Understand the rule first
A ratio tells you the relative number of equal parts. Add the parts for a total share, find the value of one part, then scale each group.
Ratio, proportion & rates 11+ practice
Use equal parts to share quantities and scale relationships accurately.
Share 48 counters in the ratio 3:5.
- There are 3 + 5 = 8 equal parts.
- One part is 48 ÷ 8 = 6.
- The shares are 3 × 6 = 18 and 5 × 6 = 30.
A common misconception
Using the ratio numbers as the actual amounts instead of as numbers of equal parts.
Reusable method: Label what one part represents before scaling.Question 1 of 10 MathscoreShare £63 in the ratio 2:5. What is the larger share?
- A£18
- B£35
- C£45
- D£50
Need a hint?
There are seven equal parts altogether.
Show worked answer
Answer C: £45
2 + 5 = 7; £63 ÷ 7 = £9 per part; 5 × £9 = £45.
Quick method: Label what one part represents before scaling.
Question 2 of 10 MathscoreRed and blue beads are in the ratio 3:4. There are 24 blue beads. How many red beads are there?
- A18
- B21
- C27
- D32
Need a hint?
Four parts represent 24 beads.
Show worked answer
Answer A: 18
One part is 24 ÷ 4 = 6; red beads = 3 × 6 = 18.
Quick method: Label what one part represents before scaling.
Question 3 of 10 MathscoreA map scale is 1 cm : 6 km. Two towns are 7.5 cm apart on the map. What is the real distance?
- A13.5 km
- B42 km
- C45 km
- D75 km
Need a hint?
Multiply each map centimetre by six kilometres.
Show worked answer
Answer C: 45 km
7.5 × 6 = 45 km.
Quick method: Label what one part represents before scaling.
Question 4 of 10 Mathsexam-styleThe ratio of adults to children is 2:7. There are 54 people altogether. How many are children?
- A12
- B14
- C40
- D42
Need a hint?
Nine parts represent all 54 people.
Show worked answer
Answer D: 42
2 + 7 = 9; 54 ÷ 9 = 6; children = 7 × 6 = 42.
Quick method: Label what one part represents before scaling.
Question 5 of 10 Mathsexam-stylePaint is mixed yellow:blue in the ratio 5:3. If 15 ml of blue is used, how much paint is made altogether?
- A25 ml
- B50 ml
- C60 ml
- D40 ml
Need a hint?
Three parts represent 15 ml; then find all eight parts.
Show worked answer
Answer D: 40 ml
One part is 15 ÷ 3 = 5 ml. Eight parts make 8 × 5 = 40 ml.
Quick method: Label what one part represents before scaling.
Question 6 of 10 MathscoreShare 84 in the ratio 3:4. What is the smaller share?
- A36
- B42
- C48
- D56
Need a hint?
There are seven equal parts altogether.
Show worked answer
Answer A: 36
84 ÷ 7 = 12 per part; the smaller share is 3 × 12 = 36.
Quick method: Label what one part represents before scaling.
Question 7 of 10 MathscoreA recipe uses flour and sugar in the ratio 5:2. If 750 g of flour is used, how much sugar is needed?
- A250 g
- B300 g
- C350 g
- D375 g
Need a hint?
Find the mass represented by one part.
Show worked answer
Answer B: 300 g
Five parts equal 750 g, so one part is 150 g. Sugar is two parts: 300 g.
Quick method: Label what one part represents before scaling.
Question 8 of 10 MathscoreThe ratio of boys to girls in a club is 7:9. There are 64 children. How many more girls than boys are there?
- A2
- B4
- C8
- D16
Need a hint?
Find the value of one of the 16 equal parts.
Show worked answer
Answer C: 8
64 ÷ 16 = 4 per part. The difference is two parts, so 2 × 4 = 8.
Quick method: Label what one part represents before scaling.
Question 9 of 10 MathsexamA map scale is 1:50,000. Two places are 7.6 cm apart on the map. What is the real distance?
- A0.38 km
- B1.52 km
- C38 km
- D3.8 km
Need a hint?
Convert 7.6 × 50,000 cm into kilometres.
Show worked answer
Answer D: 3.8 km
7.6 × 50,000 = 380,000 cm = 3,800 m = 3.8 km.
Quick method: Label what one part represents before scaling.
Question 10 of 10 MathsstretchRed and blue counters are in the ratio 4:7. After 6 red counters are added, the ratio becomes 5:7. How many counters were there originally?
- A66
- B44
- C55
- D77
Need a hint?
The blue amount is unchanged, so keep its seven parts fixed.
Show worked answer
Answer A: 66
The added red counters increase red from four parts to five parts, so one part is 6. Originally there were 11 parts: 11 × 6 = 66.
Quick method: Label what one part represents before scaling.