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Exercise Multiply. 5 • 7 = 35
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Exercise Multiply. 5 (– 7) = – 35
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Exercise Multiply. – 5 (– 7) = 35
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Exercise Simplify. (– 5)2 = 25
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Exercise Simplify. (– 5)3 = – 125
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1 2 shaded 1 2 of shaded 1 3 1 6 shaded
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1 2 1 3 x 1 x 1 3 x 2 = 1 6 =
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Multiplying Rational Numbers
To multiply two rational numbers, multiply the first numerator times the second numerator and the first denominator times the second denominator. Express the product in lowest terms.
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Multiplying Rational Numbers
For all rational numbers and (b ≠ 0, d ≠ 0), x = a b c d a x c b x d
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Example 1 4 5 7 9 Multiply x 4 5 7 9 x 4 x 7 5 x 9 = = 2845
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Example 2 4 7 2 5 Multiply – x 4 7 2 5 x – – 4 x 2 7 x 5 = = 8 35 –
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Example 3 2 3 3 Evaluate 2 3 3 2 3 x = 2 x 2 x 2 3 x 3 x 3 = = 8 27
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Example 4 5 2 3 Evaluate . – 5 2 3 – = 5 3 – 5 3 – 5(– 5) 3(3) = =
5 2 3 Evaluate – 5 2 3 – = 5 3 – 5 3 – 5(– 5) 3(3) = = 25 9
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Example 4 5 3 3 Evaluate . – 5 3 3 – = 5 3 – 5 3 = 25 9 – 5 3 = 125 27
5 3 3 Evaluate – 5 3 3 – = 5 3 – 5 3 = 25 9 – 5 3 = 125 27 –
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dividing both the numerator and the denominator by the same number
canceling simplifying reducing
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5 9 3 4 x 3 x 5 2 x 2 x 3 x 3 = 5 12 =
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Example 5 3 4 5 9 Multiply . x 1 3 4 5 9 3 4 5 9 x x = 3 1 x 5 4 x 3
5 12
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Example 6 4 9 2 5 15 16 Multiply . – – – 1 3 = – 4 9 2 5 – 15 16 x 1 2
Multiply – – – 1 3 = – 4 9 2 5 – x 1 2 – 4 9 2 5 – x –1(1)(–1) 3(1)(2) = = 1 6
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Example 7 1 6 Multiply . 2 x 9 13 6 2 3 9 1 x = 1 6 9 x 2 13 6 9 1 x =
39 2
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Example Cancel before multiplying. 5 12 8 25 = 2 15 •
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Example Cancel before multiplying. – 7 8 10 21 – 9 25 = 3 20 • •
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Example Cancel before multiplying. 3 2 5 = 4 9 •
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Example Multiply the mixed numbers. 5 8 1 3 = 14 2 x 5
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753 1,000 35 100 x 0.753 x 0.35 26, ,000 = =
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Example 8 Multiply x 2.06. 2.06 x 824 618
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Example Multiply the decimals. 34,000 x = 10.2
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Example Multiply the decimals. 2.3 x 40 x 0.03 = 2.76
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Example Multiply the decimals. x 0.01 =
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