CHAPTER 9 Introduction to Real Numbers and Algebraic Expressions Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 9.1Introduction to Algebra 9.2The Real Numbers 9.3Addition of Real Numbers 9.4Subtraction of Real Numbers 9.5Multiplication of Real Numbers 9.6Division of Real Numbers 9.7Properties of Real Numbers 9.8Simplifying Expressions; Order of Operations

OBJECTIVES 9.5 Multiplication of Real Numbers Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aMultiply real numbers. bSolve applied problems involving multiplication of real numbers.

9.5 Multiplication of Real Numbers PRODUCT OF A POSITIVE NUMBER AND A NEGATIVE NUMBER Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To multiply a positive number and a negative number, multiply their absolute values. The answer is negative.

EXAMPLE 9.5 Multiplication of Real Numbers a Multiply real numbers. Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Multiply.

9.5 Multiplication of Real Numbers THE PRODUCT OF TWO NEGATIVE NUMBERS Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To multiply two negative numbers, multiply their absolute values. The answer is positive.

9.5 Multiplication of Real Numbers Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To multiply two nonzero real numbers: a) Multiply the absolute values. b) If the signs are the same, the answer is positive. c) If the signs are different, the answer is negative.

9.5 Multiplication of Real Numbers THE MULTIPLICATION PROPERTY OF ZERO Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 9.5 Multiplication of Real Numbers a Multiply real numbers. Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

9.5 Multiplication of Real Numbers a Multiply real numbers. Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. When multiplying more than two real numbers, we can choose order and grouping as we please.

EXAMPLE 9.5 Multiplication of Real Numbers a Multiply real numbers. Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Multiply.

9.5 Multiplication of Real Numbers Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The product of an even number of negative numbers is positive. The product of an odd number of negative numbers is negative.

EXAMPLE 9.5 Multiplication of Real Numbers a Multiply real numbers. 17 Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 9.5 Multiplication of Real Numbers a Multiply real numbers. 18 Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To make sense of the substitutions and computations, we introduce extra grouping symbols into the expressions.

EXAMPLE 9.5 Multiplication of Real Numbers b Solve applied problems involving multiplication of real numbers. 19Chemical Reaction Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. During a chemical reaction, the temperature in a beaker decreased by 2 C every minute until 10:23 A.M. If the temperature was 17 C at 10:00 A.M., when the reaction began, what was the temperature at 10:23 A.M.?

EXAMPLE 9.5 Multiplication of Real Numbers b Solve applied problems involving multiplication of real numbers. 19Chemical Reaction Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. This is a multistep problem. We first find the total number of degrees that the temperature dropped, using –2 C for each minute. Since it dropped 2 C for each of the 23 minutes, we know that the total drop d is given by

EXAMPLE 9.5 Multiplication of Real Numbers b Solve applied problems involving multiplication of real numbers. 19Chemical Reaction Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.