Why does adding 1 to the top and the bottom change the value?

It changes how large each piece is. For 5/6 against 6/7 the cross products are 35 and 36, so they differ. 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 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 than a long decimal.

Primary 4 Maths: Equivalent Fractions and Decimals — Practice Paper 1 (10 Questions)

2026-10-29

Tutor Prep Guide · Primary Maths

Paper 1 follows the three steps in the lesson plan: make equivalent fractions by expanding and reducing, rewrite between fractions and decimals, then compare by common denominator or by decimal. The last item returns to adding 1 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 of equivalent fractions, convert both ways, and compare a fraction with a decimal; item 10 redoes adding 1 to the numerator and denominator.

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: 3/4 = ?/20. What replaces the question mark?
FoundationReduce 18/24 to its simplest form.
FoundationWrite 5/8 as a decimal.
IntermediateWrite 0.45 as a fraction in its simplest form.
IntermediateWhich is larger, 3/7 or 4/9?
IntermediateWhich is larger, 2/5 or 3/8?
Challenge1/2 = 2/4 = 4/8 = ?/16. What replaces the question mark, and why are all these fractions equal?
ChallengeWrite 7/20 as a decimal, and 0.6 as a fraction in its simplest form.
ChallengeWhich is larger, 3/8 or 0.4? Explain with two methods.
Error redoA student writes “5/6 = 6/7 because 1 is added to the top and the bottom”. What is wrong, and what is a correct equivalent fraction?

03　Answers and one-line notes

#	Answer	One-line note
1	15 (that is, 15/20)	The denominator goes from 4 to 20 by times 5, so the numerator takes the same times 5: 3 × 5 = 15 and 3/4 = 15/20. Multiplying top and bottom by the same number keeps the value; adding does not.
2	3/4	Divide top and bottom by a common factor: by 2 gives 9/12, then by 3 gives 3/4. The highest common factor of 18 and 24 is 6, so dividing once by 6 lands on 3/4 directly.
3	0.625	A fraction is the top divided by the bottom: 5 ÷ 8 = 0.625. Check afterwards: 5/8 is less than 1, so the answer must be below 1 — 6.25 would be a misplaced decimal point.
4	9/20	0.45 is 45 hundredths, that is 45/100. Dividing top and bottom by 5 gives 9/20, and 9 and 20 share no further factor, so 9/20 is simplest.
5	4/9 is larger	Different denominators cannot be compared by the numerators. As decimals, 3 ÷ 7 ≈ 0.429 and 4 ÷ 9 ≈ 0.444, so 4/9 is larger; with a common denominator, 3/7 = 27/63 and 4/9 = 28/63.
6	2/5 is larger	2/5 = 2 ÷ 5 = 0.4 and 3/8 = 3 ÷ 8 = 0.375, so 2/5 is larger. With 40 as the common denominator it is 16/40 against 15/40, the same verdict.
7	8 (that is, 8/16)	Each step multiplies top and bottom by 2: 1/2 → 2/4 → 4/8 → 8/16. The pieces get smaller and more numerous while the amount taken stays the same, so all four equal one half.
8	0.35; 3/5	7 ÷ 20 = 0.35, and 20 expands to 100 as 35/100. 0.6 is six tenths, 6/10, which reduces to 3/5. Both directions rest on the same fact: divide, or read straight off tenths and hundredths.
9	0.4 is larger	As decimals, 3 ÷ 8 = 0.375, below 0.4. As fractions, 0.4 = 4/10 = 2/5, and over 40 that is 15/40 against 16/40, the same verdict. Fractions and decimals compare fine once both are in one form.
10	Adding the same number does not keep the value; 10/12 or 20/24 is correct	5 × 7 = 35 but 6 × 6 = 36, so the cross products differ and 5/6 (about 0.833) is not 6/7 (about 0.857). Equivalence comes from multiplying or dividing both parts: 5/6 = 10/12 = 20/24.

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.

Find a tutor free

Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.