Fractions
Parts of a whole — adding, simplifying, fractions of an amount, common 11+ traps.
A fraction is just a way of sharing something into equal pieces. The bottom number tells you how many pieces the whole is cut into, and the top number tells you how many pieces you get.
Fraction of an amount — divide, then times
Step 1 · divide by the bottom
20 ÷ 5 = 4
Step 2 · times by the top
4 × 3 = 12
That was 3/5 of 20. Cut 20 into 5 equal pieces (each piece is 4), then take 3 of them. 12.
Remember it like this
“Divide by the bottom, times by the top.”
Works for every fraction-of-an-amount question, no matter how big the numbers get.
⚠ Watch out
Never add fractions straight across. 1/2 + 1/3 is NOT 2/5 — make the bottoms match first: 1/2 = 3/6 and 1/3 = 2/6, so the answer is 5/6. The wrong options in the exam are built from exactly this mistake.
Adding fractions with different bottoms
Calculate 1/3 + 2/5
- Find a number both 3 and 5 divide into — the smallest is 15
- Convert each: 1/3 = 5/15 and 2/5 = 6/15
- Add the tops: 5/15 + 6/15
11/15
Simplifying
Write 24/36 in its simplest form.
- Find the biggest number that divides both 24 and 36 — it is 12
- Divide top and bottom by 12: 24 ÷ 12 = 2 and 36 ÷ 12 = 3
2/3
⚠ Watch out
"Half of half" is 1/4, not 1/2 — you are halving twice. And read carefully: "what fraction is LEFT?" is a different question from "what fraction was EATEN?"
✏ Your turn
What is 3/4 of 60?
Show the answerHide the answer
- Divide by the bottom: 60 ÷ 4 = 15
- Times by the top: 15 × 3
45
For parents — the full topic guide
A fraction is a way to show part of a whole.
What the parts mean
When you see a fraction like 3/4:
- The bottom number (4) tells you how many equal parts the whole is split into.
- The top number (3) tells you how many of those parts you have.
So 3/4 means: split something into 4 equal pieces, take 3 of them.
The bottom is called the denominator (think "down"). The top is the numerator.
Equivalent fractions
The same amount can be written as many different fractions:
1/2 = 2/4 = 3/6 = 4/8 = 50/100
To make an equivalent fraction, multiply (or divide) the top and the bottom by the same number:
- 1/2 → multiply both by 3 → 3/6 ✓
- 6/8 → divide both by 2 → 3/4 ✓ (this is called simplifying)
Adding and subtracting fractions
Same bottom? Just add or subtract the tops.
1/5 + 2/5 = 3/5
Different bottoms? Make them match first.
1/4 + 1/2
Notice 1/2 = 2/4. So:
1/4 + 2/4 = 3/4
Fractions of an amount
To find 3/5 of 20:
- Divide 20 by the bottom (5) → 4
- Multiply by the top (3) → 12
So 3/5 of 20 = 12.
Comparing fractions
If the bottoms match, the bigger top wins:
4/7 > 3/7
If they don't, make them match first. Which is bigger, 2/3 or 3/5?
- 2/3 = 10/15
- 3/5 = 9/15
- 10/15 is bigger, so 2/3 wins.
Common 11+ traps
⚠️ "Half of half" = 1/4, not 1/2. (You're halving twice.)
⚠️ "Two-thirds" means split into 3 and take 2 — NOT split into 2 and take 3.
⚠️ 1/2 + 1/3 ≠ 2/5. You cannot add numerators and denominators directly. Always make the bottoms match first. (The correct answer is 5/6.)
⚠️ Read carefully: "What fraction is left?" is different from "What fraction was eaten?"
Worked examples
Read through each example. Cover the steps and try it yourself first if you can.
- 1
Fraction of an amount
What is 3/4 of 60?
Steps
- Divide 60 by the bottom number (4): 60 ÷ 4 = 15
- Multiply by the top number (3): 15 × 3 = 45
Answer
45
- 2
Adding fractions with different bottoms
Calculate 1/3 + 2/5
Steps
- Find a number both 3 and 5 divide into. Smallest is 15.
- Convert each: 1/3 = 5/15 and 2/5 = 6/15
- Add the tops: 5/15 + 6/15 = 11/15
Answer
11/15
- 3
Simplifying a fraction
Write 24/36 in its simplest form.
Steps
- Find the biggest number that divides both 24 and 36. (It is 12.)
- Divide top and bottom by 12: 24 ÷ 12 = 2 and 36 ÷ 12 = 3
Answer
2/3
Ready to practise this topic?
Try a full paper — questions on fractions show up in most 11+ maths and VR papers.