Why can the 24 sweets not be used directly for a quarter of what is left?

Because the second person is working from the 16 sweets that remain, not the original 24. A fraction is always a fraction of one named whole, so write the whole down before multiplying.

Why does dividing by a fraction become multiplying by its reciprocal?

The question asks how many quarters fit into 2 1/2 kg, that is 5/2 ÷ 1/4. Four quarters make one whole, so flipping and multiplying counts them in one step: 5/2 × 4 = 10.

Primary 5 Maths: Fraction Word Problems — Practice Paper 4 (10 Questions)

2026-10-29

Tutor Prep Guide · Primary Maths

Paper 4 works on what the whole is: a stated amount means subtraction, a fraction of the whole means multiplication, and the second person may be working from what is left rather than the original.

Quick answer　10 questions, about 25 minutes. Items 01 and 04 separate subtraction from the whole, items 02 and 03 are basic multiplication, item 05 uses a reciprocal, items 06 and 07 change the whole, item 08 works back from what is left, item 10 is the commonest slip.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10 questions
Suggested time	25 minutes
Difficulty mix	Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1
Chapter	Chapter: Primary 5 Maths: Fraction Word Problems — Tutor Lesson Plan
Level	Primary 5

02　Questions (10 items)

FoundationA bottle holds 4/5 L of water and 1/4 L is drunk. How much is left?
FoundationA strip is 96 cm long and 5/8 of it is used. How many cm are left?
FoundationA class has 42 pupils and 3/7 of them are boys. How many boys?
FoundationIf 4/9 of a length is used, what fraction of the length remains?
IntermediateA bag of rice weighs 2 1/2 kg and 1/4 kg is used per meal. How many meals?
IntermediateA ribbon is 9/10 m long and 2/3 of its whole length is used. How many metres are left?
IntermediateThere are 24 sweets. A eats 1/3 of them and B eats 1/4 of what is left. How many does B eat?
ChallengeOn day one a quarter of a book is read, on day two 2/5 of what remains, and 45 pages are left. How many pages has the book?
ChallengeTwo ribbons are the same length. One loses 3/8 of its length and the other 2/5. By what fraction of the length does the second use more?
Error redoA rope is 7/8 m long and 3/8 m is cut off. How much is left? (common slip: writing 7/8 × 5/8)

03　Answers and one-line notes

#	Answer	One-line note
1	11/20 L	A stated amount means subtraction: 4/5 − 1/4 = 16/20 − 5/20 = 11/20 L.
2	36 cm	Find the fraction left first: 1 − 5/8 = 3/8, then 96 × 3/8 = 36 cm.
3	18 pupils	Divide by the denominator, then multiply by the numerator: 42 ÷ 7 = 6 and 6 × 3 = 18.
4	5/9	The whole is 1, written 9/9: 1 − 4/9 = 5/9.
5	10 meals	2 1/2 ÷ 1/4 = 5/2 × 4 = 10; dividing by a fraction means multiplying by its reciprocal.
6	3/10 m	The word whole signals multiplication: 1 − 2/3 = 1/3 left, and 9/10 × 1/3 = 3/10 m.
7	4 sweets	Find what is left: 24 × 2/3 = 16. That 16 is B whole amount, and 16 × 1/4 = 4.
8	100 pages	After two days 3/4 × 3/5 = 9/20 is left, so 45 ÷ 9/20 = 100; 100 − 25 − 30 = 45 checks it.
9	1/40	Use a common denominator of 40: 2/5 = 16/40 and 3/8 = 15/40, a difference of 1/40.
10	1/2 m	The unit m means subtraction: 7/8 − 3/8 = 4/8 = 1/2 m. Only a fraction of the whole calls for multiplication.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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