Prealgebra for Two-Year Colleges/Appendix (procedures)/Reducing fractions

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

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

represent the same amount. The latter fraction has a smaller denominator, so we say the fraction has been reduced.

You can reduce a fraction by dividing the numerator and denominator by the same number. For example,

$\frac{75}{100}=\frac{75÷5}{100÷5}=\frac{15}{20}$

and

$\frac{15}{20}=\frac{15÷5}{20÷5}=\frac{3}{4}$.

When we ask you to simplify a fraction or reduce a fraction such as 75/100, we want you to find the equivalent fraction with the smallest possible denominator. In this case, the fully reduced form is 3/4. The only number that we could divided into both 3 and 4 would be 1, but that would not reduce the fraction any further.

$\frac{3}{4}=\frac{3÷1}{4÷1}=\frac{3}{4}$.

You are also allowed to multiply the numerator and denominator by the same number. We usually call this [[../Finding equivalent fractions|finding equivalent fractions]].