Why must fractions be put over a common denominator to compare?

Different denominators mean different sized pieces: one fifth is bigger than one eighth, so comparing numerators alone can reverse the answer. With a common denominator every piece is the same size.

How do I spot a share of what is left?

The phrase what is left resets the whole: first find how much remains, then take the fraction of that. A share of the total would use the original amount instead.

Primary 5 Maths: Fraction Word Problems — Practice Paper 3 (10 Questions)

2026-10-29

Tutor Prep Guide · Primary Maths

Paper 3 adds comparing and multiples: which ribbon used more, how many times as long A is, which cake has more left, and a three-person share. Write down what the whole is before starting each item.

Quick answer　10 questions, about 25 minutes. Items 04 and 05 test multiples and comparison by common denominator, item 06 mixes subtracting and multiplying, item 07 works back to the whole, items 08 and 09 need the whole fixed first, 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)

FoundationTwenty-four sweets, 5/8 of them eaten. How many are left?
FoundationWhat is 2/5 of 3/4?
FoundationA class of 36 has 5/9 girls. How many girls?
FoundationRibbon A is 4/5 m and ribbon B is 2/5 m. How many times as long is A?
IntermediateTwo ribbons of the same length: 2/5 of A is used and 3/8 of B is used. Which used more?
IntermediateA cloth is 5/6 m long; 1/4 m is cut off, then 2/5 of what remains is cut off. How much is left?
IntermediateAfter 3/8 of a book is read, 75 pages remain. How many pages has the book?
ChallengeA box of 60 chocolates: A takes 1/4 of all, B takes 1/3 of what is left, C takes the rest. How many does C get?
ChallengeTwo identical cakes: 3/5 of one is left and 5/8 of the other. Which has more left, and by how much?
Error redoA rope is 5/8 m long and 2/8 m is used. How much is left? (common slip: multiplying 5/8 by 6/8)

03　Answers and one-line notes

#	Answer	One-line note
1	9 sweets	Three eighths remain: 24 ÷ 8 = 3, then 3 × 3 = 9; or find the 15 eaten and subtract.
2	3/10	The word of means multiply: 3/4 × 2/5 gives 6/20 across the top and bottom, which simplifies to 3/10.
3	20 girls	36 ÷ 9 = 4, then 4 × 5 = 20; dividing first keeps the numbers small.
4	2 times	How many times is a division: (4/5) ÷ (2/5) = 4/2 = 2. With equal denominators, compare the numerators.
5	A used more (2/5 = 16/40, 3/8 = 15/40)	Use a common denominator of 40: 16/40 beats 15/40 by 1/40. Comparing the numerators 2 and 3 alone gets it wrong.
6	7/20 m	The first cut is a fixed length, so subtract: 5/6 − 1/4 = 7/12. The second is 2/5 of the remainder, leaving 3/5, so multiply to get 7/20.
7	120 pages	The remainder is 5/8 of the book, so divide: 75 ÷ 5/8 = 75 × 8/5 = 120, and 120 × 5/8 checks back to 75.
8	30 chocolates	B takes 1/3 of the remainder, not of the whole: 60 × 3/4 = 45, then 45 × 1/3 = 15, leaving C 45 − 15 = 30.
9	The 5/8 cake, by 1/40	Common denominator 40: 3/5 = 24/40 and 5/8 = 25/40, a difference of 1/40. Both fractions must refer to the same whole.
10	3/8 m	A length with a unit is taken away, so subtract: 5/8 − 2/8 = 3/8. Multiplying would mean a fraction 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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