Method

Simplifying a Fraction

Fractions of the same value can be written using different pairs of numerators and denominators. This is why some fractions can be simplified to equivalent fractions with a smaller numerator and denominator. Consider the following example. 18/66 In order to simplify this fraction, there are three steps to follow.

Determine Whether the Fraction Can Be Simplified

To determine whether the given fraction can be simplified, split the numerator and denominator into prime factors and see if there are any common factors other than 1. 18 &= 2* 3* 3 66 &= 2* 3* 11 The numerator and denominator share factors 2 and 3. Therefore, the fraction can be simplified. If the numerator and denominator did not have common factors other than 1, the fraction would be said to be simplified or written in its simplest form.

Find the Greatest Common Factor

The greatest common factor (GCF) of the numbers 18 and 66 can be found by multiplying all their common factors. GCF(18,66) = 2* 3= 6 If the numerator and denominator share only one common factor, then that factor is their GCF.

Reduce the Fraction

Finally, to reduce the fraction, divide its numerator and denominator by their GCF. 18/66=18/ 6/66/ 6=3/11 As a result, an equivalent fraction of 311 was obtained. It is the simplest form of the given fraction 1866.

Extra

Simplification of Different Fractions

The applet below illustrates how different fractions are simplified.

$Applet that shows how to simplify different fractions$

Extra

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