Fractions, decimals & percentages
Fractions of a quantity
A fraction is a division waiting to happen. Divide by the bottom number, multiply by the top — in that order.
A fraction is a division
Cut a cake into 5 equal pieces and each piece is 1/5 of the cake. That is the same as 1 ÷ 5. Every fraction can be read as a division: the numerator divided by the denominator. That is why 3 cakes shared between 4 children gives each child 3/4 of a cake.
Finding a fraction of an amount
Two steps, always in this order: 1. DIVIDE by the denominator (the bottom number). 2. MULTIPLY by the numerator (the top number). To find 2/3 of 15: 15 ÷ 3 = 5, then 5 × 2 = 10. Dividing first keeps the numbers small and easy.
Getting the order right
Arun says: 'To find 3/10 of 20, I divide by 3 and multiply by 10.' He has it backwards. You divide by the DENOMINATOR and multiply by the NUMERATOR — so divide by 10 and multiply by 3. 20 ÷ 10 = 2, then 2 × 3 = 6. The denominator tells you how many parts to cut into, so it must come first.
Working backwards to the whole
Sometimes you know the part and want the whole. One quarter of a number is 8. Since a quarter is one of four equal parts, the whole is 8 × 4 = 32. Zara has 1/4 of a bottle left and that is 100 ml. The full bottle held 100 × 4 = 400 ml. To undo 'divide then multiply', do the opposite both ways round.
Worked examples
2/3 of 15
- Divide by the denominator: 15 ÷ 3 = 5.
- Multiply by the numerator: 5 × 2 = 10.
Answer: 2/3 of 15 = 10
3/5 of 60
- 60 ÷ 5 = 12.
- 12 × 3 = 36.
Answer: 3/5 of 60 = 36
Correcting Arun
- He wants 3/10 of 20 but divided by 3 and multiplied by 10.
- You divide by the denominator, which is 10.
- 20 ÷ 10 = 2, then 2 × 3 = 6.
Answer: 3/10 of 20 = 6
Sharing 3 cakes between 4 children
- Each child gets 3 ÷ 4 of a cake.
- A fraction is a division, so that is 3/4.
Answer: Each child gets 3/4 of a cake
One quarter of a number is 8
- A quarter means one of 4 equal parts.
- So the whole is 4 times as big.
- 8 × 4 = 32.
Answer: The number is 32
Where you see this in real life
- Sharing a bill of $60 so that one person pays 2/5 of it.
- A recipe for 4 people scaled to 3 people uses 3/4 of each amount.
- A sale sign saying 'one third off' means finding 1/3 of the price.
Key words
- Numerator
- The top number of a fraction.
- Denominator
- The bottom number of a fraction.
- Fraction
- A number written as one whole divided into equal parts.
- Of
- In fractions, 'of' means multiply.
- Whole
- The complete amount before it is divided.
- Equal parts
- Parts that are exactly the same size.