Expansion of Fractions

Expansion of Fractions

The process of making a 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?’

Let’s find out;

Let the fraction be;  \( \displaystyle \frac{2}{3} \)

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

Let’s expand this fraction by 2 without changing its value. We will carry out the expansion with multiplication. We know this; when we multiply a unit/ a number 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?

By expansion, the value of the fraction does not change; you only have more pieces that are smaller. While we had 2 big pieces with the first fraction, with the second fraction we have 4 pieces. The total value for both 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 \( \displaystyle 3 \)

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

In conclusion;

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 controlling the unit fraction, we make the fraction more useful. 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.