POC01234 SCU Online Proof of Concept

Simplifying fractions using common factors

We can simplify fractions if the numerator and the denominator can both be divided by the same number (we can say the numerator and the denominator ‘have a common factor’).

In the case of \(\frac{4}{8}\), both numerator and denominator can be divided by 4 (4 is the common factor of 4 and 8).

\[4\div4=1\]

\[8\div4=2\]

 

Dividing both numerator and denominator by the same number doesn’t change the value of the fraction.

\[\frac{4}{8}=\frac{4\div4}{8\div4}=\frac{1}{2}\]

4 slices of an 8-slice chocolate cake is still \(\frac{1}{2}\) of an 8-slice chocolate cake. The two fractions are equivalent.

We could have also simplified \(\frac{4}{8}\) as \(\frac{2}{4}\)

\(\frac{4}{8}\) of a chocolate cake = \(\frac{2}{4}\) of a chocolate cake.

But \(\frac{2}{4}\) of a chocolate cake also equals \(\frac{1}{2}\) of a chocolate cake – as 2 and 4 can both be divided by the same number to simplify \(\frac{2}{4}\) further (2 is the common factor of 2 and 4).

\[2\div2=1\]

\[4\div2=2\]

so

\[\begin{align}\frac{2}{4}&=\frac{2\div2}{4\div2}\\&=\frac{1}{2}\end{align}\]

So we can say that both \(\frac{4}{8}\) and \(\frac{2}{4}\) expressed in their simplest form \(=\frac{1}{2}\)

 

Any fraction can be expressed in its simplest form by dividing both the numerator and the denominator by the highest (or largest) common factor.

If there is no common factor (higher than 1), the fraction is already in its simplest form.