Fractions made simple

← All articles·Study guide·6 min read

Fractions feel tricky at first, but they are all around us at home. Half an apple, a quarter of a pizza, three quarters of an hour. This guide builds fractions up slowly using real things, so they make sense before any rules appear.

What the two numbers mean

Every fraction has a top number and a bottom number. The bottom number tells you how many equal parts the whole is split into. The top number tells you how many of those parts you are talking about.

Step 1: start with things you can see

Fractions make far more sense when a child can hold them. Use food and toys before you use numbers on paper.

• Cut a piece of toast into 2 equal pieces to show halves, then into 4 to show quarters.
• Share a bar of chocolate into equal rows and talk about how many parts each person gets.
• Fold a piece of paper in half, then in half again, and count the equal parts you have made.

Step 2: the same amount can have different names

This is one of the most useful ideas in fractions. Two fractions can look different but be worth exactly the same. These are called equivalent fractions.

• 2 quarters is the same amount as 1 half.
• 2 out of 4 is the same as 1 out of 2.
• 5 out of 10 is also the same as 1 half.

Step 3: comparing fractions

When the bottom numbers are the same, comparing is easy. You just look at the top numbers. When the bottom numbers are different, it helps to picture the parts.

• If the bottom numbers match, the bigger top number is the bigger fraction. 3 fifths is more than 2 fifths.
• If the top numbers match, the smaller bottom number is the bigger fraction, because the parts are bigger. 1 half is more than 1 quarter.

Step 4: finding a fraction of a number

To find a fraction of an amount, first share the amount into the number of parts on the bottom, then count the number of parts on top.

1. To find 1 quarter of 12, share 12 into 4 equal groups. Each group has 3, so 1 quarter of 12 is 3.
2. To find 3 quarters of 12, do the same sharing, then take 3 of the groups. That is 9.

Practise together

Try these, then check the answers below.

1. How many quarters make a whole?
2. Which is bigger, 1 half or 1 third?
3. What is another name for 2 quarters?
4. What is 1 half of 10?
5. What is 1 quarter of 8?
6. What is 3 quarters of 8?

Four golden rules

1. The bottom number is how many equal parts the whole is cut into.
2. The top number is how many of those parts you have.
3. The parts must be equal in size to count as a fraction.
4. To find a fraction of an amount, divide by the bottom number then times by the top number.