To find 3/4 of 20, draw a bar for the 20 and split it into 4 equal boxes. One box is 20 ÷ 4 = 5. Three boxes are 3 × 5 = 15. Divide by the denominator to find one part, then multiply by the numerator. If you know a part and need the whole, work backwards: find one box first, then all the boxes.
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Equal parts, equal wholes
2/4 = 4/8
Both bars are the same length. Find a division of the second bar that lines up exactly with the coloured edge.
Words to know
- unit fraction
- a fraction with 1 on top, like 1/4
- bar model
- a drawing of a bar split into equal boxes
- whole
- the full amount before it is split
Worked examples
What is 3/4 of 20?
- 1.One quarter: 20 ÷ 4 = 5.
- 2.Three quarters: 3 × 5 = 15.
= 15
What is 2/5 of 45?
- 1.One fifth: 45 ÷ 5 = 9.
- 2.Two fifths: 2 × 9 = 18.
= 18
3/4 of a number is 18. What is the number?
- 1.3 quarters are 18, so one quarter is 18 ÷ 3 = 6.
- 2.The whole is 4 quarters: 4 × 6 = 24.
= 24
For parents
Method: Bar model: divide, then multiply
What to say: What is one box worth? How many boxes do you need?
Common mistakes:
- Finds one part (divides by the denominator) and stops, forgetting to multiply by the numerator.
- Divides by the numerator and multiplies by the denominator (uses b/a instead of a/b).
- Gives the amount left over after taking the fraction, instead of the fraction itself.
- Gives the denominator (the number of groups) instead of the size of one group.
- Given a part of the whole, takes the fraction of that part instead of working back to the whole.
- Works out one part of the whole and gives that as the whole.
- Treats the given part as one unit part and multiplies it by the denominator.