2. 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

3. OBJECTIVES 9.6 Division of Real Numbers Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aDivide integers. bFind the reciprocal of a real number. cDivide real numbers. dSolve applied problems involving division of real numbers.

4. 9.6 Division of Real Numbers DIVISION Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

5. EXAMPLE 9.6 Division of Real Numbers a Divide integers. Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

6. 9.6 Division of Real Numbers Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To multiply or divide two real numbers (where the divisor is nonzero): a) Multiply or divide the absolute values. b) If the signs are the same, the answer is positive. c) If the signs are different, the answer is negative.

7. 9.6 Division of Real Numbers EXCLUDING DIVISION BY 0 Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

8. 9.6 Division of Real Numbers DIVIDENDS OF 0 Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

9. EXAMPLE 9.6 Division of Real Numbers a Divide integers. Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Divide.

10. 9.6 Division of Real Numbers RECIPROCALS Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Two numbers whose product is 1 are called reciprocals, or multiplicative inverses, of each other.

11. EXAMPLE 9.6 Division of Real Numbers b Find the reciprocal of a real number. Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Find the reciprocal.

12. 9.6 Division of Real Numbers RECIPROCAL PROPERTIES Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

13. 9.6 Division of Real Numbers THE SIGN OF A RECIPROCAL Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The reciprocal of a number has the same sign as the number itself.

14. 9.6 Division of Real Numbers c Divide real numbers. Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. We know that we can subtract by adding an opposite. Similarly, we can divide by multiplying by a reciprocal.

15. 9.6 Division of Real Numbers RECIPROCALS AND DIVISION Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

16. EXAMPLE 9.6 Division of Real Numbers c Divide real numbers. Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

17. 9.6 Division of Real Numbers c Divide real numbers. Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. When actually doing division calculations, we sometimes multiply by a reciprocal and we sometimes divide directly. With fraction notation, it is usually better to multiply by a reciprocal. With decimal notation, it is usually better to divide directly.

18. EXAMPLE 9.6 Division of Real Numbers c Divide real numbers. 19 Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Divide by multiplying by the reciprocal of the divisor.

19. 9.6 Division of Real Numbers c Divide real numbers. Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. With decimal notation, it is easier to carry out long division than to multiply by the reciprocal.

20. EXAMPLE 9.6 Division of Real Numbers c Divide real numbers. 22 Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

21. 9.6 Division of Real Numbers SIGN CHANGES IN FRACTION NOTATION Slide 21Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. For any numbers a and b, b 0: 1. (The opposite of a number a divided by the opposite of another number b is the same as the quotient of the two numbers a and b.)

22. 9.6 Division of Real Numbers SIGN CHANGES IN FRACTION NOTATION Slide 22Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 2. (The opposite of a number a divided by another number b is the same as the number a divided by the opposite of the number b, and both are the same as the opposite of a divided by b.)

23. EXAMPLE 9.6 Division of Real Numbers d Solve applied problems involving division of real numbers. 24Chemical Reaction Slide 23Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. During a chemical reaction, the temperature in a beaker decreased every minute by the same number of degrees. The temperature was 56 F at 10:10 A.M. By 10:42 A.M., the temperature had dropped to –12 F. By how many degrees did it change each minute?

24. EXAMPLE 9.6 Division of Real Numbers d Solve applied problems involving division of real numbers. 24Chemical Reaction Slide 24Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.