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Ratio (Difficult)

This 11 Plus Maths quiz challenges pupils to apply ratio knowledge to more complex problems, involving scaling, unit conversions, and mathematical reasoning.

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Fascinating Fact:

The ratio of the circumference of the Earth to its diameter is always pi, whether you measure a marble or a planet.

In 11 Plus Maths, understanding ratios helps pupils solve real-world problems involving scale, fractions, and proportions. Ratios form a bridge between arithmetic and algebra, preparing students for higher-level mathematics.

Key Terms

Unit Ratio: A ratio where one term is compared to a single unit, helping simplify comparisons.
Constant Ratio: A fixed relationship between quantities, even when they are scaled up or down.
Rate: A ratio comparing two quantities with different units, such as speed being distance per time.

Learn more about 11 Plus topics in our guide for parents.

Frequently Asked Questions (Click to see answers)

What makes a ratio difficult to solve?

Ratios become difficult when they involve more than two quantities, require conversion to fractions or percentages, or include different units that must be standardised.

How do ratios link to algebra?

Ratios can be expressed as equations, helping pupils form algebraic relationships. For example, if 2x = 6y, the ratio x:y equals 3:1.

Where do ratios appear in advanced maths?

Ratios are used in geometry, trigonometry, and physics to describe relationships such as angles, forces, or speed. They provide the foundation for proportional reasoning.

Try These Related Quizzes

1 .

How else can the ratio 7:1.5 be written?

3:14

7:3

14:3

14:1.5

7:1.5 = 14:3 (multiply by 2)

2 .

What are the fractional parts of the ratio 2:9?

²⁄₇ and ⁹⁄₇

⁹⁄₁₁ and ²⁄₉

²⁄₁₁ and ⁹⁄₁₁

²⁄₉ and ¹¹⁄₉

2 + 9 = 11 which becomes the denominator in the fractional parts

3 .

What are the fractional parts of the ratio 2:3:4?

²⁄₂, ³⁄₂ and ⁴⁄₂

²⁄₉, ³⁄₉ and ⁴⁄₉

²⁄₃, ³⁄₃ and ⁴⁄₃

²⁄₅, ³⁄₅ and ⁴⁄₅

2 + 3 + 4 = 9 which becomes the denominator in the fractional parts

4 .

How else can the ratio 5:1.25:3 be written?

5:20:12

20:5:12

20:12:5

12:5:20

5:1.25:3 = 20:5:12 (multiply by 4)

5 .

Granny gave Dave, Harry and Mary £600. If the money was shared out in the ratio 1:4:5 respectively, how much did each person get?

Dave £60, Harry £240 and Mary £300

Dave £240, Harry £60 and Mary £300

Dave £300, Harry £240 and Mary £60

Dave £240, Harry £300 and Mary £60

1 + 4 + 5 = 10 ? the fractional parts are as follows: Dave, ¹?₁₀ × £600 = £60; Harry, ⁴?₁₀ × £600 = £240; Mary, ⁵?₁₀ × £600 = £300

6 .

William, Anna and Terry all have their birthdays on the same day. If their ages are in the ratio 1:4:5 respectively, and their combined age is 140, how old are they?

William 70, Anna 56, and Terry 14

William 14, Anna 70, and Terry 56

William 56, Anna 14, and Terry 70

William 14, Anna 56, and Terry 70

1 + 4 + 5 = 10 ? the fractional parts are as follows: William, ¹?₁₀ × 140 = 14; Anna, ⁴?₁₀ × 140 = 56; Terry, ⁵?₁₀ × 140 = 70

7 .

The workload has to be shared out between three workers, A, B and C in the ratio 2:6:3 respectively. If the work consists of 1,100 units, how many units will each of the workers have to do?

A 600, B 200 and C 300

A 300, B 600 and C 200

A 200, B 600 and C 300

A 300, B 200 and C 600

2 + 6 + 3 = 11 ? the fractional parts are as follows: A, ²?₁₁ × 1,100 = 200; B, ⁶?₁₁ × 1,100 = 600; C, ³?₁₁ × 1,100 = 300

8 .

What are the fractional parts of 12:4:8?

³⁄₁₂, ¹⁄₁₂ and ²⁄₁₂

³⁄₆, ¹⁄₆ and ²⁄₆

³⁄₃, ¹⁄₃ and ²⁄₃

³⁄₂, ¹⁄₂ and ²⁄₂

12:4:8 = 3:1:2 (dividing by 4). 3 + 1 + 2 = 6 which becomes the denominator in the fractional parts. Always try and simplify your ratios BEFORE you work out the fractional parts

9 .

If 1,000 toy soldiers are divided into three parts, Alan gets 260, Brian gets 340 and Charles gets 400, what is this as the ratio A:B:C in its lowest form?

13:17:20

17:13:20

17:20:13

20:17:13

A:B:C: = 260:340:400 = 26:34:40 (dividing by 10) = 13:17:20 (dividing by 2)

10 .

How else can the ratio 0.125:1.25:2.125 be written?

10:1:17

17:10:1

17:1:10

1:10:17

0.125:1.25:2.125 = 1:10:17 (multiplying by 8). This example should show you why it is important to be able to simplify ratios