Edexcel · GCSE Maths · 1MA1 · Foundation and Higher
M22 · Ratio and sharing
Revision notes, worked examples and methods for ratio and sharing.
Notes and quizzes ready · 50 questions · Video coming soon.
Foundation shows shared notes and questions. Higher includes the shared content and labelled Higher extensions. Changing tier starts the notes and a new quiz set.
Revise the key ideas
Ratios and fractions
A ratio compares quantities in a specified order. Red : blue = 2 : 3 means two red parts for every three blue parts; reversing the order changes the ratio.
Simplify by dividing all parts by their HCF: 18 : 24 = 3 : 4. For three parts, 12 : 18 : 30 = 2 : 3 : 5.
Convert quantities to the same units before comparing: 50 cm : 2 m = 50 : 200 = 1 : 4.
A part-to-part ratio 2 : 3 gives part-to-whole fractions 25 and 35. The first part is 23 of the second part, but 25 of the total. Ratio bar for sharing eighty-four pounds
To express one quantity as a fraction of another, use first quantitysecond quantity with matching units. The fraction can exceed 1.
Sharing and finding totals
Worked example: Share £84 in ratio 2 : 5. There are 7 parts; each is £12, so the shares are £24 and £60. Check both their total and their simplified ratio.
Worked example: A : B = 3 : 7 and B is 28. One part is 28 ÷ 7 = 4, so A = 12 and the total is 40. Do not divide 28 by all 10 parts.
Worked example: Two shares are in ratio 3 : 5 and differ by £18. Two parts represent £18, so one part is £9; the shares are £27 and £45.
For mixing, preserve the ratio when scaling quantities. A drink mixed concentrate : water = 1 : 4 needs 200 ml concentrate and 800 ml water for 1 litre of drink.
If a ratio describes concentrations or mixtures, be clear whether it is a mass ratio or volume ratio. Do not combine incompatible units silently.
Linking ratios and relationships
Equivalent ratios have equal quotients: a : b = c : d means ab = cd where denominators are non-zero. This links ratios to proportional relationships.
If x : y = 2 : 5, then y = 52x. On a y-against-x graph this is a straight line through the origin.
To combine A : B = 2 : 3 and B : C = 4 : 5, make B match: 8 : 12 and 12 : 15, so A : B : C = 8 : 12 : 15.
Adding the same amount to both quantities generally changes their ratio. A 2 : 3 mixture does not stay in that ratio if you add 1 litre to each component.
After a change, work with actual quantities or parts before simplifying the new ratio. Multiplying both quantities by the same factor preserves the ratio; adding does not.
Test yourself
50 questions · Sets of 10 from the selected tier. For fractions, use / when typing; for powers, use superscripts or ^. Follow each question's answer format. These quick checks support revision; practise full written solutions and proofs too.
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