# Introducing fractions

If you get $${7}$$ out of $${10}$$ in a test, you can write your score as $$\frac{7}{10}$$.

$${7}$$ expressed as a fraction of $${10}$$ is $$\frac{7}{10}$$.

Similarly, if there are $${20}$$ socks in a drawer and $${4}$$ of them are blue, $$\frac{4}{20}$$ of the socks are blue.

$${4}$$ expressed as a fraction of $${20}$$ is $$\frac{4}{20}$$. We can put this into its simplest form by dividing the top and bottom numbers by $${4}$$, so we get $$\frac{1}{5}$$.

Question

a) What fraction of the large shape is the small one?

b) What fraction of the small shape is the large one?

a) The small shape is $$\frac{3}{10}$$ of the large shape.

b) The large shape is $$\frac{10}{3}$$ or $${3}\frac{1}{3}$$ of the small shape.

If you are expressing a number as a fraction of a second number, the first number goes on the top and the second number on the bottom.
Question

What fraction of $${1}$$ metre is $${42}~cm$$? Give your answer in its simplest form.

$${42}~cm$$ as a fraction of $${100}~cm$$ is:

$\frac{42}{100}=\frac{21}{50}$