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Chapter 1. 1-5 Properties of Numbers. Commutative: a + b = b + a Associative: (a + b) + c = a + (b + c) Identity Property of Zero: a + 0 = a. Addition Properties. Commutative: a * b = b * a Associative: (a * b) * c = a (b * c) Identity Property of 1: a * 1 = a.
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Chapter 1 1-5 Properties of Numbers
Commutative: a + b = b + a • Associative: (a + b) + c = a + (b + c) • Identity Property of Zero: a + 0 = a Addition Properties
Commutative: a * b = b * a • Associative: (a * b) * c = a (b * c) • Identity Property of 1: a * 1 = a Multiplication Properties
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Tell which property is represented. • 1 + (6 + 7) = (1 + 6) + 7 • 1 x 10 = 10 • 3 x 5 = 5 x 3 • 6 + 0 = 6 • 4 x (4 x 2) = (4 x 4) x 2 • x + y = y + x Examples
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Simplify each expression. Justify each step. • 8 + 23 + 2 • 2 x (17 x 5) • (25 x 11) x 4 • 17 + 29 + 3 • 16 + (17 + 14) • 5 x 19 x 20 Examples
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Use the Distributive Property to find each product. • 2(19) • 5(31) • (22)2 • (13)6 • 8(26) • (34)6 Examples
To find the area of a loft, the architect multiplies the length and the width: (14 + 8) x 10. Use the Distributive Property to find the area of the loft. • A student simplified the expression 6 x (9 + 12) as shown. What is the student’s error. 6 x (9 + 12) = 6 x 9 + 12 = 54 + 12 = 66 Word Problems