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# 6.6: Expression Evaluation with Fractions

Difficulty Level: At Grade Created by: CK-12
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Practice Expression Evaluation with Fractions
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Have you ever shared a sandwich with someone else? Sharing involves fractions. Take a look.

Travis and his Uncle are eating a foot long sandwich on their lunch break. First, the sandwich had been cut into fifths, so Travis took one fifth, then added two - fifths and then gave one - fifth back to his Uncle.

Here is what the numerical expression looked like.

$\frac{1}{5} + \frac{2}{5} - \frac{1}{5} = \underline{\;\;\;\;\;\;\;\;\;}$

To figure this out, Travis will need to evaluate the numerical expression. Let's stop right there.

This Concept is all about evaluating numerical expressions. Evaluating this one will make perfect sense by the end of the Concept.

### Guidance

Sometimes, we can have a numerical expression that involves both the sums and differences of fractions with common denominators. This means that we will see more than one operation in an expression. We will need to evaluate the expression to find its value.

$\frac{9}{10} - \frac{3}{10} + \frac{1}{10}$

To evaluate this expression, we first need to ensure that the fractions all have a same common denominator. In this case, they all have a common denominator of 10.

Next, we work with the numerators. We are going to add or subtract in order from left to right.

$9 - 3 = 6 + 1 = 7$

Our final step is to put this answer over the common denominator.

$\frac{7}{10}.$

Before we can say our answer is finished, we need to see if we can simplify our answer. There isn’t a common factor between 7 and 10 because 7 is prime, so our fraction is in its simplest form.

Our final answer is $\frac{7}{10}$ .

Evaluate the following numerical expressions. Be sure that your answer is in simplest form.

#### Example A

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

Solution: $\frac{5}{7}$

#### Example B

$\frac{3}{4} + \frac{3}{4} - \frac{1}{4}$

Solution: $\frac{5}{4}$ = $1 \frac{1}{4}$

#### Example C

$\frac{7}{8} + \frac{3}{8} - \frac{2}{8}$

Solution: $\frac{8}{8}$ = 1

Now back to Travis and the sandwich.

Travis and his Uncle are eating a foot long sandwich on their lunch break. First, the sandwich had been cut into fifths, so Travis took one fifth, then added two - fifths and then gave one - fifth back to his Uncle.

Here is what the numerical expression looked like.

$\frac{1}{5} + \frac{2}{5} - \frac{1}{5} = \underline{\;\;\;\;\;\;\;\;\;}$

To figure this out, Travis will need to evaluate the numerical expression.

First, we can add the numerators of the first two fractions with the denominators staying the same.

$\frac{3}{5}$

Next, we can subtract one - fifth from this sum.

Our answer is $\frac{2}{5}$ .

### Guided Practice

Here is one for you to try on your own.

$\frac{8}{9} + \frac{4}{9} - \frac{1}{9}$

The fractions in this expression all have a common denominator, so we can add/subtract the numerators in order from left to right.

$8 + 4 = 12 - 1 = 11$

Next, we write this answer over the common denominator.

$\frac{11}{9}$

Uh oh! We have an improper fraction. An improper fraction is NOT in simplest form, so we need to change this to a mixed number.

$11$ $\div$ 9 $=$ 1 with two-ninths left over.

Our final answer is $1 \frac{2}{9}$ .

### Explore More

Directions : Evaluate the following numerical expressions. Be sure your answer is in simplest form.

1. $\frac{7}{9} + \frac{2}{9} - \frac{6}{9}$

2. $\frac{3}{10} + \frac{4}{10} - \frac{1}{10}$

3. $\frac{8}{9} + \frac{1}{9} - \frac{3}{9}$

4. $\frac{8}{12} + \frac{1}{12} - \frac{4}{12}$

5. $\frac{13}{14} + \frac{3}{14} - \frac{9}{14}$

6. $\frac{9}{17} - \frac{5}{17} + \frac{3}{17}$

7. $\frac{8}{11} + \frac{2}{11} - \frac{6}{11}$

8. $\frac{13}{16} + \frac{1}{16} - \frac{6}{16}$

9. $\frac{12}{17} - \frac{6}{17} + \frac{3}{17}$

10. $\frac{8}{10} + \frac{9}{10} - \frac{7}{10}$

11. $\frac{11}{14} + \frac{3}{14} - \frac{10}{14}$

12. $\frac{19}{24} + \frac{13}{24} - \frac{20}{24}$

13. $\frac{12}{13} + \frac{1}{13} - \frac{8}{13}$

14. $\frac{23}{24} + \frac{1}{24} - \frac{12}{24}$

15. $\frac{11}{15} + \frac{2}{15} - \frac{8}{15}$

Oct 29, 2012

Feb 15, 2015