Fractions Explained

What you will learn

• Say what the numerator and denominator mean.
• Read, write and draw fractions such as $\frac{3}{8}$.
• Explain why the parts must be equal.
• See that a fraction is also a division.

Before you start: you should be able to count and divide a number into equal groups. See Division: Sharing and Grouping.

The idea

Cut a pizza into 8 equal slices and eat 3 of them. You have eaten $\frac{3}{8}$ of the pizza. That is all a fraction is: a way to name part of a whole.

The number on the bottom, the denominator, tells you how many equal parts the whole is split into. The number on top, the numerator, tells you how many of those parts you are talking about.

The parts must be equal

A fraction only works when every part is the same size. A shape cut into 3 pieces of different sizes does not have thirds. Fold, measure or draw carefully so the parts match.

Unit fractions

A fraction with $1$ on top is a unit fraction: $\frac{1}{2}$, $\frac{1}{5}$, $\frac{1}{10}$. The bigger the number on the bottom, the smaller each part, because the whole is shared between more parts.

Counting parts

A fraction such as $\frac{3}{4}$ is three of the unit fraction $\frac{1}{4}$. Count them like you count anything else: one quarter, two quarters, three quarters. When you have all the parts, such as $\frac{4}{4}$, you have one whole.

A fraction is a division

$\frac{3}{4}$ also means $3 \div 4$. Share 3 pizzas between 4 people and each person gets $\frac{3}{4}$ of a pizza. This is how you turn a fraction into a decimal: $3 \div 4 = 0.75$. See Decimals Explained.

Worked examples

Example 1: Name the fraction

A strip is split into 6 equal parts and 5 are shaded. What fraction is shaded, and what fraction is not?

1. The whole has 6 equal parts, so the denominator is $6$.
2. Five parts are shaded, so the numerator is $5$.
3. The fraction shaded is $\frac{5}{6}$.
4. One part is not shaded, so $\frac{1}{6}$ is not shaded. Check: $\frac{5}{6} + \frac{1}{6} = \frac{6}{6} = 1$.

Answer: $\frac{5}{6}$ shaded and $\frac{1}{6}$ not shaded.

Example 2: Share equally

Four friends share 3 equal flapjacks. What fraction of a flapjack does each friend get?

1. Sharing 3 between 4 is $3 \div 4$.
2. As a fraction, $3 \div 4 = \frac{3}{4}$.
3. Check by cutting each flapjack in 4 quarters: that makes 12 quarters, and 12 shared between 4 friends is 3 quarters each.

Answer: $\frac{3}{4}$ of a flapjack each.

Example 3: Which is bigger?

Which is bigger, $\frac{1}{8}$ or $\frac{1}{6}$ of the same cake?

1. The cake cut into 6 equal slices has bigger slices than the cake cut into 8.
2. So one sixth is bigger than one eighth.

Answer: $\frac{1}{6}$

Watch out: a bigger denominator means smaller parts. $\frac{1}{10}$ is smaller than $\frac{1}{2}$, even though $10$ is bigger than $2$.

Why it matters

Fractions turn up whenever something is shared or cut. Half a pizza, a quarter of an hour, three quarters of a cup of flour: we use them all without thinking. Musicians count beats in halves and quarters, and builders measure in fractions of a metre.

Fractions are also the first step to decimals, percentages, ratios and algebra. Once equal parts make sense, the rest builds on it.