Chapter 2 Multiplying and Dividing Fractions © 2010 Pearson Education, Inc. All rights reserved.

2.6 Applications of Multiplication Objectives Slide Solve fraction application problems using multiplication. Copyright © 2010 Pearson Education, Inc. All rights reserved.

Many application problems are solved by multiplying fractions. Use the following indicator words for multiplication. product double triple times of (when “of” follows a fraction) twice twice as much Slide Copyright © 2010 Pearson Education, Inc. All rights reserved.

Megan Paten has of her income deposited into a vacation fund. In one pay period she earns $966. How much money does she deposit in her vacation fund per pay period? Parallel Example 1 Applying Indicator Words Step 1 Step 2 Slide Read the problem. The problem asks us to find the amount of money she deposits into her vacation fund. Work out a plan. The indicator word is of; Paten deposits of her income. When it follows a fraction, the word of indicates multiplication, so find the amount deposited by multiplying and $966. Copyright © 2010 Pearson Education, Inc. All rights reserved.

Megan Paten has of her income deposited into a vacation fund. In one pay period she earns $966. How much money does she deposit in her vacation fund per pay period? Parallel Example 1 continued Applying Indicator Words Step 3 Step 4 Slide Estimate a reasonable answer. Round the income of $966 to $1000. Then divide 1000 by ten to find of the income. Our estimate is $1000 ÷ 10 = $100. Solve the problem Copyright © 2010 Pearson Education, Inc. All rights reserved.

Parallel Example 1 continued Applying Indicator Words Slide Step 5State the answer. Paten deposits $138 in her vacation fund per pay period. Step 6Check. The exact answer $138, is close to the estimate of $100. Copyright © 2010 Pearson Education, Inc. All rights reserved. Megan Paten has of her income deposited into a vacation fund. In one pay period she earns $966. How much money does she deposit in her vacation fund per pay period?

Of the 48 kittens in the shelter, are males. How many male kittens are there? Parallel Example 2 Solving a Fraction Application Problem Step 1 Step 2 Slide Read the problem. The problem asks to find the number of male kittens in the shelter. Work out a plan. Reword the problem to read Indicator word for multiplication when it follows a fraction. Copyright © 2010 Pearson Education, Inc. All rights reserved.

Of the 48 kittens in the shelter, are males. How many male kittens are there? Parallel Example 2 continued Solving a Fraction Application Problem Step 3 Step 4 Slide Estimate a reasonable answer. Round the number of kittens from 48 to 50. Then of 50 is 25. Since is more than, our estimate is that more than 25 kittens are males. Solve the problem. 16 Copyright © 2010 Pearson Education, Inc. All rights reserved. 1

Parallel Example 2 continued Solving a Fraction Application Problem Slide Step 5State the answer. There are 32 male kittens in the shelter. Step 6Check. The exact answer 32, fits our estimate of more than 25. Of the 48 kittens in the shelter, are males. How many male kittens are there? Copyright © 2010 Pearson Education, Inc. All rights reserved.

In Anne’s sport card collection, of all of her cards are baseball cards. Of those baseball cards, of them are of the New York Yankees. What fraction of the total cards are of the New York Yankees? Parallel Example 3 Finding a Fraction of a Fraction Step 1 Step 2 Slide Read the problem. The problem asks for the fraction of the baseball cards that are the New York Yankees. Work out a plan. Reword the problem to read Indicator word for multiplication when it follows a fraction Copyright © 2010 Pearson Education, Inc. All rights reserved.

Parallel Example 3 continued Finding a Fraction of a Fraction Step 3 Step 4 Slide Estimate a reasonable answer. If the cards are divided into 2 equal piles and each of these pile was divided into 3 equal parts, we would have 2 ∙ 3 = 6 equal parts. Our estimate is. Solve the problem. In Anne’s sport card collection, 1/2 of all of her cards are baseball cards. Of those baseball cards, 1/3 of them are of the New York Yankees. What fraction of the total cards are of the New York Yankees? Copyright © 2010 Pearson Education, Inc. All rights reserved.

Parallel Example 3 continued Finding a Fraction of a Fraction Slide Step 5State the answer. The New York Yankees cards make up of Anne’s collection. Step 6 Check. The exact answer, matches our estimate. Copyright © 2010 Pearson Education, Inc. All rights reserved. In Anne’s sport card collection, of all of her cards are baseball cards. Of those baseball cards, of them are of the New York Yankees. What fraction of the total cards are of the New York Yankees?

The circle graph, or pie chart, shows where children 8 to 17 years of age make food purchases when away from home. If 2500 children were in the survey, find the number of children who buy food from the vending machine. Parallel Example 4 Using Fractions with a Circle Graph Slide Copyright © 2010 Pearson Education, Inc. All rights reserved.

Parallel Example 4 continued Using Fractions with a Circle Graph Step 1 Step 2 Slide Read the problem. The problem asks for the number of children who buy food from the vending machine. Work out a plan. Reword the problem to read Indicator word for multiplication when it follows a fraction Step 3Estimate a reasonable answer. ¼ of 2500 people is 625 people. 1/5 is less than ¼, so our estimate is less than 625 people. Copyright © 2010 Pearson Education, Inc. All rights reserved.

Parallel Example 4 continued Using Fractions with a Circle Graph Step 4 Step 5 Slide Step 6 Solve the problem State the answer. 500 children buy food from the vending machine. Check. The exact answer, 500 children, fits our estimate of “less than 625 children.” Copyright © 2010 Pearson Education, Inc. All rights reserved.