What is the first step when sharing in a ratio?

Add the parts to get the total number of parts, then divide the amount by that total.

What does a scale of 1 : 20000 mean?

One centimetre on the map stands for 20000 cm, that is 200 metres, in reality.

P6 maths ratio and proportion paper 2 (intermediate): sharing and scale

2026-11-10

Tutor Prep Guide · P6 Maths Ratio and Proportion

Ten intermediate items: decimal and fraction ratios, three-part sharing, missing terms, map scale and school totals.

Direct answers　Write the total number of parts before multiplying, then check the notes in the answer table.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	20
Difficulty mix	Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1
Chapter	Chapter: P6 Maths Ratio and Proportion
Level	P6

02　Questions (10 items)

FoundationShare $240 between A and B in the ratio 3 : 5. How much does each receive?
FoundationWrite 1.5 : 2.5 in simplest form.
FoundationWrite the ratio 3/4 : 5/8 in simplest form.
IntermediateIn a sugar solution the ratio of sugar to water is 2 : 7. If there is 30 g of sugar, how much water is there?
IntermediateDivide 81 into three parts in the ratio 2 : 3 : 4. What is each part?
IntermediateGiven 8 : x = 12 : 15, find x.
ChallengeA map has a scale of 1 : 20000. What real distance does 4 cm on the map represent?
ChallengeIn a school the ratio of boys to girls is 5 : 4 and there are 540 pupils. How many boys and girls are there?
ChallengeThree brothers share $450 in the ratio 4 : 5 : 6. How much does each receive?
Error redoA pupil shared $420 in the ratio 3 : 4 but took 420 ÷ 4 = 105 as one part, getting $315 and $420. What is correct?

03　Answers and one-line notes

#	Answer	One-line note
1	A gets $90 and B gets $150	There are 8 parts, 240 ÷ 8 = 30 dollars per part, so A gets 3 × 30 = 90 and B gets 5 × 30 = 150.
2	3 : 5	Multiply both terms by 10 to get 15 : 25, then divide by 5 to reach 3 : 5.
3	6 : 5	Multiply both terms by 8: 3/4 × 8 = 6 and 5/8 × 8 = 5, giving 6 : 5.
4	105 g	2 parts weigh 30 g, so 1 part is 15 g and the water is 7 × 15 = 105 g, giving 135 g of solution in all.
5	18, 27 and 36	There are 9 parts, 81 ÷ 9 = 9 per part, so the parts are 18, 27 and 36.
6	x = 10	Cross-multiply: 12x = 8 × 15 = 120, so x = 10.
7	800 m	The real length is 4 × 20000 = 80000 cm, which is 800 m after dividing by 100.
8	300 boys and 240 girls	There are 9 parts, 540 ÷ 9 = 60 pupils per part, so 5 × 60 = 300 boys and 4 × 60 = 240 girls.
9	$120, $150 and $180	There are 15 parts, 450 ÷ 15 = 30 dollars per part, giving 120, 150 and 180 dollars.
10	A gets $180 and B gets $240	Add the parts first: 3 + 4 = 7, then 420 ÷ 7 = 60 per part and multiply by 3 and 4; dividing by 4 is not the number of parts.

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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