# 6.6: Expression Evaluation with Fractions

**At Grade**Created by: CK-12

**Practice**Expression Evaluation with Fractions

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.

\begin{align*}\frac{1}{5} + \frac{2}{5} - \frac{1}{5} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

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

**in an expression. We will need to**

*operation***the expression to find its value.**

*evaluate*
\begin{align*}\frac{9}{10} - \frac{3}{10} + \frac{1}{10}\end{align*} **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.**

\begin{align*}9 - 3 = 6 + 1 = 7\end{align*}

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

\begin{align*}\frac{7}{10}.\end{align*}

**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** \begin{align*}\frac{7}{10}\end{align*}.

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

#### Example A

\begin{align*} \frac{6}{7} - \frac{2}{7} + \frac{1}{7}\end{align*}

**Solution: \begin{align*} \frac{5}{7}\end{align*}**

#### Example B

\begin{align*} \frac{3}{4} + \frac{3}{4} - \frac{1}{4}\end{align*}

**Solution: \begin{align*} \frac{5}{4}\end{align*} = \begin{align*}1 \frac{1}{4}\end{align*}**

#### Example C

\begin{align*} \frac{7}{8} + \frac{3}{8} - \frac{2}{8}\end{align*}

**Solution: \begin{align*} \frac{8}{8}\end{align*} = 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.

\begin{align*}\frac{1}{5} + \frac{2}{5} - \frac{1}{5} = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}

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.

\begin{align*} \frac{3}{5}\end{align*}

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

**Our answer is \begin{align*} \frac{2}{5}\end{align*}.**

### Vocabulary

Here are the vocabulary words in this Concept.

- Like Denominators
- when the denominators of fractions being added or subtracted are the same.

- Simplifying
- dividing the numerator and the denominator of a fraction by its greatest common factor. The result is a fraction is simplest form.

- Difference
- the answer to a subtraction problem

- Numerical Expression
- an expression with multiple numbers and multiple operations

- Operation
- the four operations in math are addition, subtraction, multiplication and division

- Evaluate
- to find the value of a numerical expression.

### Guided Practice

Here is one for you to try on your own.

\begin{align*} \frac{8}{9} + \frac{4}{9} - \frac{1}{9}\end{align*} The fractions in this expression all have a common denominator, so we can add/subtract the numerators in order from left to right.

\begin{align*} 8 + 4 = 12 - 1 = 11\end{align*}

Next, we write this answer over the common denominator.

\begin{align*}\frac{11}{9}\end{align*}

**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.**

\begin{align*}11 \end{align*} \begin{align*}\div\end{align*} 9 \begin{align*}=\end{align*} 1 with two-ninths left over.

**Our final answer is** \begin{align*}1 \frac{2}{9}\end{align*}.

### Video Review

Khan Academy Adding and Subtracting Fractions

### Practice

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

1. \begin{align*} \frac{7}{9} + \frac{2}{9} - \frac{6}{9}\end{align*}

2. \begin{align*} \frac{3}{10} + \frac{4}{10} - \frac{1}{10}\end{align*}

3. \begin{align*} \frac{8}{9} + \frac{1}{9} - \frac{3}{9}\end{align*}

4. \begin{align*} \frac{8}{12} + \frac{1}{12} - \frac{4}{12}\end{align*}

5. \begin{align*} \frac{13}{14} + \frac{3}{14} - \frac{9}{14}\end{align*}

6. \begin{align*} \frac{5}{17} + \frac{3}{17} - \frac{9}{17}\end{align*}

7. \begin{align*} \frac{8}{11} + \frac{2}{11} - \frac{6}{11}\end{align*}

8. \begin{align*} \frac{13}{16} + \frac{1}{16} - \frac{6}{16}\end{align*}

9. \begin{align*} \frac{6}{17} + \frac{3}{17} - \frac{12}{17}\end{align*}

10. \begin{align*} \frac{8}{10} + \frac{9}{10} - \frac{7}{10}\end{align*}

11. \begin{align*} \frac{11}{14} + \frac{3}{14} - \frac{10}{14}\end{align*}

12. \begin{align*} \frac{19}{24} + \frac{13}{24} - \frac{20}{24}\end{align*}

13. \begin{align*} \frac{12}{13} + \frac{1}{13} - \frac{8}{13}\end{align*}

14. \begin{align*} \frac{23}{24} + \frac{1}{24} - \frac{12}{24}\end{align*}

15. \begin{align*} \frac{11}{15} + \frac{2}{15} - \frac{8}{15}\end{align*}

Difference

The result of a subtraction operation is called a difference.Evaluate

To evaluate an expression or equation means to perform the included operations, commonly in order to find a specific value.Like Denominators

Two or more fractions have like denominators when their denominators are the same. "Common denominators" is a synonym for "like denominators".Numerical expression

A numerical expression is a group of numbers and operations used to represent a quantity.Simplify

To simplify means to rewrite an expression to make it as "simple" as possible. You can simplify by removing parentheses, combining like terms, or reducing fractions.### Image Attributions

Here you'll learn to evaluate numerical expressions involving the sums and differences of fractions.

## Concept Nodes:

Difference

The result of a subtraction operation is called a difference.Evaluate

To evaluate an expression or equation means to perform the included operations, commonly in order to find a specific value.Like Denominators

Two or more fractions have like denominators when their denominators are the same. "Common denominators" is a synonym for "like denominators".Numerical expression

A numerical expression is a group of numbers and operations used to represent a quantity.Simplify

To simplify means to rewrite an expression to make it as "simple" as possible. You can simplify by removing parentheses, combining like terms, or reducing fractions.