Ratio and sharing | AQA GCSE Maths Notes

Visual model

Ratio bars show equal parts clearly

A:B=3:2

add parts, then find one part

Gold-standard guide

20 mins

What you will learn

Simplify ratios and divide amounts into given parts.

Use a clear step-by-step method for ratio and sharing.

Check your answer and avoid the most common exam mistake.

Useful before you start

Core number skillsEarlier ratio, proportion and rates of change skillsShowing clear working

Core knowledge

Know the rule, then use it

These are the short notes. Read each one, then check you can use it in the worked example below.

Method

Find the total number of parts, calculate one part's value, then multiply for each share

Step 1

Add the parts to find the total number of parts

3 + 4 + 7 = 14 parts

Step 2

Find the value of one part

£420 ÷ 14 = £30 per part

Step 3

Multiply for each share

3 × £30 = £90

Watch out

Students find one part correctly but forget to multiply for each different ratio value

One part

$one part = tota\frac{l}{total} number of ratio parts.$

$share = one part \times that person's ratio number.$

Worked example

Share £420 in the ratio 3:4:7.

Add the parts to find the total number of parts: 3 + 4 + 7 = 14 parts.

Find the value of one part: £420 ÷ 14 = £30 per part.

Multiply for each share: 3 × £30 = £90. 4 × £30 = £120. 7 × £30 = £210.

Check that the shares sum to the total: £90 + £120 + £210 = £420. ✓

Final answer

£90, £120 and £210

Question ladder

Build up to the hardest questions

Do them in order. If you miss a step, read the solution, then redo the question without looking.

Workedreasoning

Share £420 in the ratio 3:4:7.

4 marks4 minsratio-and-sharing-worked

Show solution

Worked solution

1.Add the parts to find the total number of parts: 3 + 4 + 7 = 14 parts.
2.Find the value of one part: £420 ÷ 14 = £30 per part.
3.Multiply for each share: 3 × £30 = £90. 4 × £30 = £120. 7 × £30 = £210.
4.Check that the shares sum to the total: £90 + £120 + £210 = £420. ✓

Final answer

£90, £120 and £210

Mark points

M1: add the parts to find the total number of parts
M1: find the value of one part
M1: multiply for each share
M1: check that the shares sum to the total
A1: £90, £120 and £210

Watch out

Students find one part correctly but forget to multiply for each different ratio value.Always write 'one part = …' explicitly, then multiply each part of the ratio separately.

Diagnosticrecall

Share 360 g in the ratio 1:2:3.

1 mark2 minsratio-and-sharing-q1

Show solution

Worked solution

1.Spot the skill: Find the total number of parts, calculate one part's value, then multiply for each share.
2.Use the add the parts to find the total number of parts stage first, then find the value of one part.
3.Keep the final answer visible: 60 g, 120 g and 180 g.

Final answer

60 g, 120 g and 180 g

Mark points

M1: use the correct find the total number of parts, calculate one part's value, then multiply for each share.simplify ratios first by dividing all parts by their hcf. check: shares must sum to the total.
A1: 60 g, 120 g and 180 g

Watch out

Students find one part correctly but forget to multiply for each different ratio value.Always write 'one part = …' explicitly, then multiply each part of the ratio separately.

Easyprocedure

Two people share profit in ratio 5:3. Total profit £640. Find each share.

2 marks3 minsratio-and-sharing-q2

Show solution

Worked solution

1.Spot the skill: Find the total number of parts, calculate one part's value, then multiply for each share.
2.Use the find the value of one part stage first, then multiply for each share.
3.Keep the final answer visible: £400 and £240.

Final answer

£400 and £240

Mark points

M1: use the correct find the total number of parts, calculate one part's value, then multiply for each share.simplify ratios first by dividing all parts by their hcf. check: shares must sum to the total.
A1: £400 and £240

Watch out

Students find one part correctly but forget to multiply for each different ratio value.Always write 'one part = …' explicitly, then multiply each part of the ratio separately.

Mediumreasoning

Simplify the ratio 24:36:60.

3 marks4 minsratio-and-sharing-q3

Show solution

Worked solution

1.Spot the skill: Find the total number of parts, calculate one part's value, then multiply for each share.
2.Use the multiply for each share stage first, then check that the shares sum to the total.
3.Keep the final answer visible: 2:3:5.

Final answer

2:3:5

Mark points

M1: use the correct find the total number of parts, calculate one part's value, then multiply for each share.simplify ratios first by dividing all parts by their hcf. check: shares must sum to the total.
A1: 2:3:5

Watch out

Students find one part correctly but forget to multiply for each different ratio value.Always write 'one part = …' explicitly, then multiply each part of the ratio separately.

Hardproblem solving

A:B = 3:5 and B:C = 2:7. Find A:B:C.

3 marks5 minsratio-and-sharing-q4

Show solution

Worked solution

1.Spot the skill: Find the total number of parts, calculate one part's value, then multiply for each share.
2.Use the check that the shares sum to the total stage first, then add the parts to find the total number of parts.
3.Keep the final answer visible: 6:10:35.

Final answer

6:10:35

Mark points

M1: use the correct find the total number of parts, calculate one part's value, then multiply for each share.simplify ratios first by dividing all parts by their hcf. check: shares must sum to the total.
A1: 6:10:35

Watch out

Students find one part correctly but forget to multiply for each different ratio value.Always write 'one part = …' explicitly, then multiply each part of the ratio separately.

Exam-stylemulti-step

Mortar is made from sand and cement in ratio 4:1 by mass. How much sand is in 15 kg of mortar?

4 marks6 minsratio-and-sharing-q5

Show solution

Worked solution

1.Spot the skill: Find the total number of parts, calculate one part's value, then multiply for each share.
2.Use the add the parts to find the total number of parts stage first, then find the value of one part.
3.Keep the final answer visible: 12 kg.

Final answer

12 kg

Mark points

M1: use the correct find the total number of parts, calculate one part's value, then multiply for each share.simplify ratios first by dividing all parts by their hcf. check: shares must sum to the total.
A1: 12 kg

Watch out

Students find one part correctly but forget to multiply for each different ratio value.Always write 'one part = …' explicitly, then multiply each part of the ratio separately.

Grade 9 stretchproblem solving

Share £540 in the ratio 2:3:4. Find the largest share.

4 marks7 minsratio-g9

Show solution

Worked solution

1.Add the ratio parts.
2.Find the value of one part.
3.Multiply by the largest number of parts.

Final answer

£240

Mark points

M1: total 9 parts
M1: one part = £60
A1: £240

Watch out

Do not rush straight into arithmetic. Select the relevant method and show a complete chain of working.

Timed checkpoint

12 mins - 9 marks

Switch between skills

Set a timer and attempt all four questions before opening any answers. This is closer to the way skills appear in a real paper.

1Ratio and sharing - 2 marksShare 360 g in the ratio 1:2:3.Mark answer

Answer

60 g, 120 g and 180 g

2Fractions and ratios - 2 marksIn a ratio 3:7, what fraction of the total does the first part represent?Mark answer

Answer

$\frac{3}{1}0$

3Direct and inverse proportion - 2 marksF is directly proportional to m × a. When m = 2 and a = 3, F = 24. Find F when m = 5 and a = 4.Mark answer

Answer

4Percentage change - 3 marksA car depreciates by 20% per year. It was worth £12,000 new. Find its value after 2 years.Mark answer

Answer

£7,680

Mastery check

I can explain the method for ratio and sharing.
I can show clear working without skipping key steps.
I can avoid this mistake: Students find one part correctly but forget to multiply for each different ratio value.Always write 'one part = …' explicitly, then multiply each part of the ratio separately.

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