1. Preview
Warm Up
California Standards
Lesson Presentation

2. Warm Up Add or subtract. 1. 2.5 – 3.7 2. 3. Multiply or divide.–
Multiply or divide.
(4.8) 6. –12 ÷ 1.5
–1.2
1920 12 6
0.144 –8

3. AF1.3 Simplify numerical expressions by applying properties of rational numbers (e.g. identity, inverse, distributive, associative, commutative) and justify the process used.
California
Standards

4. Vocabulary Commutative Property Associative Property
Distributive Property

6. Name the property that is illustrated in each equation.
Additional Example 1: Identifying Properties of Addition and Multiplication
Name the property that is illustrated in each equation.
A. (–4)  9 = 9  (–4) B.
(–4)  9 = 9  (–4)
The order of the numbers changed.
Commutative Property of Multiplication
The factors are grouped differently.
Associative Property of Addition

7. Name the property that is illustrated in each equation.
Check It Out! Example 1
Name the property that is illustrated in each equation.
A. (–13)2 = 2(–13)
B. (18 + 4) + 6 = 18 + (4 + 6)
The order of the numbers changed.
(–13)2 = 2(–13)
Commutative Property of Multiplication
The factors are grouped differently.
(18 + 4) + 6 = 18 + (4 + 6)
Associative Property of Addition

8. Additional Example 2A: Using the Commutative and Associate Properties
Simplify each expression. Justify each step.
Commutative Property of Addition =
Associative Property of Addition
= (29 + 1) + 37 =
Add.
= 67

9. Additional Example 2B: Using the Commutative and Associate Properties
Simplify each expression. Justify each step.
7  
2 9
1 7
7   = 7  
2 9
1 7
Commutative Property of Multiplication
= (7  ) 
2 9
1 7
Associative Property of Multiplication
= 1 
2 9
Multiply. =
2 9

10. Check It Out! Example 2A
Simplify each expression. Justify each step.
Commutative Property of Addition =
Associative Property of Addition
= (13 + 7) + 14 =
Add.
= 34

11. Check It Out! Example 2B
Simplify each expression. Justify each step.
4  3 
1 4
4  3  = 4   3
1 t4
1 4
Commutative Property of Multiplication
= (4  )  3
1 4
Associative Property of Multiplication
= 1  3
Multiply.
= 3

12. The Distributive Property is also helpful when you do math mentally
The Distributive Property is also helpful when you do math mentally. When you need to find the product of two numbers, write one of the numbers as a sum or difference. Then use the Distributive Property to help you find the product mentally.

13. Additional Example 3A: Using the Distributive Property
Write each product using the Distributive Property. Then simplify.
9(31)
9(31) = 9(30 + 1)
Rewrite 31 as a sum.
= (9  30) + (9  1)
Distributive Property =
Multiply.
= 279
Add.

14. Additional Example 3B: Using the Distributive Property
Write each product using the Distributive Property. Then simplify.
8(59)
8(59) = 8(60 – 1)
Rewrite 59 as a difference.
= (8  60) – (8  1)
Distributive Property
= 480 – 8
Multiply.
= 472
Subtract.

15. Check It Out! Example 3A
Write each product using the Distributive Property. Then simplify.
8(19)
8(19) = 8(10 + 9)
Rewrite 19 as a sum.
= (8  10) + (8  9)
Distributive Property =
Multiply.
= 152
Add.

16. Check It Out! Example 3B
Write each product using the Distributive Property. Then simplify.
5(48)
5(48) = 5(50 – 2)
Rewrite 48 as a difference.
= (5  50) – (5  2)
Distributive Property
= 250 – 10
Multiply.
= 240
Subtract.

17. Lesson Quiz Name the property that is illustrated in each equation.
1. (–3 + 1) + 2 = –3 + (1 + 2)
2. 6  y  7 = 6 ● 7 ● y
Simplify the expression. Justify each step. 3.
Write each product using the Distributive Property. Then simplify
4. 4(98)
5. 7(32)
Associative Property of Add.
Commutative Property of Multiplication 22
392
224