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,

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

and

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

and

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

When you are [[../Adding fractions|adding fractions]] or [[../Subtracting fractions|subtracting fractions]], you will want to find an equivalent fraction with a certain denominator. For example,

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

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

$\frac{3}{5}=\frac{3\times 9}{5\times 9}=\frac{27}{45}.$

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