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.