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Ch 2.5 Objective: To multiply integers. Properties Commutative Property: a * b = b * a Two numbers can be multiplied in either order and the result is always the same. For example: 4 * 6 = 6 * 4 Associative Property: (a * b) * c = a * (b * c) Three numbers can be multiplied in any order and the result will always be the same. For example: (1 * 2) * 3 = 1 * (2 * 3) More Properties Identity Property: 1 * a = a The product of 1 and a number will always be the number. For example: 1 * 11 = 11 Inverse Property: a * (1/a) = 1 The product of a number and its reciprocal will always equal one. For example: 10 * (1/10) = 1 Property & Definition Zero Product Property: a * 0 = 0 The product of zero and any number will always equal zero. For example: 5 * _____ = 0 Reciprocal: The reciprocal of a number is 1 divided by the number. For example: Reciprocal of a is 1/a. Reciprocal of 1/a is a. Rules for Multiplying Integers Same Sign (+) Evaluate 2 numbers at a time. If they have the same sign, the result is always positive. For example: 4 * 5 = 20 -4 (– 5) = 20 Opposite Signs (-) Evaluate 2 numbers at a time. If they have opposite signs, the result is always negative. For example: 4 (–7) = -28 -4 (7) = -28 Odd # of Negatives = Negative Even # of Negatives = Positive Simplify. 1) 3 8 -24 5) 5 (8) -40 2) 4 ( 9) +36 6) 10 (4) +40 3) 6 7 -42 7) 6 (4) (2) 24 (-2) = -48 8) 5 (4) 2 20 2 = +40 4) ( 2)( 5)( 3) +30 Review Simplify the following. 1) -6(7) = -42 5) (-9) -5 = -14 2) 6(-7) = -42 6) -9(-5) = +45 3) (6) -7 = -1 7) (+9) -5 = +4 4) (-6) -7 = -13 8) +9(-5) = -45 Simplify the following. 1) 34 4 2) (3) 3) 4 3 4) ( 4) 3 5) ( 2) 4 -81 6) (7 2) 2 25 +81 7) 7 22 -64 8) 6(3)2 54 3 -64 9) 6 16 10) 12 0 1 2 -36 Simplify the following. 1) 3(x)( x) 3x 6) 1(a) 2 2 2) 4(a) 5 4a 3) 6(k) 5 10 6k 10 a 2 7) x( x)(x) 8) 4(y) 5 x 3 4y 5 4 7 4) 5(m) 5m 7 5) (b)(b)(b)(b) b 4 9) 3(t) 3t 4 10) 10( y) 2 10y 2