2. CHAPTER 3 Fraction Notation: Multiplication and Division Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 3.1Multiples and Divisibility 3.2Factorizations 3.3Fractions and Fraction Notation 3.4Multiplication and Applications 3.5Simplifying 3.6Multiplying, Simplifying, and More with Area 3.7Reciprocals and Division 3.8Solving Equations: The Multiplication Principle

3. OBJECTIVES 3.4 Multiplication and Applications Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aMultiply an integer and a fraction. bMultiply using fraction notation. cSolve problems involving multiplication of fractions.

4. 3.4 Multiplication and Applications a Multiply an integer and a fraction. Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

5. Title 3.4 Multiplication and Applications Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

6. EXAMPLE 3.4 Multiplication and Applications a Multiply an integer and a fraction. Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Multiply.

7. EXAMPLE 3.4 Multiplication and Applications a Multiply an integer and a fraction. Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

8. 3.4 Multiplication and Applications b Multiply using fraction notation. Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To visualize we first represent. Next, we divide the shaded area into 5 equal parts (using horizontal lines) and take 2 of them.

9. 3.4 Multiplication and Applications b Multiply using fraction notation. Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The entire object has now been divided into 20 parts, and we have shaded 6 of them twice. Thus,

10. Title 3.4 Multiplication and Applications Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

11. EXAMPLE 3.4 Multiplication and Applications b Multiply using fraction notation. Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Multiply.

12. EXAMPLE 3.4 Multiplication and Applications c Solve problems involving multiplication of fractions. 9 Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. A dude ranch owns a square mile of land. The owner gives of it to her daughter who, in turn, gives of her share to her son. How much land goes to the daughter’s son?

13. EXAMPLE 3.4 Multiplication and Applications c Solve problems involving multiplication of fractions. 9 Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1. Familiarize.

14. EXAMPLE 3.4 Multiplication and Applications c Solve problems involving multiplication of fractions. 9 Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

15. EXAMPLE 3.4 Multiplication and Applications c Solve problems involving multiplication of fractions. 9 Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 2. Translate. We let n = the part of the land that goes to the daughter’s son. 3. Solve.

16. EXAMPLE 3.4 Multiplication and Applications c Solve problems involving multiplication of fractions. 9 Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 5. State. The daughter’s son gets of a square mile of land. 4. Check. We can check this in the figure, where we see that 8 of 15 equally sized parts will go to the daughter’s son.

17. EXAMPLE 3.4 Multiplication and Applications c Solve problems involving multiplication of fractions. 11 Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. A recipe for oatmeal chocolate chip cookies calls for cup of rolled oats. Monica is making of the recipe. How much oats should she use?

18. EXAMPLE 3.4 Multiplication and Applications c Solve problems involving multiplication of fractions. 11 Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1. Familiarize. We let n = the amount of oats that Monica should use.

19. EXAMPLE 3.4 Multiplication and Applications c Solve problems involving multiplication of fractions. 11 Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 2. Translate. 3. Solve.

20. EXAMPLE 3.4 Multiplication and Applications c Solve problems involving multiplication of fractions. 11 Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4. Check. We check by repeating the calculation. This is left to the student. 5. State. Monica should use cup of oats.