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Farmer Bull has 20 cows. How many sheep does he have?

Ratio 2 (Medium)

This 11 Plus Maths quiz looks at how ratios appear in everyday life, from simple comparisons to the famous golden ratio seen in nature and design.

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Fascinating Fact:

The golden ratio, approximately 1.618, appears in art, nature, and even seashells, known as the most beautiful ratio in the world.

In 11 Plus Maths, pupils explore ratios to compare quantities, scale drawings, and solve problems involving relationships between numbers. Ratios help develop proportional reasoning and a sense of balance in problem solving.

Key Terms

Golden Ratio: A special number, about 1.618, found when two quantities are in the most pleasing proportion to the human eye.
Proportion: When two ratios are equal, showing a consistent relationship between quantities.
Scale: A ratio used to show how measurements in a drawing or model relate to real-life size.

Learn more about 11 Plus exam content in our guide for parents.

Frequently Asked Questions (Click to see answers)

What is the golden ratio used for today?

The golden ratio is used in art, design, and architecture to create visually pleasing layouts. It also appears naturally in plants, shells, and human body proportions.

How do you simplify a ratio?

To simplify a ratio, divide both sides by their highest common factor. For example, 12:18 simplifies to 2:3 because both numbers divide by 6.

Why do artists and architects use ratios?

Ratios help maintain proportion, symmetry, and balance in designs. Using ratios ensures that features or spaces relate harmoniously to each other.

Try These Related Quizzes

1 .

Seventy photographs are to be displayed in a gallery. If the ratio of portrait pictures to landscape pictures has to be 3:4, how many portrait pictures and landscape pictures have to be selected?

30 portrait pictures and 40 landscape pictures

35 portrait pictures and 35 landscape pictures

25 portrait pictures and 45 landscape pictures

45 portrait pictures and 25 landscape pictures

3 + 4 = 7 ? the fractional parts are ³?₇ × 70 = 30 portrait pictures and ⁴?₇ × 70 = 40 landscape pictures. CHECK 30:40 = 3:4 (dividing by 10). Your answer MUST preserve (keep) the same ratio

2 .

Farmer Bull has 20 cows. How many sheep does Farmer Bull have if the ratio of cows to sheep is 5:6?

5:6 = 1:1.2 (dividing by 5). This means that there is 1 cow for every 1.2 sheep ? there are 1.2 as many sheep as there are cows = 1.2 × 20 = 24. CHECK 20:24 = 1:1.2 (dividing by 20). Your answer MUST preserve (keep) the same ratio. ALWAYS try to REDUCE your ratios so as to get a '1' in one of the terms of the ratio. Incidentally, 20 + 24 = 44 animals in all!

3 .

The ratio of cheese sandwiches to ham sandwiches is 7:5. If there are 36 sandwiches in all, how many ham sandwiches are there?

7 + 5 = 12 so ⁷?₁₂ of the sandwiches are cheese and ⁵?₁₂ are ham. 36 ÷ 12 = 3 so each unit in the ratio represents 3 sandwiches. 3 x 7 = 21 and 3 x 5 = 15. There are 21 cheese sandwiches and 15 ham sandwiches

4 .

The ratio of red roses to white roses is 7:9. What fraction of the roses are white?

⁹⁄₈

⁷⁄₁₆

⁷⁄₈

⁹⁄₁₆

7 + 9 = 16. You DON'T have to know what the total number of items is in order to find the fractional amounts of each type of item

5 .

How else can the ratio 9:24 be written?

3:8

4:12

1:3

18:46

9:24 = 3:8 (dividing by 3)

6 .

The following ratios show the ratio of wins to defeats for four football teams. If all four teams have played the same number of games, which team has won the most often?

1:1

9:10

21:17

14:24

1:1 represents an equal number of wins and defeats. 9:10 and 14:24 both represent fewer wins than defeats. Only 21:17 represents more games won than lost

7 .

⁴⁄₇ of the children in a class are girls. What is the ratio of girls to boys in the class?

3:4

4:3

4:7

7:4

If ⁴?₇ of the children in a class are girls, then ³?₇ of the children must be boys

8 .

Which of the following is not a way of expressing the ratio 5:6?

10:12

25:30

45:54

60:78

10:12 is the same as 5:6 (multiply by 2), 25:30 is the same as 5:6 (multiply by 5), 45:54 is the same as 5:6 (multiply by 9). 60:78 is NOT the same as 5:6 – the 5 has been multiplied by 12 but the 6 has been multiplied by 13

9 .

How else can the ratio 1.75:2 be written?

7:8

6:7

5:6

4:5

1.75:2 = 7:8 (multiplying by 4)

10 .

If the ratio of swimmers to non-swimmers is 9:2, which of the following statements is correct?

There are more swimmers than non-swimmers

There are an equal amount of swimmers and non-swimmers

There are more non-swimmers than swimmers

There is not enough information to answer the question

9 is greater than 2 and it represents the number of swimmers. There are clearly more swimmers than non-swimmers

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)

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