2. CHAPTER 2 Whole Numbers Slide 2Copyright 2011 Pearson Education, Inc. 2.1Factorizations 2.2Divisibility 2.3Fractions and Fraction Notation 2.4Multiplication and Applications 2.5Simplifying 2.6Multiplying, Simplifying, and Applications 2.7Division and Applications

3. OBJECTIVES 2.7 Division and Applications Slide 3Copyright 2011 Pearson Education, Inc. aFind the reciprocal of a number. bDivide and simplify using fraction notation. cSolve equations of the type a ∙ x = b and x ∙ a = b where a and b may be fractions. dSolve applied problems involving division of fractions.

4. If the product of two numbers is 1, we say that they are reciprocals of each other. To find the reciprocal of a fraction, interchange the numerator and denominator. Number  Reciprocal 2.7 Division and Applications Reciprocals Slide 4Copyright 2011 Pearson Education, Inc.

5. EXAMPLE Solution 1. The reciprocal of is 2. The reciprocal of is 3. The reciprocal of is 4. The reciprocal of is 2.7 Division and Applications a Find the reciprocal of a number. AFind the reciprocal: 1. 2. 3. 4. Slide 5Copyright 2011 Pearson Education, Inc.

6. The number 0, or has no reciprocal. (Recall that is not defined.) 2.7 Division and Applications 0 Has No Reciprocal Slide 6Copyright 2011 Pearson Education, Inc.

7. To divide fractions, multiply the dividend by the reciprocal of the divisor. Multiply by the reciprocal of the divisor. 2.7 Division and Applications Division of Fractions Slide 7Copyright 2011 Pearson Education, Inc.

8. EXAMPLE Multiply by the reciprocal of the divisor Factoring and identifying a common factor Removing a factor equal to 1 Solution 2.7 Division and Applications b Divide and simplify using fraction notation. BDivide and simplify: Slide 8Copyright 2011 Pearson Education, Inc.

9. EXAMPLE Multiply by the reciprocal of the divisor Factoring and identifying a common factor Removing a factor equal to 1 Solution 2.7 Division and Applications b Divide and simplify using fraction notation. CDivide and simplify: Slide 9Copyright 2011 Pearson Education, Inc.

10. EXAMPLE Dividing by 4/5 on both sides Multiplying by the reciprocal Solution 2.7 Division and Applications c Solve equations of the type a ∙ x = b and x ∙ a = b where a and b may be fractions. DSolve: Slide 10Copyright 2011 Pearson Education, Inc.

11. EXAMPLE Solution 2.7 Division and Applications c Solve equations of the type a ∙ x = b and x ∙ a = b where a and b may be fractions. ESolve: Slide 11Copyright 2011 Pearson Education, Inc.

12. EXAMPLE 30 lb in all n packages in all … Solution Familiarize. Make a drawing. Repeated subtraction or division, will work here. 2.7 Division and Applications d Solve applied problems involving division of fractions. FSofo’s Market pre-packages mozzarella cheese in ¾ pound packages. How many packages can be made from a 30-lb block of cheese? (continued) Slide 12Copyright 2011 Pearson Education, Inc.

13. EXAMPLE Translate. The problem can be translated to the following equation. 2.7 Division and Applications d Solve applied problems involving division of fractions. FContinued (continued) Slide 13Copyright 2011 Pearson Education, Inc.

14. EXAMPLE 2.7 Division and Applications d Solve applied problems involving division of fractions. FContinued (continued) Slide 14Copyright 2011 Pearson Education, Inc. Solve.

15. EXAMPLE Check. If each of the 40 packages took ¾ pound of cheese, we would know that: Our answer checks. State. Sofo’s Market can fill 40 packages with cheese. 2.7 Division and Applications d Solve applied problems involving division of fractions. FContinued Slide 15Copyright 2011 Pearson Education, Inc.