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Estimation of Sums of Mixed Numbers and Fractions

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Estimation of Sums of Mixed Numbers and Fractions

Remember the blueberries from the Add Fractions and Mixed Numbers Concept? Well, there is another blueberry dilemma here.

Teri and Ren finished baking pies and muffins and have moved on t0 scones.

Teri tells Ren that they need 4 \frac{3}{4} cups of blueberries for the scones. Plus she will need an additional \frac{3}{4} of a cup for decorating the topping.

About how many blueberries are need in all?

You can figure out an estimate of this sum. Pay attention to this Concept and you will learn exactly how to do this.

Guidance

Estimation is a method for finding an approximate solution to a problem.

The sum of 22 and 51 is exactly 73. We can estimate the sum by rounding to the tens place and adding 20 + 50. Then we can say the sum of 22 and 51 is “about 70.”

Previously we worked with three benchmarks (0, \frac{1}{2} and 1) to get a sense of the approximate value of different fractions. We can use this same technique to estimate sums of two or more fractions and mixed numbers.

First, we approximate the value of each fraction or mixed number using the benchmarks 0, \frac{1}{2} and 1.

Next, we find the sum of the approximate values.

When you are approximating the value of mixed numbers, first figure out the approximate value of the fraction and then add it to the whole number. For example, the approximate value of 2 \frac{3}{4} is 3 because the approximate value of \frac{3}{4} is 1 (2 +1 = 3).

Even when you are asked to find an exact answer, estimation is a useful way to get an idea of a reasonable solution to a problem. Once you have finished solving for an exact answer to a problem, you can check your answer against the estimate. Refer back to the following steps if necessary.

Estimating sums of fractions and mixed numbers:

  1. Approximate the value of each of the fractions or mixed numbers by using the benchmarks 0, \frac{1}{2} and 1
  2. Add these approximate values to get an estimated sum

Write these steps in your notebook and then continue with the Concept.

Estimate the following sum, \frac{5}{9} + \frac{1}{77}

First, we approximate the value of the individual fractions. \frac{5}{9} is approximately \frac{1}{2} and \frac{1}{77} is approximately 0. Now, we rewrite the problem substituting the approximate values: \frac{1}{2} + \frac{0.5}{9} + \frac{1}{77} is about \frac{1}{2}.

Estimate the following sum, 3 \frac{6}{7} + 1 \frac{4}{9}

First, we approximate the value of each of the mixed numbers. The approximate value of 3 \frac{6}{7} is 4 because the approximate value of the fraction \frac{6}{7} is 1 (3 + 1 = 4). The approximate value of 1 \frac{4}{9} is 1 \frac{1}{2} because the approximate value of \frac{4}{9} is \frac{1}{2}. We rewrite the problem with the approximate values of the mixed numbers and it looks like this: 4 + 1 \frac{1}{2}. We estimate that the sum of 3 \frac{6}{7} and 1 \frac{4}{9} is about 5 \frac{1}{2}.

Try a few on your own. Estimate the following sums.

Example A

\frac{6}{7}+\frac{1}{2}

Solution: 1 + \frac{1}{2} = 1 \frac{1}{2}

Example B

\frac{29}{30}+7 \frac{8}{10}

Solution: 8 + 1 = 9

Example C

1 \frac{1}{2}+ 3 \frac{5}{6}

Solution:1 \frac{1}{2} + 1 = 2 \frac{1}{2}

Now back to the blueberries.

Teri and Ren finished baking pies and muffins and have moved on t0 scones.

Teri tells Ren that they need 4 \frac{3}{4} cups of blueberries for the scones. Plus she will need an additional \frac{3}{4} of a cup for decorating the topping.

About how many blueberries are need in all?

To figure out this estimate, we must first use benchmarks to estimate each fraction or mixed number.

4 \frac{3}{4} = 5

\frac{3}{4} = 1

5 + 1 = 6

Teri and Ren will need about 6 cups of blueberries. This is our estimate.

Vocabulary

Fraction
a part of a whole
Mixed Number
a whole number and a fraction

Guided Practice

Here is one for you to try on your own.

\frac{18}{20} + 5 \frac{9}{10}

Answer

First, we have to estimate each fraction or mixed number by using the common benchmarks.

\frac{18}{20} = 1

5 \frac{9}{10} = 6

Here is our solution.

1 + 6 = 7

This is our estimate of the sum.

Video Review

http://www.youtube.com/watch?v=TVK_T3TgU5k - This is a James Sousa video on adding mixed numbers. It is a supporting video for this Concept.

Practice

Directions: Estimate the sums.

1. \frac{1}{29} + \frac{4}{5}

2. \frac{9}{11} + \frac{4}{10}

3. \frac{2}{5} + \frac{12}{13}

4. \frac{2}{71} + \frac{1}{29}

5. \frac{1}{29} + \frac{4}{5}

6. \frac{3}{20} + \frac{14}{15}

7. \frac{6}{7} + \frac{1}{5}

8. \frac{9}{18} + \frac{5}{6}

9. \frac{12}{13} + \frac{1}{25}

10. \frac{7}{9} + \frac{1}{30}

Directions: Estimate the sums.

11. 3 \frac{6}{7}+ 2 \frac{10}{11}

12. 8 \frac{1}{12} + 6 \frac{3}{7}

13. 2 \frac{9}{10} + 3 \frac{1}{17}

14. 1 \frac{2}{12} + \frac{44}{46}

15. 8 \frac{1}{29} + 10 \frac{4}{5}

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