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Chapter 2 Section 5 Multiplying Integers

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Multiplying Two Integers with Different Signs Words: The product of two integers with different signs. Numbers: 3(-2) = -6, -2(3) = -6

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Example 1 Find each product. 6(-8) 6(-8) = 6 ∙ -8 = -48 The factors have different signs, so the answer will be negative.

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Example 2 Find each product. -5(9) -5(9) = -5 ∙ 9 = -45 The factors have different signs, so the answer will be negative.

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Your Turn Find each product. 10(-3)

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Your Turn Find each product. -7(7)

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Your Turn Find each product. 15(-3)

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Multiplying Two Integers with the Same Signs Words: The product of two integers with the same signs is positive. Numbers: 3(2) = 6, -2(-3) = 6

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Example 3 Find each product. 15(2) 15(2)= 15 ∙ 2 = 30 The factors have the same signs, so the answer will be positive.

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Example 4 Find each product. -5(-6) -5(-6) = -5 ∙ -6 = 30 The factors have the same signs, so the answer will be positive.

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Your Turn Find each product. 11(9)

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Your Turn Find each product. -6(-7)

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Your Turn Find each product. -10(-8)

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To find the product of three or more numbers, multiply the first two numbers. Then multiply the results by the next number, until you come to the end.

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Example 5 Find each product. 8(-10)(-4) 8(-10) = -80 -80(-4)= 320

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Example 5 Find each product. 5(-3)(-2)(-2) 5(-3) = -15 -15(-2)= 30 30(-2)= -60

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Your Turn Find each product. -2(-3)(4)

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Your Turn Find each product. 6(-2)(3)

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Your Turn Find each product. (-1)(-5)(-2)(-3)

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You can use the rules for multiplying integers to evaluate algebraic expressions and to simplify expressions.

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Example 7 Evaluate 2xy of x = -4 and y = -2. 2xy = 2(-4)(-2) or 2 ∙ -4 ∙ -2 = -8(-2) = 16

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Example 8 Simplify (2a)(-5b). (2a) (-5b) = (2)(a)(-5)(b) = 2 ∙ -5 (a)(b) = -10ab

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Your Turn Evaluate -5n if n = -7.

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Your Turn Simplify 12(-3z)

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