Ratio & Proportion
If one part changes, all parts change together
Ratios compare quantities. Proportion problems scale them up or down. The key: find the value of one part first.
See It in Action
The Problem
Orange juice and water are mixed in a ratio of 3:7. How much orange juice is needed to make 500 mL of the mixture?
Common Mistake
3:7 means 3 out of 7 is orange juice. So orange juice = 3/7 × 500 ≈ 214 mL.
The denominator should be 3+7=10 (total parts), not 7 (just water parts). The ratio 3:7 means 3 parts juice and 7 parts water, making 10 parts total.
Correct Approach
Total parts = 3 + 7 = 10. Orange juice fraction = 3/10. Orange juice = 3/10 × 500 = 150 mL.
Answer: 150 mL
Water = 7/10 × 500 = 350 mL. 150 + 350 = 500 mL total. ✓
The Core Concept
A ratio compares two or more quantities. The ratio 2:3 means for every 2 of the first thing, there are 3 of the second. When you share something in a ratio, the total is split into parts — and the trick is always to find what one part is worth.
For sharing in a ratio, add the parts to find the total number of parts. Then divide the total quantity by that number to find one part's value. Then multiply for each share. For 2:3 sharing $40: 2+3=5 parts, one part = $40÷5 = $8. First share: 2×$8=$16. Second: 3×$8=$24. Check: $16+$24=$40. ✓
For proportion (scaling), the key is identifying the multiplier. If 5 books cost $30, what do 8 books cost? One book costs $6, so 8 books cost $48. Or use cross-multiplication: 5/30 = 8/x, so x = 8×30÷5 = 48.
Common Mistakes to Avoid
Using one part as the denominator instead of the total parts
In ratio 3:7, total parts = 10. Orange juice is 3/10 of the total, not 3/7. The "7" is just the water portion, not the whole.
Not simplifying ratios before using them
6:4 and 3:2 describe the same proportion. Simplify first to keep numbers small and reduce errors.
Forgetting to check that parts add back to the total
Always verify: (share 1) + (share 2) = original total. If not, you've made an error somewhere.
Confusing ratio with fraction
A ratio 3:7 does NOT mean 3/7. It means 3/(3+7) = 3/10 of the total is the first quantity.
Try It Yourself
Flour and sugar are mixed in a ratio of 5:2. If 350 g of flour is used, how much sugar is needed?
Hint: Find what one part is worth using the flour amount (5 parts = 350 g). Then find sugar (2 parts).
Key Tips
Always add the ratio parts first to find the total number of parts.
Find "one part" by dividing the known quantity by its number of parts.
Check: all parts should add back to the original total.
Ready to practise Ratio & Proportion?
Reading is the start. The Maths Gym has exercises designed around this skill — with instant feedback and progress tracking.