Part-Whole is the engine room of the paper · Jump to the worked examples →

Shown working, not just shown off

PSLE part-whole and fraction word problems, shown working.

The short version

Part-whole and fraction word problems describe one quantity split into parts, often a fraction of a fraction. You solve them by naming the whole in units that divide every fraction cleanly, so each fraction becomes a tidy count of units. Then one given difference fixes the value of a unit, and the rest is multiplication.

From GPA's tagged index of 709 PSLE questions, with frequency based on the 664 questions from the 14 papers sat 2012 to 2025, MOE Specimen reported separately · every solution worked independently then checked against the verified GPA key · Mrs Eileen Toh signs off the mathematics · last reviewed 22 Jun 2026

The engine room of the paper

Two thinking habits underlie about 44% of every non-routine PSLE question.

When we tagged every question and counted, two habits kept appearing together: "units and parts" and "part-whole". Fractions, the most-tested content area, runs underneath both, and turns up in every single year. Learn to name the whole in units, and most of the paper stops being a fresh puzzle each time.

98

Units and parts

Questions that turn on naming the whole as a count of units.

95

Part-whole

Questions that split one quantity into parts and a remainder.

78

Fractions

The most-tested content area, appearing in every one of the fourteen years.

Together, units and parts (98) and part-whole (95) underlie about 44% of every non-routine PSLE question across fourteen years. Source: GPA tagged index of 709 PSLE questions; frequency uses the 664 questions from the 14 papers sat 2012 to 2025, MOE Specimen reported separately.

How these questions work

Name the whole in units, and the fractions go quiet.

A part-whole question hands you a few fractions of the same total, sometimes a fraction of a fraction. The method is always the same. Name the whole in units that divide every fraction cleanly. Pick one denominator big enough that every fraction lands on whole units, so nothing has to be a guess.

From there the rest follows. Match numerators when amounts are equal, which lets you compare totals that looked impossible to compare. And read each "one to the rest" ratio as a fraction of the whole, so a ratio like 1 : 3 quietly becomes one quarter of the same total everyone else is sharing.

Each card below names the lock, how a child tends to mis-read the question, then the key, the one move that opens it, then the clean steps and the answer. Not one of these is won by faster arithmetic. Each turns on naming the whole first.

2020 · Paper 2 · Q17 fraction of a fraction

Mrs Wu's dress, blouses and watch

Where to find it

This is a worded PSLE question, so we don’t reproduce it here. Find it in your Ten-Year Series (TYS) or the official paper — 2020 Paper 2, Q17, parts (a) and (b) (the spend-in-fractions money question) — then follow our worked solution below.

Video: a Genius Plus Academy teacher solving PSLE 2020 Paper 2 Question 17 Teacher video · 2020 P2 Q17

The lock

Three fractions sit on different bases: 1/6 of everything, then 3/4 of the remainder. A child who keeps switching the base drowns. Choose one unit for the whole so every fraction becomes a tidy count of units.

The key

Let the whole be a number of units that all the fractions divide cleanly, here 30.

Her money as 30 units:

dress 3u 2 blouses 2u watch 18.75u (3/4 of the 25u remaining) left 6.25u

Worked steps

  1. (a) The dress plus 2 blouses make 1/6 of her money, and the dress is 3 blouses, so that 1/6 is shared as 5 blouse-portions. Each blouse \(= \frac{1}{6} \div 5 = \frac{1}{30}\) of her money.
  2. (b) Let her money be 30 units. Then 2 blouses \(=\) 2u, dress \(=\) 3u, and the first 1/6 is 5u, leaving 25u.
  3. The watch is 3/4 of the remaining 25u \(= 18.75\)u.
  4. Watch minus dress \(= 18.75\text{u} - 3\text{u} = 15.75\text{u} = 220.50\), so 1u \(= 14\).
  5. Her money \(= 30 \times 14 = 420\).

Answer: (a) 1/30. (b) $420 at first.

What makes it click. Choosing 30 units up front turns three competing fractions into whole-number parts. The awkward 3/4 becomes a clean 18.75u, and one subtraction unlocks the value of a unit.

Independently solved, matches the GPA marking-scheme key. Open the full worked solution →

2024 · Paper 2 · Q16 shared numerator

Three children, one shared numerator

Where to find it

This is a worded PSLE question, so we don’t reproduce it here. Find it in your Ten-Year Series (TYS) or the official paper — 2024 Paper 2, Q16, parts (a) and (b) (the fractions-of-money donation question) — then follow our worked solution below.

Video: a Genius Plus Academy teacher solving PSLE 2024 Paper 2 Question 16 Teacher video · 2024 P2 Q16

The lock

Three different fractions of three different totals look impossible to compare. The line "Devi and Eric donated the same amount" lets you rewrite the fractions so they share a numerator, and the comparison becomes obvious.

The key

Match numerators, then read off the units.

Worked steps

  1. Devi gave \(\frac{1}{4} = \frac{2}{8}\) of her money; Eric gave \(\frac{2}{7}\) of his. Same numerator (2), so Devi's money \(=\) 8 units and Eric's \(=\) 7 units, each donating 2 units.
  2. Haziq donated \(3 \times\) Eric's donation \(= 3 \times 2 = 6\) units; that is 2/5 of his money, so Haziq's money \(=\) 15 units.
  3. (a) Most at first: Haziq (15u); least: Eric (7u).
  4. (b) Total \(= 8 + 7 + 15 = 30\) units \(= 1560\), so 1 unit \(= 52\). Haziq donated 6 units \(= 312\).

Answer: (a) Haziq most, Eric least. (b) $312.

What makes it click. Forcing 1/4 into 2/8 so it shares Eric's numerator is the whole trick: equal donations plus equal numerators turn three tangled fractions into one clean string of units.

Independently solved, matches the GPA marking-scheme key. Open the full worked solution →

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The 10 PSLE Question Types, cheat sheet

A one-page map of the ten structures that recur across the paper, with the lock and key for each. One email, no spam.

PSLE Intensive · Type 1 two ratios, one whole

Two ratios that share one gift

Where to find it

This is a worded PSLE question, so we don’t reproduce it here. Find it in your Ten-Year Series (TYS) or the official paper — 2021 PSLE Paper 2 (the shared-cost ratio question) — then follow our worked solution below.

The lock

A child treats the two ratios as separate puzzles. "Alan to the rest = 1 : 3" simply means Alan is 1/4 of the whole, and "Ben to the rest = 1 : 5" means Ben is 1/6 of the same whole. Both ratios speak about one common total.

The key

Convert each ratio to a fraction of the whole, then put everyone on a common number of units (12).

The gift as 12 units:

Alan 3u Ben 2u Chandra 7u

Worked steps

  1. Alan : (Ben + Chandra) \(=\) 1 : 3, so Alan \(= \frac{1}{4}\) of the total \(=\) 3 units out of 12.
  2. Ben : (Alan + Chandra) \(=\) 1 : 5, so Ben \(= \frac{1}{6}\) of the total \(=\) 2 units out of 12.
  3. Chandra \(= 12 - 3 - 2 = 7\) units.
  4. Chandra minus Ben \(= 7 - 2 = 5\) units \(= 80\), so 1 unit \(= 16\).
  5. Gift \(= 12\) units \(= 12 \times 16 = 192\).

Answer: the gift cost $192.

What makes it click. Each "one to the rest" ratio is secretly a fraction of the whole. Translate both onto 12 units and the three shares line up, so a single $80 difference scales the lot. This is the Lock and Key reflex in miniature.

From the GPA PSLE Intensive corpus (based on 2021 PSLE), independently solved, the typed and handwritten keys agree.

The trap that costs marks

Children keep switching what the fraction is "of".

In a fraction of a fraction, the danger is silent. A child reads "1/6 of her money", works happily, then reads "3/4 of what remained" and quietly slides the 3/4 back onto the whole instead of the remainder. The arithmetic looks fine; the base has moved underneath them, and the answer is wrong by a step nobody can see.

The fix is a habit, not a formula. Commit to one denominator for the whole, big enough that every fraction lands on whole units. Once the whole is 30 units, "3/4 of the remaining 25u" is forced to be 18.75u, and there is nowhere for the base to drift. Name the whole first, and the trap simply cannot spring.

From one habit to the full reflex

Name the whole here; recognise every structure there.

This trains naming the whole in units that divide everything; the PSLE Math Intensive trains structure-recognition across all ten question types, with 158 worked examples.

Explore the PSLE Intensive →

Keep reading

The full picture this habit sits inside, the hardest questions it unlocks, and the sibling structures.

Pillar guide

Most-tested PSLE Math topics, counted

What 709 tagged questions show the paper rewards.

 Worked solutions

The hardest PSLE Math questions

Twelve demanding questions, each hard because of structure.

 Type guide

Percentage questions

Anchor the percentage to what stays equal across the change.

 Type guide

Proportion questions

Keep the unchanged quantity fixed while the rest scales.

Questions parents ask

What is a part-whole question in PSLE Math?

It is a problem that splits one quantity into parts and a remainder, usually described with fractions, sometimes a fraction of a fraction. You solve it by naming the whole in units that divide every fraction cleanly, so each fraction becomes a tidy count of units and one given difference fixes the value of a unit.

How often do part-whole and fraction questions appear?

In GPA's tagged index, two habits dominate: "units and parts" appears in 98 questions and "part-whole" in 95, and together they underlie about 44% of every non-routine PSLE question across fourteen years. Fractions, the most-tested content area, appears 78 times and in every one of the fourteen years. This is analysis of past papers, not a forecast.

What trips children up most in a fraction of a fraction?

They keep switching what the fraction is "of", sliding a fraction of the remainder back onto the whole. The fix is to commit to one denominator for the whole, big enough that every fraction lands on whole units. Once the whole is named in units, the base cannot drift.

Are these solutions reliable?

Each solution here was worked independently and then checked against the verified GPA key: the official marking scheme for the 2020 and 2024 questions, and for the Type 1 example, the typed and handwritten keys from the Intensive corpus. All three agreed on every answer. Mrs Eileen Toh signs off the mathematics.

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