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How to Add and Subtract Fractions with Equal Denominators

In fractional arithmetic, addition and subtraction follow the same rules. When you add two fractions, you add the numerators to each other. When you subtract two fractions from each other, you subtract the numerators from each other. When adding and subtracting fractions, there are two cases you will encounter: The case where the denominators have the same value, and the case where the denominators are different from each other.

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Rule

Addition of Fractions with Equal Denominators

\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

When adding fractions, you should begin by looking at the denominators. If the fractions have equal denominators, you can just add the numerators together and keep the denominator as it is.

Example 1

Find $\frac{1}{5} + \frac{2}{5}$ .

You can see that the denominator is $5$ in both of the fractions, which means that you can just add the numerators to each other. It looks like this:

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

Example 2

Find $\frac{2}{9} + \frac{1}{9} + \frac{5}{9}$ .

You can see that the denominator is $9$ in all of the fractions, which means that you can just add the numerators to each other. It looks like this:

\frac{2}{9} + \frac{1}{9} + \frac{5}{9} = \frac{2 + 1 + 5}{9} = \frac{8}{9}

Example 3

Find $\frac{4}{7} + \frac{3}{7}$ .

You can see that the denominator is $7$ in both of the fractions, which means that you can just add the numerators to each other. It looks like this:

\frac{4}{7} + \frac{3}{7} = \frac{4 + 3}{7} = \frac{7}{7} = 1

Example 4

Find $\frac{4}{17} + \frac{8}{17} + \frac{1}{17} + \frac{3}{17}$ .

You can see that the denominator is $17$ in all of the fractions, which means that you can just add the numerators to each other. It looks like this:

\begin{array}{l} \frac{4}{17} + \frac{8}{17} + \frac{1}{17} + \frac{3}{17} & = \frac{4 + 8 + 1 + 3}{17} \\ = \frac{16}{17} \end{array}

\frac{4}{17} + \frac{8}{17} + \frac{1}{17} + \frac{3}{17} = \frac{4 + 8 + 1 + 3}{17} = \frac{16}{17}

Two jumps of length 1/5 on the number line from 1/5 to 3/5

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When subtracting fractions, you should begin by looking at the denominators. If the fractions have equal denominators, you can just subtract the numerators from each other and keep the denominator as it is.

Rule

Subtraction of Fractions with Equal Denominators

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

Example 5

Find $\frac{4}{7} - \frac{2}{7}$ .

You can see that the denominator is $7$ in both of the fractions, which means that you can just subtract the numerators from each other. It looks like this:

\frac{4}{7} - \frac{2}{7} = \frac{4 - 2}{7} = \frac{2}{7}

Example 6

Find $\frac{- 4}{17} - \frac{8}{17} - \frac{3}{17}$ .

You can see that the denominator is $17$ in all of the fractions, which means that you can just subtract the numerators from each other. It looks like this:

\frac{- 4}{17} - \frac{8}{17} - \frac{3}{17} = \frac{- 4 - 8 - 3}{17} = \frac{- 15}{17}

Example 7

Find $\frac{- 2}{9} - \frac{1}{9} - \frac{5}{9}$ .

You can see that the denominator is $9$ in all of the fractions, which means that you can just subtract the numerators from each other. It looks like this:

\frac{- 2}{9} - \frac{1}{9} - \frac{5}{9} = \frac{- 2 - 1 - 5}{9} = \frac{- 8}{9}

Example 8

Find $\frac{13}{9} - \frac{4}{9}$ .

You can see that the denominator is $9$ in both of the fractions, which means that you can just subtract the numerators from each other. It looks like this:

\frac{13}{9} - \frac{4}{9} = \frac{13 - 4}{9} = \frac{9}{9} = 1

Two jumps of length 1/7 on the number line from 4/7 to 2/7

Think About This

Fraction arithmetic will follow you throughout your years in school. You will work with fractions until the day you learning mathematics. Being able to do arithmetic with fractions is just as important as doing arithmetic with integers.

In social studies, you will encounter fractions in various explanations of population and politics.

If you decide to become super good at fractions and become comfortable with the methods connected to them, your future self will be grateful. Fractions will be important throughout all grade levels!

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How to Add and Subtract Fractions with Different Denominators

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