# How do you add or subtract fractions?

Jan 18, 2017

Give them a common denominator...

#### Explanation:

The top of a fraction is called the numerator and the bottom the denominator...

$\text{numerator"/"denominator}$

In order to add or subtract two fractions they need to have the same denominator. Then you can simply add or subtract the numerators.

What if they don't?

If you multiply both the numerator and denominator of a fraction by the same non-zero number, then the resulting fraction is equivalent to the one you started with.

So given a couple of fractions $\frac{a}{b}$ and $\frac{c}{d}$ to add, we could proceed as follows:

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

In practice you really want to use a multiplier that results in the denominator of both fractions being the least common multiple (LCM) of the two denominators.

For example, the LCM of $6$ and $10$ is $30$, so:

$\frac{1}{6} + \frac{1}{10} = \frac{1 \cdot 5}{6 \cdot 5} + \frac{1 \cdot 3}{10 \cdot 3} = \frac{5}{30} + \frac{3}{30} = \frac{5 + 3}{30} = \frac{8}{30} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \cdot 4}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \cdot 15} = \frac{4}{15}$