Use the Distributive Property to rewrite
(x – 16).

21. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
7. Mr. Ito needs to buy batting helmets for the baseball
team. The helmets he plans to buy are $19.95 each.
Find the total cost if Mr. Ito needs to buy 9 batting
helmets for the team.
Distributive Property
Multiply.
Rename $19.95 as $20.00 – $0.05. Then use the Distributive
Property to find the total cost mentally.
= $180 – $0.45
Subtract.= $179.55
= 9($20.00) – 9($0.05)9($20.00 – $0.05)
The total cost of the helmets is $179.55.

22. Answer
Need Another Example?
Fifteen students are buying T-shirts that cost
$10.60 each. Use the Distributive Property to
find the total cost of the shirts.
$159; 15($10 + $0.60)
= 15 • 10 + 15 • 0.6 = 150 + 9, or 159

23. How did what you learned
today help you answer the
HOW can you use numbers and symbols
to represent mathematical ideas?
Course 2, Lesson 5-4
Expressions and Equations

24. How did what you learned
today help you answer the
HOW can you use numbers and symbols
to represent mathematical ideas?
Course 2, Lesson 5-4
Expressions and Equations
Sample answers:
• By using the Distributive Property to evaluate
numerical expressions
• By using the Distributive Property to rewrite algebraic
expressions
• By using the Distributive Property to solve real-world
problems

25. Explain how today’s lesson
on the Distributive Property
will help you with simplifying
algebraic expressions.
Ratios and Proportional RelationshipsExpressions and Equations
Course 2, Lesson 5-4
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