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,
 * $$\frac{75}{100} = \frac{75 {\color{Red}\div 5}}{100 {\color{Red}\div 5}} = \frac{15}{20}$$

and
 * $$\frac{15}{20} = \frac{15 {\color{Red}\div 5}}{20 {\color{Red}\div 5}} = \frac{3}{4}$$.

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.
 * $$\frac{3}{4} = \frac{3 {\color{Red}\div 1}}{4 {\color{Red}\div 1}} = \frac{3}{4}$$.

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