Sheet 5 of 10 · Maths
Ratio and proportion
Simplifying, sharing, the unitary method, scaling and maps. 8 rules, each with a worked example.
Ratio basics
Ratio notation
a : b compares one part with another part
Example3 red and 5 blue: red : blue = 3 : 5, and red is 3/8 of the totalSimplifying a ratio
Divide every part by the same number (the HCF)
Example12 : 18 = 2 : 3 (both ÷ 6)Tip: Make the units match first: 50p : £2 = 50 : 200 = 1 : 4
Sharing in a ratio
Total parts method
Add the parts → find one part → multiply
ExampleShare £45 in the ratio 2 : 3: 5 parts, 1 part = £9, so £18 and £27When you know one share
Use the share you know to find one part
ExampleBoys : girls = 3 : 4 with 12 boys: 1 part = 4, so 16 girls (28 children)
Proportion
Unitary method
Find the value of ONE, then multiply
Example5 pens cost £3.50 → 1 pen costs 70p → 8 pens cost £5.60Scaling a recipe
New amount equals old amount ÷ old servings × new servings
Example300 g flour serves 4. For 6: 300 ÷ 4 × 6 = 450 gDirect and inverse proportion
Direct: both go up together · Inverse: one goes up, the other goes down
- Inverse: workers × days stays the same (4 × 6 = 24 = 8 × 3)
Example4 workers take 6 days → 1 worker takes 24 days → 8 workers take 3 daysScale drawings and maps
Real length equals map length × scale
- Convert at the end: 100 cm = 1 m, 1000 m = 1 km
ExampleScale 1 : 50,000: 4 cm on the map = 200,000 cm = 2 km
Want the full explanation?
The study guide goes through each rule step by step, with more examples.