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Chapter 9 Signed Numbers Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 9.3 Multiplying and Dividing Signed Numbers Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Multiplication with Different Signs Notice the following pattern when multiplying numbers with different signs. This number decreases by 1 each time. 3(4) = 2(4) = 12 8 1(4) = 0(4) = –1(4) = 4 0 –4 –2(4) = –3(4) = –8 –12 This number decreases by 4 each time. The pattern suggests that when we multiply a positive number by a negative number, we get a negative number. Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Multiplication with Different Signs Multiplication of Signed Numbers with Different Signs To multiply two numbers with different signs, multiply the absolute value. The result is negative. Example: Multiply. –6(4) –6(4) = –24 Example: Multiply. 12(–9) The result will always be negative. 12(–9) = –108 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Division with Different Signs Division of Signed Numbers with Different Signs To divide two numbers with different signs, divide the absolute value. The result is negative. Example: Divide. –36 ÷ 4 –36 ÷ 4 = – 9 Example: Divide. 100 ÷ (–20) The result will always be negative. 100 ÷ (–20) = –5 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Multiplication with Same Signs Notice the following pattern when multiplying two negative numbers. This number decreases by 1 each time. 3(–4) = –12 2(–4) = –8 1(–4) = –4 0(–4) = –1(–4) = –2(–4) = 0 4 8 –3(–4) = 12 This number increases by 4 each time. The pattern suggests that when we multiply two negative numbers, we get a positive number. (The same is true for division of signed numbers with the same sign.) Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Multiplication with Same Signs Multiplication and Division of Signed Numbers with the Same Signs To multiply or divide two numbers with the same sign, multiply or divide the absolute values. The result is positive. Example: Divide. –75 ÷ (– 3) –75 ÷ (– 3) = 25 Example: 2 Multiply. 5 12 3 The result will always be positive. 1 5 2 5 12 3 18 6 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Multiplying Three or More Signed Numbers Example: Multiply. –8(–3)(2) –8(–3)(2) = 24(2) First multiply –8(–3) = 24. = 48 Then multiply 24(2) = 48. Example: 2 2 3 Perform the operations. 3 3 5 2 2 3 2 3 3 3 3 5 3 2 5 To divide the first two fractions, invert and multiply the second 3 1 fraction. 5 3 5 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.