Preview Warm Up California Standards Lesson Presentation

Warm Up Add or subtract. 1. 2.5 – 3.7 2. 3. Multiply or divide. 1. 2.5 – 3.7 2. 3. Multiply or divide. 4. 5. 0.03(4.8) 6. –12 ÷ 1.5 –1.2 1920 12 6 0.144 –8

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

Vocabulary Commutative Property Associative Property Distributive Property

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

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

Additional Example 2A: Using the Commutative and Associate Properties Simplify each expression. Justify each step. 29 + 37 + 1 Commutative Property of Addition 29 + 37 + 1 = 29 + 1 + 37 Associative Property of Addition = (29 + 1) + 37 = 30 + 37 Add. = 67

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

Check It Out! Example 2A Simplify each expression. Justify each step. 13 + 14 + 7 Commutative Property of Addition 13 + 14 + 7 = 13 + 7 + 14 Associative Property of Addition = (13 + 7) + 14 = 20 + 14 Add. = 34

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

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.

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 = 270 + 9 Multiply. = 279 Add.

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.

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 = 80 + 72 Multiply. = 152 Add.

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.

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