More About Fraction Operations

Fraction operations are among the core math competencies taught in elementary school, although the ability of conduct such operations can suffer a bit without practicing it frequently.

● The most basic fraction operation is the sum of two fractions. For example, we may want to compute:

\[\frac{1}{3}+\frac{3}{4}\]

How to we conduct this operation? First, we need to find a common denominator. In this case, the common denominator is 12. The idea is to rewrite each fraction so that to have them both with the same denominator, and that is achieved by amplifying the fractions, so that each fraction has the same denominator. In this example, the common denominator is 12, so we conduc the following amplifications:

\[\frac{1}{3} = \frac{1}{3} \cdot \frac{4}{4} = \frac{4}{12}\] \[\frac{3}{4} = \frac{3}{4} \cdot \frac{3}{3} = \frac{9}{12}\]

So now that we have both fractions expressed with the same denominator, then the sum of the fractions is easy to calculate. We get

\[\frac{1}{3}+\frac{3}{4} = \frac{4}{12}+\frac{9}{12} = \frac{4+9}{12} = \frac{13}{12} \]

The process of finding a common denominator is also used to compute the difference between fractions

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Make sure you check our algebra calculators , that includes an array that goes way beyond fractions operations.