# Prealgebra for Two-Year Colleges/Appendix (procedures)/Finding equivalent fractions

Equivalent fractions represent the same number, although they are written differently. For example,

$\frac{1}{2}$ and $\frac{2}{4}$

represent the same amount.

You can find and equivalent fraction by multiplying the numerator and denominator by the same number. For example,

$\frac{1}{2} = \frac{1 {\color{Red} \times 2}}{2 {\color{Red} \times 2}} = \frac{2}{4}$

and

$\frac{1}{2} = \frac{1 {\color{Red} \times 3}}{2 {\color{Red} \times 3}} = \frac{3}{6}$

and

$\frac{1}{2} = \frac{1 {\color{Red} \times 4}}{2 {\color{Red} \times 4}} = \frac{4}{8}.$

When you are adding fractions or subtracting fractions, you will want to find an equivalent fraction with a certain denominator. For example,

$\frac{3}{5} = \frac{\color{Blue}\mathrm{?}}{45}$

In this case, you can see that you need to multiply the numerator and denominator by 9, because 45 divided by 5 is 9. So

$\frac{3}{5} = \frac{3{\color{Red}\times9}}{5{\color{Red}\times9}} = \frac{\color{Blue}27}{45}.$

You are also allowed to divide the numerator and denominator by the same number. We usually call this reducing fractions.