Finding a third

What is a third?

A third is a fraction. A fraction tells you how many parts of a whole you have. They are written by putting one number on top of another.

Here is a third written as a fraction:

As you can see there are two parts of a fraction.

The top number called the numerator, shows how many parts you have. It represents the whole and is 1 in this example.
The bottom number is called the denominator. It shows how many equal parts the whole has been divided into. In a third this number is 3.

A third, or \( \frac{1}{3} \), means '1 part of something that has been divided into three equal parts'.

If you add three thirds together you get a whole:

\( \frac{1}{3} \) + \( \frac{1}{3} \) + \( \frac{1}{3} \) = 1

What is a third of 36?

Working out a third of a whole is the same as dividing by 3.

Your three times table knowledge can come in handy:

36 ÷ 3 = 12

A third of 36 is 12.

What is a third of 66?

You could also use Base 10 to help you.

Here is 66 in Base 10:

You can see that there are 6 tens and 6 ones. You can divide this into three groups, with 2 tens and 2 ones in each group:

A third of 66 is 22.