2. 4.5 Problem Solving: Mixed Numbers and Estimating
Chapter 4 Rational Numbers: Positive and
Negative Fractions

3. 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.
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4. 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 .
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5. 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.
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6. Objective 1: Identify mixed numbers and graph them on a number line.
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7. Objective 2: Rewrite mixed numbers as improper fractions, or the reverse.
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8. 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
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9. Objective 2: Rewrite mixed numbers as improper fractions, or the reverse.
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10. 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.
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11. Objective 2: Rewrite mixed numbers as improper fractions, or the reverse.
Example
(continued)
In other words,
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12. 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.
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13. Objective 3: Estimate the answer and multiply or divide mixed numbers.
Example
Round to the nearest whole number.
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14. Objective 3: Estimate the answer and multiply or divide mixed numbers.
Example
Round to the nearest whole number.
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15. Objective 3: Estimate the answer and multiply or divide mixed numbers.
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16. 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:
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17. 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: =
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18. 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: =
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19. 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: =
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20. 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.
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21. 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.
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22. 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.
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23. Objective 5: Solve application problems containing mixed numbers.
Example
(continued)
Now find the exact answer.
Zenitia worked hours longer on Tuesday.
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