Expansion of Fractions

Expansion of Fractions

The process of making the unit fraction  smaller is called expansion. You may say, ‘How is it that the process of fraction becoming smaller is called expansion, isn’t this strange?’

We will find out;

Let’s take into account the fraction ; \( \displaystyle \frac{2}{3} \)

The unit fraction of  \( \displaystyle \frac{2}{3} \)  is \( \displaystyle \frac{1}{3} \)

Let’s expand the fraction by 2 without changing it’s value. I will carry out the expansion with multiplication. We know this; when we multiply a unit/ a thing by 1, it remains the same, it doesn’t change. So in fact, we do not multiply with 2 but we multiply with 1.

\( \displaystyle \frac{2}{2}=1 \)

Let’s calculate; 

\( \displaystyle \frac{2}{3}. \frac{2}{2}=\frac{4}{6}\)

What have we done?

With expansion, the value of the fraction does not change; you only have more pieces that are smaller. Whilst we had 2 big pieces with the first fraction, with the second fraction we have 4 pieces. The total value for both of them is the same. As you can see, the part that is highlighted in blue is the same.

Here we expanded the fraction by 2, you can expand it as much as you like.

Let’s expand \( \displaystyle \frac{2}{3} \) by \( \displaystyle 3 \)

\( \displaystyle \frac{2}{3}. \frac{3}{3}=\frac{6}{9}\)

Let’s summarise the topic;

The unit fractions have gotten smaller and smaller, yet the value of the fraction hasn’t changed.

Let’s give some examples of expansions in fractions.

\( \displaystyle \frac{4}{5}. \frac{7}{7}=\frac{28}{35}\)

\( \displaystyle \frac{1}{6}. \frac{4}{4}=\frac{4}{24}\)

\( \displaystyle \frac{8}{5}. \frac{2}{2}=\frac{16}{10}\)

\( \displaystyle \frac{3}{4}. \frac{100}{100}=\frac{300}{400}\)

So, why do we need expansion in fractions?

Sometimes by playing with the unit fraction, we make the fraction more useful to us. For example, addition and subtraction in fractions or in fact for division in fractions we need to pair the unit fractions. To pair the unit fractions there is a need to simply and expand the fractions.