Why is half of what remains a multiplication?

A half is not a fixed length but 1/2 of the amount that is left, so it multiplies. Cutting off 1/2 m instead is a fixed length and subtracts.

How do I work back to the whole from what is left?

Write the remainder as a fraction of the whole (1 minus the fraction used), then divide the amount left by that fraction and check by substituting back.

Primary 5 Maths: Fraction Word Problems — Practice Paper 2 (10 Questions)

2026-10-29

Tutor Prep Guide · Primary Maths

Paper 2 puts the two kinds of used into longer stories: cut a length then half of the rest, drink a share then share out the rest, and work backwards from what is left. Write one sentence about what is known first.

Quick answer　10 questions, about 25 minutes. Items 05 and 07 test a fraction of what remains, items 06 and 08 need more than one step, item 09 works back to the whole and item 10 is the same error again.

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 ribbon is 5/6 m long and 1/4 m is used. How much is left?
FoundationA strip is 84 cm long and 2/7 is used. How many cm are left?
FoundationForty sweets, 3/8 of them eaten. How many are left?
FoundationFive ninths of a rope is used. What fraction is left?
IntermediateA rope is 3/4 m long and 2/3 of the whole is used. How much is left?
IntermediateForty-five sweets, 2/5 eaten, the rest shared equally by 3 people. How many each?
IntermediateA cloth is 7/8 m long; 3/8 m is cut off, then half of what remains is cut off. How much is left?
ChallengeA bottle holds 2 1/4 L of juice; 2/9 of the whole is drunk and the rest poured equally into 5 cups. How much per cup?
ChallengeAfter 3/7 of a ribbon is used, 80 cm remains. How long was the ribbon in total?
Error redoA rope is 3/5 m long and 2/5 m is used. How much is left? (common slip: 3/5 × 3/5 = 9/25 m)

03　Answers and one-line notes

#	Answer	One-line note
1	7/12 m	The stated 1/4 m is a fixed length, so subtract: 5/6 − 1/4 = 10/12 − 3/12.
2	60 cm	Five sevenths remain: 84 ÷ 7 = 12, then 12 × 5 = 60; dividing first keeps the numbers small.
3	25 sweets	Five eighths remain: 40 ÷ 8 = 5, then 5 × 5 = 25; or find the 15 eaten and subtract.
4	4/9	The whole is 1, written 9/9: 9/9 − 5/9 = 4/9, with the denominator unchanged.
5	1/4 m	What remains is 1/3 of the whole: 3/4 × 1/3 = 1/4. Finding the amount used and subtracting gives the same answer.
6	9 sweets	Two steps: 45 × 3/5 = 27 left, then 27 ÷ 3 = 9 each. Answering 27 means the second step was dropped.
7	1/4 m	The first cut subtracts (leaving 4/8 = 1/2); only the second, half of the remainder, multiplies, giving 1/4. The order matters.
8	7/20 L	Seven ninths remain: 9/4 × 7/9 = 7/4 L, then ÷ 5 gives 7/20 L, keeping litres throughout.
9	140 cm	The remainder is 4/7 of the whole, so divide: 80 ÷ 4/7 = 80 × 7/4 = 140, and 140 × 4/7 checks back to 80.
10	1/5 m	A length with a unit is taken away, so subtract: 3/5 − 2/5 = 1/5. Multiplying would mean a share of the whole instead.

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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