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EXAMPLE 3

EXAMPLE 3. Identifying Properties. 4. 5. a. –. –. = 1. 5. 4. b. –3.5 + 3.5. = 0. c. –4 + 8. = 8 + (–4). (–7.9)(1). = –7.9. d. Tell which property is being illustrated. Inverse property of multiplication. Inverse property of addition. Commutative property of addition.

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EXAMPLE 3

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  1. EXAMPLE 3 Identifying Properties 4 5 a. – – = 1 5 4 b. –3.5 + 3.5 = 0 c. –4 + 8 = 8 + (–4) (–7.9)(1) = –7.9 d. Tell which property is being illustrated. Inverse property of multiplication Inverse property of addition Commutative property of addition Identity property of multiplication

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

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

  4. 2 7 2 a. + + 10 3 3 7 2 2 + + = 10 3 3 7 2 2 = + + 10 3 3 7 = + 0 10 7 = 10 EXAMPLE 5 Using Properties Commutative property of addition Associative property of addition Inverse property of addition Identity property of addition

  5. 5 7 4 b. 4 3 7 4 7 5 = 7 4 3 5 1 = 3 5 = 3 EXAMPLE 5 Using Properties Associative property of multiplication Inverse property of multiplication Identity property of multiplication

  6. 3. 5. (5 + 4) + 6 = 5 + (4 + 6) 3 + 0 = 3 ANSWER ANSWER Identity property of addition Associative property of addition 4. 15 8 = 8 15 ANSWER Commutative property of multiplication for Examples 3, 4, and 5 GUIDED PRACTICE Tell which property is being illustrated.

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

  8. 7. 5( 9) ( 4) [5(–4)] (–9) 5(–4) (–9) = = –20 (–9) = 180 = for Examples 3, 4, and 5 GUIDED PRACTICE Evaluate the expression. Justify each step. Commutative property of multiplication Associative property of multiplication Multiply 5 and –4, then –20 and –9

  9. 8. 6(3) ( 5) –6(–5) (3) = [–6(–5)] (3) = 30(3) = 90 = for Examples 3, 4, and 5 GUIDED PRACTICE Evaluate the expression. Justify each step. Commutative property of multiplication Associative property of multiplication Multiply –6 and –5, then 30 and 3

  10. 9. 2.8 + 7 + ( 1.8) 2.8 + (–1.8) + 7 = [2.8 + (–1.8)] + 7 = 1 + 7 = 8 = for Examples 3, 4, and 5 GUIDED PRACTICE Evaluate the expression. Justify each step. Commutative property of addition Associative property of addition Add 2.8 and –1.8, then 1 and 7

  11. 10. 0.5(7)(8) [0.5(8)](7) 0.5(8)(7) = = 4(7) = 28 = for Examples 3, 4, and 5 GUIDED PRACTICE Evaluate the expression. Justify each step. Commutative property of multiplication Associative property of multiplication Multiply 0.5 and 8, then 4 and 7

  12. 11. 0.9 + [9.1 + ( 2)] (0.9 + 9.1) + (–2) = 10 + (–2) = 8 = for Examples 3, 4, and 5 GUIDED PRACTICE Evaluate the expression. Justify each step. Associative property of addition Add 0.9 and 9.1, then 10 and –2

  13. 12. 94 + 87 + ( 94) 94 + (–94) + 87 = [94 + (–94)] +87 = 0 + 87 = 87 = for Examples 3, 4, and 5 GUIDED PRACTICE Evaluate the expression. Justify each step. Commutative property of addition Associative property of addition Inverse property of addition Identity property of addition

  14. 13. 53 + ( 25) + 53 –53 + 53 + (–25) = (–53 + 53) + (–25) = 0 + (–25) = –25 = for Examples 3, 4, and 5 GUIDED PRACTICE Evaluate the expression. Justify each step. Commutative property of addition Associative property of addition Inverse property of addition Identity property of addition

  15. 5 1 14. 3 3 6 5 5 5 5 1 1 3 = 3 3 6 6 6 6 = 3 1 = = for Examples 3, 4, and 5 GUIDED PRACTICE Evaluate the expression. Justify each step. Commutative property of multiplication Associative property of multiplication Inverse property of multiplication Identity property of multiplication

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