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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.

15+2515=\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 operation in an expression. We will need to evaluate the expression to find its value.

910310+110\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.

93=6+1=7\begin{align*}9 - 3 = 6 + 1 = 7\end{align*}

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

710.\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 710\begin{align*}\frac{7}{10}\end{align*}.

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

#### Example A

6727+17\begin{align*} \frac{6}{7} - \frac{2}{7} + \frac{1}{7}\end{align*}

Solution: 57\begin{align*} \frac{5}{7}\end{align*}

#### Example B

34+3414\begin{align*} \frac{3}{4} + \frac{3}{4} - \frac{1}{4}\end{align*}

Solution: 54\begin{align*} \frac{5}{4}\end{align*} = 114\begin{align*}1 \frac{1}{4}\end{align*}

#### Example C

78+3828\begin{align*} \frac{7}{8} + \frac{3}{8} - \frac{2}{8}\end{align*}

Solution: 88\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.

15+2515=\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.

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

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

Our answer is 25\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.

89+4919\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.

8+4=121=11\begin{align*} 8 + 4 = 12 - 1 = 11\end{align*}

Next, we write this answer over the common denominator.

119\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.

11\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 129\begin{align*}1 \frac{2}{9}\end{align*}.

### Practice

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

1. 79+2969\begin{align*} \frac{7}{9} + \frac{2}{9} - \frac{6}{9}\end{align*}

2. 310+410110\begin{align*} \frac{3}{10} + \frac{4}{10} - \frac{1}{10}\end{align*}

3. 89+1939\begin{align*} \frac{8}{9} + \frac{1}{9} - \frac{3}{9}\end{align*}

4. 812+112412\begin{align*} \frac{8}{12} + \frac{1}{12} - \frac{4}{12}\end{align*}

5. 1314+314914\begin{align*} \frac{13}{14} + \frac{3}{14} - \frac{9}{14}\end{align*}

6. 517+317917\begin{align*} \frac{5}{17} + \frac{3}{17} - \frac{9}{17}\end{align*}

7. 811+211611\begin{align*} \frac{8}{11} + \frac{2}{11} - \frac{6}{11}\end{align*}

8. 1316+116616\begin{align*} \frac{13}{16} + \frac{1}{16} - \frac{6}{16}\end{align*}

9. 617+3171217\begin{align*} \frac{6}{17} + \frac{3}{17} - \frac{12}{17}\end{align*}

10. 810+910710\begin{align*} \frac{8}{10} + \frac{9}{10} - \frac{7}{10}\end{align*}

11. 1114+3141014\begin{align*} \frac{11}{14} + \frac{3}{14} - \frac{10}{14}\end{align*}

12. 1924+13242024\begin{align*} \frac{19}{24} + \frac{13}{24} - \frac{20}{24}\end{align*}

13. 1213+113813\begin{align*} \frac{12}{13} + \frac{1}{13} - \frac{8}{13}\end{align*}

14. 2324+1241224\begin{align*} \frac{23}{24} + \frac{1}{24} - \frac{12}{24}\end{align*}

15. 1115+215815\begin{align*} \frac{11}{15} + \frac{2}{15} - \frac{8}{15}\end{align*}

### Vocabulary Language: English

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.

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