4.5 Problem Solving: Mixed Numbers and Estimating Chapter 4 Rational Numbers: Positive and Negative Fractions

4.5 Problem Solving: Mixed Numbers and Estimating Objectives Identify mixed numbers and graph them on a number line. Rewrite mixed numbers as improper fractions, or the reverse. Estimate the answer and multiply or divide mixed numbers. Estimate the answer and add or subtract mixed numbers. Solve application problems containing mixed numbers. Copyright © 2010 Pearson Education, Inc. All rights reserved.

Objective 1: Identify mixed numbers and graph them on a number line. When a fraction and a whole number are written together, the result is a mixed number. As the diagram below shows, the mixed number is equivalent to the improper fraction . Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 4.5 - 4

Objective 1: Identify mixed numbers and graph them on a number line. Example Display the mixed numbers and on the number line. The number line shows the following. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 4.5 - 5

Objective 1: Identify mixed numbers and graph them on a number line. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 4.5 - 6

Objective 2: Rewrite mixed numbers as improper fractions, or the reverse. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 4.5 - 7

Objective 2: Rewrite mixed numbers as improper fractions, or the reverse. Example Write as an improper fraction (numerator greater than denominator). Step 1 Step 2 Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 4.5 - 8

Objective 2: Rewrite mixed numbers as improper fractions, or the reverse. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 4.5 - 9

Objective 2: Rewrite mixed numbers as improper fractions, or the reverse. Example Write as an equivalent mixed number in simplest form. Divide 17 by 5. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 4.5 - 10

Objective 2: Rewrite mixed numbers as improper fractions, or the reverse. Example (continued) In other words, Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 4.5 - 11

Objective 2: Rewrite mixed numbers as improper fractions, or the reverse. Example Write as an equivalent mixed number in simplest form. Divide 26 by 4. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 4.5 - 12

Objective 3: Estimate the answer and multiply or divide mixed numbers. Example Round to the nearest whole number. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 4.5 - 13

Objective 3: Estimate the answer and multiply or divide mixed numbers. Example Round to the nearest whole number. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 4.5 - 14

Objective 3: Estimate the answer and multiply or divide mixed numbers. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 4.5 - 15

Objective 3: Estimate the answer and multiply or divide mixed numbers. Example Consider the product . First, round the numbers and estimate the answer. Then find the exact answer. Estimate: Exact Product: Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 4.5 - 16

Objective 3: Estimate the answer and multiply or divide mixed numbers. Example Consider the quotient . First, round the numbers and estimate the answer. Then find the exact answer. Estimate: Exact Quotient: = Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 4.5 - 17

Objective 4: Estimate the answer and add or subtract mixed numbers. Example Consider the sum . First, round the numbers and estimate the answer. Then find the exact answer. Estimate: Exact Sum: = Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 4.5 - 18

Objective 4: Estimate the answer and add or subtract mixed numbers. Example Consider the difference . First, round the numbers and estimate the answer. Then find the exact answer. Estimate: Exact Difference: = Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 4.5 - 19

Objective 5: Solve application problems containing mixed numbers. Example Gary needs to haul tons of sand to a construction site. His truck can carry tons. How many trips will he need to make? First, estimate the answer. Using the rounded numbers in the problem makes it easier to see that you need to divide. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 4.5 - 20

Objective 5: Solve application problems containing mixed numbers. Example (continued) Now find the exact answer. Gary needs to make 7 trips to haul all the sand. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 4.5 - 21

Objective 5: Solve application problems containing mixed numbers. Example Zenitia worked hours on Monday and hours on Tuesday. How much longer did she work on Tuesday than on Monday? First, estimate the answer. Using the rounded numbers in the problem makes it easier to see that you need to subtract. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 4.5 - 22

Objective 5: Solve application problems containing mixed numbers. Example (continued) Now find the exact answer. Zenitia worked hours longer on Tuesday. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 4.5 - 23