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

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

and

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,

and

.


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.

.

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