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

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

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

represent the same amount.

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

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

and

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

and

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

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

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

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

${\displaystyle {\frac {3}{5}}={\frac {3{\color {Red}\times 9}}{5{\color {Red}\times 9}}}={\frac {\color {Blue}27}{45}}.}$

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