 # 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.

Rule

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

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:

$\begin{array}{llll}\hfill \frac{4}{17}+\frac{8}{17}+\frac{1}{17}+\frac{3}{17}& =\frac{4+8+1+3}{17}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\frac{16}{17}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

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

### SubtractionofFractionswithEqualDenominators

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

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:

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