Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 8 Real Numbers and Introduction to Algebra

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 8.5 Multiplying and Dividing Real Numbers

Martin-Gay, Developmental Mathematics, 2e 33 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Multiplying Real Numbers 1. The product of two numbers with the same sign is a positive number. 2. The product of two numbers with different signs is a negative number. Multiplying Real Numbers

Martin-Gay, Developmental Mathematics, 2e 44 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Multiply. a. 4(–2) = –8 b. ‒ 7( ‒ 5) = 35 c. 9( ‒ 6.2) = ‒ 55.8 d. Example

Martin-Gay, Developmental Mathematics, 2e 55 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. If b is a real number, then b · 0 = 0. Also 0 ·b = 0. Example: 9(0)( ‒ 5) = 0 Products Involving Zero

Martin-Gay, Developmental Mathematics, 2e 66 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Evaluate. a. (–2) 4 = (–2)(–2)(–2)(–2) = 16 b. ‒ 7 2 = ‒ (7 ·7) = ‒ 49 Example

Martin-Gay, Developmental Mathematics, 2e 77 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Reciprocal or Multiplicative Inverse Two numbers whose product is 1 are called reciprocals or multiplicative inverse of each other. Quotients Involving Zero The number 0 does not have a reciprocal. Finding Reciprocals

Martin-Gay, Developmental Mathematics, 2e 88 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Find the reciprocal. a. 55 The reciprocal is b. Example

Martin-Gay, Developmental Mathematics, 2e 99 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Dividing Real Numbers 1. The quotient of two numbers with the same sign is a positive number. 2. The quotient of two numbers with different signs is a negative number. Dividing Real Numbers

Martin-Gay, Developmental Mathematics, 2e 10 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Divide. a. b. c. Example

Martin-Gay, Developmental Mathematics, 2e 11 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. If a and b are real numbers, and b  0, then Division Involving Zero If a is a nonzero number, then

Martin-Gay, Developmental Mathematics, 2e 12 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Use order of operations to evaluate each expression. a. b. Example

Martin-Gay, Developmental Mathematics, 2e 13 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Determine whether ‒ 8 is a solution of Example Since we have a true statement, ‒ 8 is a solution of the equation.