PSLE Maths ratio: before and after questions
A ratio on its own is easy. The marks are in the questions where something changes: items are given away, bought, swapped or added, and the ratio moves. Almost all of those come down to one question: what did not change?
What the papers ask
- Sharing in a ratio, and finding one part from another or from the total. The short questions.
- Three quantities, where two ratios share a middle term and have to be joined.
- Before and after, where one change moves the ratio. The structured questions of Paper 2.
- Several changes at once, a swap and then a sale, or a third quantity added partway. These are among the hardest questions in the paper.
Three questions for any before-and-after problem
Did one amount stay the same?
Only one side changed. Give that side the same number of units in both ratios.
Did the total stay the same?
Something moved from one side to the other. Make the totals of the two ratios equal.
Did the difference stay the same?
Both sides changed by the same amount, as with ages. Make the differences equal.
None of them?
Then work out how the gap between the two sides changed, step by step, as in the example below.
The mistakes that cost marks
| Mistake | What to do instead |
|---|---|
| The before-ratio used where the after-ratio is needed | Label every ratio "before" or "after" as it is written down. |
| Units of the two ratios treated as the same size | A unit before and a unit after are only equal once the unchanged quantity has been matched. |
| A ratio of two parts read as a fraction of the total | 3 : 5 means 3 out of 8, not 3 out of 5. |
| The answer given as the number of units | Find the value of 1 unit, then multiply back to what was asked. |
A worked example
A shop had the same number of red pens and blue pens. It exchanged 14 of its red pens for 14 blue pens with another shop. Then it sold 77 red pens. The ratio of red pens to blue pens became 1 : 4.
(a) How many pens did the shop have in the end?
(b) How many red pens did the shop have at first?
What makes it hard: both amounts change, so no single quantity stays fixed. Follow the gap instead.
At first the gap between blue and red was 0. The exchange took 14 from red and added 14 to blue, so the gap became 2 × 14 = 28. Selling 77 red pens widened it to 28 + 77 = 105.
(a) In the end, blue is 4 units and red is 1 unit, a gap of 3 units. So 3 units = 105 and 1 unit = 35. Altogether: 5 × 35 = 175 pens.
(b) Red in the end is 1 unit, 35 pens. Undo the changes: 35 + 77 + 14 = 126 red pens at first. Check: blue is 126 + 14 = 140, which is 4 × 35.
Common questions about PSLE ratio
How do you solve PSLE ratio before and after questions?
Find the quantity that does not change: one of the two amounts, the total, or the difference between them. Give it the same number of units before and after, and the change becomes a number of units you can match to the numbers in the question.
Is ratio taught in Primary 5 or Primary 6?
In the current syllabus, ratio is taught in Primary 6, and it is examined more deeply than it used to be. Most of the hard ratio questions in PSLE are before-and-after problems with more than one change.
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