2.04 Fractions of a quantity

Fractions describe parts of a whole, but they can also describe parts of a quantity.

Find \dfrac{1}{12} of 36.

Let's start by drawing a grid of 36.

To find one twelfth, we split this grid into 12 equal parts.

Looking at the pieces, each piece has 3 squares. So \dfrac{1}{12} of 36 is 3.

We can also work this out using arithmetic. We know that \dfrac{1}{12} of 36 can be written using multiplication, \dfrac{1}{12} \times 36.

This is the same as 1 \times \dfrac{36}{12} and \dfrac{1 \times 36}{12}. The third expression is the most useful.

First, if we evaluate the multiplication in the numerator we get \dfrac{36}{12}. Then we can cancel the greatest common factor from the numerator and denominator. In this case it is 12. This gives us \dfrac{3}{1} which is the same as 3.

We can check this answer by multiplying back. 12 \times 3 = 36, so we know that 3 is \dfrac{1}{12} of 36.

Examples