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1 Introduction to Algebra: Integers Copyright © 2014, 2010, 2007 Pearson Education, Inc. Slide 1 1.6 Multiplying Integers R.1 Fractions Objectives 1. Use a raised dot or parentheses to express multiplication. 2. Multiply integers. 3. Identify properties of multiplication. 4. Estimate answers to application problems involving multiplication. Copyright © 2014, 2010, 2007 Pearson Education, Inc. Slide 2 Use a raised dot or parentheses to express multiplication. Numbers being multiplied are called factors and the answer is called the product. Copyright © 2014, 2010, 2007 Pearson Education, Inc. Slide 3 Use a raised dot or parentheses to express multiplication. Example Rewrite the multiplication in three different ways. Identify the factor and the product. 10 × 7 The factors are 10 and 7 and the product is 70. Copyright © 2014, 2010, 2007 Pearson Education, Inc. Slide 4 Multiply integers. Multiply Two Integers If two factors have different signs, the product is negative. For example, and 4 ( 5) 20 2 6 12 If two factors have the same sign, the product is positive. For example, 7 3 21 and 3 ( 10) 30 Copyright © 2014, 2010, 2007 Pearson Education, Inc. Slide 5 Multiply integers. Example Multiply the integers. 2 • 8 2 8 16 Positive Negative The factors have different signs, so the product is negative. Copyright © 2014, 2010, 2007 Pearson Education, Inc. Slide 6 Multiply integers. Example Multiply the integers. 10( 6) 10( 6) 60 The factors have the same sign, so the product is positive. Copyright © 2014, 2010, 2007 Pearson Education, Inc. Slide 7 Multiply integers. Example Multiply the integers. 3 • (4 • 5) 3 (4 5) Multiply numbers in parentheses first. 3 20 60 Then multiply the resulting pair of numbers. Copyright © 2014, 2010, 2007 Pearson Education, Inc. Slide 8 Multiply integers. Example Multiply the integers. 2 ( 2) ( 2) 2 ( 2) ( 2) Multiply the first pair of numbers. 4 ( 2) 8 Then multiply the resulting pair of numbers. Copyright © 2014, 2010, 2007 Pearson Education, Inc. Slide 9 Identify properties of multiplication. Multiplication Property of 0 Multiplying any number by 0 gives a product of 0. Some examples are shown below. 16(0) = 0 (0)(5) = 0 32,977(0) = 0 Copyright © 2014, 2010, 2007 Pearson Education, Inc. Slide 10 Identify properties of multiplication. Multiplication Property of 1 Multiplying a number by 1 leaves the number unchanged. Some examples are shown below. 6(1) = 6 –12(1) = –12 (1)(5876) = 5876 Copyright © 2014, 2010, 2007 Pearson Education, Inc. Slide 11 Identify properties of multiplication. Copyright © 2014, 2010, 2007 Pearson Education, Inc. Slide 12 Identify properties of multiplication. Example Show that the product is unchanged and name the property that is illustrated. 7 ( 4) 4 ( 7) Both products are 28. Commutative property of multiplication Copyright © 2014, 2010, 2007 Pearson Education, Inc. Slide 13 Identify properties of multiplication. Example Show that the product is unchanged and name the property that is illustrated. 5 (10 2) (5 10) 2 5 20 50 2 100 100 Both products are 100. Associative property of multiplication Copyright © 2014, 2010, 2007 Pearson Education, Inc. Slide 14 Identify properties of multiplication. Copyright © 2014, 2010, 2007 Pearson Education, Inc. Slide 15 Identify properties of multiplication. Example Rewrite the product, using the distributive property. Show that the result is unchanged. 2( 5 1) 2( 5 1) ( 2) ( 5) ( 2) (1) 2( 4) 10 ( 2) 88 Copyright © 2014, 2010, 2007 Pearson Education, Inc. Slide 16 Estimate answers to application problems involving multiplication. Example Last year Videoland had to replace 392 defective DVDs at a cost of $19 each. How much money was lost on defective DVDs? Estimate: Use front end rounding: 392 rounds to 400 and –$19 rounds to –$20. 400 ( $20) $8000 Exact: 392 ( $19) $7448 Videoland lost $7448 in defective DVDs. Copyright © 2014, 2010, 2007 Pearson Education, Inc. Slide 17