Why does adding the same number to the top and the bottom change the value?

It changes how large each piece is. For 3/5 against 5/7 the cross products are 15 and 27, so they are not equal. Only multiplying or dividing both parts by the same number keeps the value.

To compare two fractions, is a common denominator or a decimal quicker?

For denominators like 4, 8, 20 or 25 that expand to 100, a decimal is usually quickest. For 7 or 9, where the division never ends, a common denominator or cross multiplication is steadier.

Primary 4 Maths: Equivalent Fractions and Decimals — Practice Paper 2 (10 Questions)

2026-10-29

Tutor Prep Guide · Primary Maths

Paper 2 walks the same route with a different set of numbers: expand and reduce, turn a fraction into a decimal and a decimal back into a simplest fraction, compare with a common denominator, with a chain of equivalent fractions and tenths against hundredths in between. Item 10 redoes adding the same number to the top and the bottom.

Quick answer　10 questions, about 20 minutes. Items 01 to 03 expand, reduce and turn a fraction into a decimal; items 04 to 06 write a decimal as a fraction and compare two pairs; items 07 to 09 complete a chain, write 0.35 two ways, and compare by common denominator with the difference; item 10 redoes adding the same number to both parts.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10 questions
Suggested time	20 minutes
Difficulty mix	Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1
Chapter	Chapter: Primary 4 Maths: Equivalent Fractions and Decimals — Tutor Lesson Plan
Level	Primary 4

02　Questions (10 items)

FoundationExpand 2/5 into a fraction with a denominator of 15.
FoundationReduce 24/36 to its simplest form.
FoundationWrite 3/4 as a decimal.
IntermediateWrite 0.6 as a fraction in its simplest form.
IntermediateWhich is larger, 5/8 or 0.6?
IntermediateWrite 7/25 as a decimal.
ChallengeComplete the chain of equivalent fractions: 3/4 = ?/12 = 15/?.
ChallengeWrite 0.35 as a fraction in its simplest form, then expand it to a denominator of 100.
ChallengeWhich is larger, 4/7 or 5/9, and by how much?
Error redoA pupil adds 2 to the top and the bottom of 3/5 to get 5/7, and says the two are equal. Is that right?

03　Answers and one-line notes

#	Answer	One-line note
1	6/15	2 × 3 = 6 and 5 × 3 = 15, so both parts are multiplied by 3.
2	2/3	Divide both parts by 12: 24 ÷ 12 = 2 and 36 ÷ 12 = 3.
3	0.75	3 ÷ 4 = 0.75, which is the same as 3/4 = 75/100.
4	3/5	0.6 = 6/10, and dividing both parts by 2 gives 3/5.
5	5/8 is larger	5/8 = 0.625, which is 0.025 more than 0.6.
6	0.28	7/25 = 28/100 = 0.28, since multiplying 25 by 4 gives 100.
7	9/12 and 15/20	Multiplying both parts of 3/4 by 3 gives 9/12, and by 5 gives 15/20.
8	7/20, which is 35/100	0.35 = 35/100, and dividing by 5 gives 7/20; multiplying 7/20 by 5 returns 35/100.
9	4/7 is larger by 1/63	With denominator 63: 4/7 = 36/63 and 5/9 = 35/63, a difference of 1/63.
10	No; 3/5 = 0.6 while 5/7 is about 0.714	Only multiplying or dividing both parts by the same number keeps the value; adding changes the size of each piece.

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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