PSLE Maths fractions: fraction of a remainder, and of two wholes
Fraction arithmetic is mostly done by P5. What decides the P6 marks is the word problem, and in particular one question: a fraction of what?
What the papers ask
- Dividing by a fraction, and how many of one fraction fit in another, often with a remainder to be given as a quantity.
- Fraction of a remainder: 2/5 is spent, then 1/3 of what is left, then what remains is known. Worked backwards to the start.
- Fractions of two different wholes: different fractions are taken from two groups, and the amounts left are equal. A favourite last question of P5 end-of-year papers.
- Two things priced in terms of each other: a book costs as much as three files, so everything becomes files.
The mistakes that cost marks
| Mistake | What to do instead |
|---|---|
| The second fraction taken of the original, not the remainder | Write "of what?" next to every fraction in the question. |
| Fractions of two different wholes compared directly | 3/8 of one group and 3/5 of another are not the same size. Make the numerators equal and use units. |
| Dividing by a fraction without inverting | Dividing by 2/3 is multiplying by 3/2. |
| A leftover given as a number of packets, not an amount | If the question asks what is left over, give it in the unit of the thing, such as kilograms. |
A worked example
A shop had 54 more roses than lilies. It sold 5/8 of the roses and 2/5 of the lilies. After that, the shop had the same number of roses and lilies left.
(a) How many roses and lilies were there at first?
(b) How many flowers were left altogether?
What makes it hard: the two fractions are of two different wholes, so they cannot be compared as they stand.
Roses left: 3/8 of the roses. Lilies left: 3/5 of the lilies. These are equal, and the numerators are already the same, so 1/8 of the roses equals 1/5 of the lilies.
(a) Roses are 8 units and lilies are 5 units. The difference is 3 units = 54, so 1 unit = 18. Roses: 8 × 18 = 144. Lilies: 5 × 18 = 90. Altogether 234 flowers.
(b) Each has 3 units left, 3 × 18 = 54, so 108 flowers were left. Check: 3/8 of 144 = 54 and 3/5 of 90 = 54.
How to practise fractions
- Draw the model for every remainder question until the "of what?" is automatic.
- Practise equal-numerator questions with numerators that need making equal, not just ones that already are.
- Work fraction-of-remainder questions backwards from the amount left.
Fraction word problems are in every paper in our courses, from the November P5 papers to the August prelim papers. See the course dates.
Common questions about PSLE fractions
What does "of the remainder" mean in a PSLE fraction question?
The fraction is taken of what was left after the first step, not of the original amount. If 1/4 is spent and then 1/3 of the remainder, the second amount is 1/3 of 3/4, which is 1/4 of the original, not 1/3 of it.
How do you compare fractions of two different amounts?
Make the numerators the same. If 3/8 of one group equals 3/5 of another, the first group is 8 units and the second is 5 units, and the difference between the groups is 3 units.
Practise it, free
Each is a full Paper 1 and Paper 2, marked the moment it is handed in, with a report on what went wrong.
20 seats. One paper a day.
Online P6 Maths crash courses in the school holidays: one full paper a day, marked before class, a report to parents every night.
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