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EXAMPLE 3

1. 7 + 4 = 4 + 7. 13 = 1. 13. EXAMPLE 3. Identify properties of real numbers. Identify the property that the statement illustrates. SOLUTION. Commutative property of addition. SOLUTION. Inverse property of multiplication. a + (2 – a ). = a + [2 + (– a )]. EXAMPLE 4.

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EXAMPLE 3

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  1. 1 7 + 4 = 4 + 7 13 = 1 13 EXAMPLE 3 Identify properties of real numbers Identify the property that the statement illustrates. SOLUTION Commutative property of addition SOLUTION Inverse property of multiplication

  2. a + (2 – a) = a + [2 + (– a)] EXAMPLE 4 Use properties and definitions of operations Use properties and definitions of operations to show that a + (2 – a) = 2. Justify each step. SOLUTION Definition of subtraction = a + [(– a) + 2] Commutative property of addition = [a + (– a)] + 2 Associative property of addition = 0 + 2 Inverse property of addition Identity property of addition = 2

  3. (2 3) 9 = 2 (3 9) 15 + 0 = 15 for Examples 3 and 4 GUIDED PRACTICE Identify the property that the statement illustrates. SOLUTION Associative property of multiplication. SOLUTION Identityproperty of addition.

  4. 4(5 + 25) = 4(5) + 4(25) 1 500 = 500 for Examples 3 and 4 GUIDED PRACTICE Identify the property that the statement illustrates. SOLUTION Distributive property. SOLUTION Identityproperty of multiplication.

  5. b (4 b) = 4 whenb = 0 1 1 1 b (4 b) = b (4 ) b b b = b ( 4) = (b ) 4 = 1 4 for Examples 3 and 4 GUIDED PRACTICE Use properties and definitions of operations to show that the statement is true. Justify each step. SOLUTION Def. of division Comm. prop. of multiplication Assoc. prop. of multiplication Inverse prop. of multiplication = 4 Identity prop. of multiplication

  6. 3x + (6 + 4x) = 7x + 6 3x + (6 + 4x) = 3x + (4x + 6) for Examples 3 and 4 GUIDED PRACTICE Use properties and definitions of operations to show that the statement is true. Justify each step. SOLUTION Comm. prop. of addition = (3x + 4x) + 6 Assoc. prop. of addition Combine like terms. = 7x + 6

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