📏 Maths · Paper 2 · Fractions (of remainder)

Three fractions, each is a fraction of something different

PSLE 2020 Paper 2, Question 17 is Pattern 1 from our fractions guide — work backwards from the remainder.

PSLE 2020 · Paper 2 · Q17 5 marks (1 + 4) Fraction of remainder
The question

📝 PSLE 2020, Paper 2, Question 17 — 5 marks

Mrs Wu spent 1⁄6 of her money on a dress and 2 blouses. The dress cost 3 times as much as each blouse. Mrs Wu spent 3⁄4 of her remaining money on a watch. She spent $220.50 more on the watch than on the dress.

(a) What fraction of Mrs Wu's money was spent on each blouse? [1]
(b) How much money did Mrs Wu have at first? [4]

📈 Read the mark split before you start

Part (a) is worth 1 mark, Part (b) is worth 4 marks, which is where the method marks live. Budget your time accordingly.

💡 How to start any “fraction of remainder” question

Our fractions guide gives one rule for such questions: express every quantity as a fraction of the original whole first.

Before any calculation, read each fraction and ask a fraction of what?

  • 1⁄6 is a fraction of all her money. It covers the dress and both blouses together.
  • “3 times as much” is a split inside that 1⁄6. Dress : blouse : blouse = 3 : 1 : 1, so the 1⁄6 is 5 equal units.
  • 3⁄4 is a fraction of the remainder only. The remainder is 5⁄6, so the watch is 3⁄4 of 5⁄6 of her money.
Worked solution

Part (a): What fraction of Mrs Wu's money was spent on each blouse?

🔍 Start at the end: what is being asked?

Not a sum of money — a fraction of her total money. So the answer must come out as a fraction with no dollar sign anywhere near it. The route is: split the 1⁄6 into equal units, find what one unit is worth as a fraction of the whole.

  1. 1 Turn the comparison into equal units.

    Let each blouse be 1 unit. The dress costs 3 times as much, so the dress is 3 units. Together: 3 + 1 + 1 = 5 units.

  2. 2 Match those units to the fraction given.

    Those 5 units are the 1⁄6 she spent. So 5 units = 1⁄6 of her money.

  3. 3 Share it out — a fraction divided by a whole number.

    1 unit = 1⁄6 ÷ 5 = 1⁄6 × 1⁄5 = 1⁄30

All of Mrs Wu’s money, in sixths 1/6 remaining money = 5/6 The 1/6, enlarged: 1 unit 1 unit 1 unit 1 unit 1 unit Dress = 3 units Blouse Blouse 5 equal units make up 1/6 of her money, so 1 unit = 1/6 ÷ 5 = 1/30 of her money

Answer — part (a)

1⁄30 of Mrs Wu’s money was spent on each blouse.

✍ Carry this forward

The dress is 3 units, so the dress = 3 × 1⁄30 = 3⁄30 = 1⁄10 of her money. Write that line down now. Part (b) compares the watch with the dress, so this is the bridge between the two parts.

Worked solution

Part (b): how much money did Mrs Wu have at first?

🔍 Start at the end: what would unlock it?

$220.50 is the gap between the watch and the dress. If both of those can be written as fractions of the same whole — all her money — then their difference is also a fraction of that whole, and one number stands against one fraction.

The dress is already done: 1⁄10, from part (a). So there is exactly one missing piece: the watch, as a fraction of all her money. Find it and part (b) drops out. That is the plan.

  1. 1 Find the remainder as a fraction of the whole.

    She spent 1⁄6, so what was left is 1 − 1⁄6 = 5⁄6 of her money.

  2. 2 Convert the watch from a fraction of the remainder to a fraction of the whole.

    The 3⁄4 applies to the 5⁄6, not to everything. “Of” means multiply:

    Watch = 3⁄4 × 5⁄6 = 15⁄24 = 5⁄8 of her money.

  3. 3 Subtract to get the gap as a fraction.

    Watch − dress = 5⁄8 − 1⁄10. Common denominator: LCM of 8 and 10 = 40.

    25⁄40 − 4⁄40 = 21⁄40 of her money = $220.50

  4. 4 Find the whole from a part — divide, don’t multiply.

    21 parts (out of 40) = $220.50, so 1 part = $220.50 ÷ 21 = $10.50.

    All her money = 40 parts = $10.50 × 40 = $420
    Or in one line: total = $220.50 ÷ 21⁄40 = $220.50 × 40⁄21 = $420.

Everything as a fraction of the same whole — all her money 1/10 Watch = 5/8 of her money not spent 2 blouses, 1/30 each Dress = 1/10  ·  each blouse = 1/30  ·  dress + 2 blouses = 1/6  ·  remainder = 5/6 Now line up the two the question compares: Watch — 5/8 Dress — 1/10 21/40 of her money = $220.50 1/40 → $220.50 ÷ 21 = $10.50  →  40/40 → $10.50 × 40 = $420

Answer — part (b)

Mrs Wu had $420 at first.

📏 Alternative method

If you find fractions of fractions slippery, the entire question can be run in whole numbers instead. Pick a total that divides cleanly by 6, by 5 and by 4: 120 units works.

  • All her money = 120u. First spend = 1⁄6 × 120u = 20u.
  • Split 20u as 3 : 1 : 1 → dress = 12u, each blouse = 4u.
  • Remainder = 100u, so watch = 3⁄4 × 100u = 75u.
  • 75u − 12u = 63u = $220.50, so 1u = $3.50.
  • 120u = $3.50 × 120 = $420.
Check & review

Plug your answer back in the question to check

Fast way to double-check if you get it right.

  • ✓Start with $420.1⁄6 of $420 = $70 spent on the dress and 2 blouses.
  • ✓Split $70 as 3 : 1 : 1.Dress $42, each blouse $14 — and $42 is indeed 3 × $14.
  • ✓Remainder $350, watch 3⁄4 of it.3⁄4 × $350 = $262.50.
  • ✓$262.50 − $42 = $220.50.Matches the question exactly, so both the 5⁄8 and the 1⁄10 were right.
  • ✓And part (a) rechecks too.$14 out of $420 = 14⁄420 = 1⁄30.

★ Teacher’s power tip

Before writing a single calculation, annotate the question: circle each fraction and write beside it what it is a fraction of. On this question that produces three notes — “of all her money”, “of the 1⁄6”, “of the remainder” — and the third one is where the marks are won or lost.

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