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**Tell which property is being illustrated.**

EXAMPLE 3 Identifying Properties Tell which property is being illustrated. = 1 a. 5 4 – Inverse property of multiplication b. – = 0 Inverse property of addition c. –4 + 8 = 8 + (–4) Commutative property of addition d. (–7.9)(1) = –7.9 Identity property of multiplication

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**Evaluate the expression. Justify each step.**

EXAMPLE 4 Using Familiar Properties Evaluate the expression. Justify each step. ( 4.4) a. = 3 + ( 10.6) + ( 4.4) Commutative property of addition = 3 + [( 10.6) + ( 4.4)] Associative property of addition = 3 + ( 15) Add –10.6 and –4.4. = 12 Add 3 and –15.

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**Evaluate the expression. Justify each step.**

EXAMPLE 4 Using Familiar Properties Evaluate the expression. Justify each step. –25(7)(–4) b. = 7( 25)( 4) Commutative property of multiplication = 7[( 25)( 4)] Associative property of multiplication = 7(100) = 700 Multiply –25 and –4, multiply 7 and 100.

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EXAMPLE 5 Using Properties 3 2 a. + 10 7 = 3 2 + 10 7 Commutative property of addition 3 2 + 10 7 = Associative property of addition = 10 7 + 0 Inverse property of addition 10 7 = Identity property of addition

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**EXAMPLE 5 3 5 7 4 b. 7 4 3 5 = 3 5 1 = 3 5 = Using Properties**

Associative property of multiplication 3 5 1 = Inverse property of multiplication 3 5 = Identity property of multiplication

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**Tell which property is being illustrated.**

GUIDED PRACTICE for Examples 3, 4, and 5 Tell which property is being illustrated. 3. 3 + 0 = 3 Identity property of addition ANSWER 4. = Commutative property of multiplication ANSWER 5. (5 + 4) + 6 = 5 + (4 + 6) ANSWER Associative property of addition

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**Evaluate the expression. Justify each step.**

GUIDED PRACTICE for Examples 3, 4, and 5 Evaluate the expression. Justify each step. 6. 3.5 + [( 3) + 6.5] 3.5 + [6.5 + (–3)] Commutative property of addition = ( ) + (–3) Associative property of addition = 10 + (– 3) = 7 Add 3.5 and 6.5, then 10 and – 3

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**Evaluate the expression. Justify each step.**

GUIDED PRACTICE for Examples 3, 4, and 5 Evaluate the expression. Justify each step. 7. 5( 9) ( 4) = 5(–4) (–9) Commutative property of multiplication = [5(–4)] (–9) Associative property of multiplication = –20 (–9) = 180 Multiply 5 and –4, then –20 and –9

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**Evaluate the expression. Justify each step.**

GUIDED PRACTICE for Examples 3, 4, and 5 Evaluate the expression. Justify each step. 8. 6(3) ( 5) = –6(–5) (3) Commutative property of multiplication = [–6(–5)] (3) Associative property of multiplication = 30(3) = 90 Multiply –6 and –5, then 30 and 3

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**Evaluate the expression. Justify each step.**

GUIDED PRACTICE for Examples 3, 4, and 5 Evaluate the expression. Justify each step. 9. ( 1.8) = 2.8 + (–1.8) + 7 Commutative property of addition = [2.8 + (–1.8)] + 7 Associative property of addition = 1 + 7 = 8 Add 2.8 and –1.8, then 1 and 7

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**Evaluate the expression. Justify each step.**

GUIDED PRACTICE for Examples 3, 4, and 5 Evaluate the expression. Justify each step. 0.5(7)(8) 10. = 0.5(8)(7) Commutative property of multiplication = [0.5(8)](7) Associative property of multiplication = 4(7) = 28 Multiply 0.5 and 8, then 4 and 7

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**Evaluate the expression. Justify each step.**

GUIDED PRACTICE for Examples 3, 4, and 5 Evaluate the expression. Justify each step. 0.9 + [9.1 + ( 2)] 11. = ( ) + (–2) Associative property of addition = 10 + (–2) = 8 Add 0.9 and 9.1, then 10 and –2

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**Evaluate the expression. Justify each step.**

GUIDED PRACTICE for Examples 3, 4, and 5 Evaluate the expression. Justify each step. ( 94) 12. = 94 + (–94) + 87 Commutative property of addition = [94 + (–94)] + 87 Associative property of addition = 0 + 87 Inverse property of addition = 87 Identity property of addition

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**Evaluate the expression. Justify each step.**

GUIDED PRACTICE for Examples 3, 4, and 5 Evaluate the expression. Justify each step. 53 + ( 25) + 53 13. = – (–25) Commutative property of addition = (– ) + (–25) Associative property of addition = 0 + (–25) Inverse property of addition = –25 Identity property of addition

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**Evaluate the expression. Justify each step.**

GUIDED PRACTICE for Examples 3, 4, and 5 Evaluate the expression. Justify each step. 3 1 6 5 14. = 6 5 3 1 Commutative property of multiplication = 6 5 3 1 Associative property of multiplication = 6 5 1 Inverse property of multiplication = 6 5 Identity property of multiplication

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