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GCSE · Ratio, Proportion and Rates of Change

3.4 Writing and Simplifying Ratio

EDEXCEL 1MA1 · Calculator allowed · about 75 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A bag contains 8 red sweets and 12 green sweets. Write down the ratio of red sweets to green sweets.

(Total for Question 1 is 1 mark)

At a rescue centre there are 5 dogs and 9 cats. Write down the ratio of cats to dogs.

(Total for Question 2 is 1 mark)

Write the ratio 10:15 in its simplest form.

(Total for Question 3 is 1 mark)

Which of these ratios is equivalent to 2:5?

A) 4:10
B) 5:2
C) 2:10
D) 4:8

(Total for Question 4 is 1 mark)

Simplify the ratio 24:36.

(Total for Question 5 is 2 marks)

Simplify the ratio 6:9:15 fully.

(Total for Question 6 is 2 marks)

Simplify the ratio 40 minutes : 2 hours, giving your answer in its simplest form.

(Total for Question 7 is 3 marks)

Simplify the ratio 750 g : 3 kg, giving your answer in its simplest form.

(Total for Question 8 is 3 marks)

Nadia has 45p and her sister has £2.25. Simplify the ratio of Nadia's money to her sister's money.

(Total for Question 9 is 3 marks)

Write the ratio 9:36 in the form 1:n.

(Total for Question 10 is 2 marks)

Write the ratio 18:8 in the form n:1.

(Total for Question 11 is 2 marks)

In Ms Okafor's class there are 30 students. 12 of them are boys. Write the ratio of boys to girls in its simplest form.

(Total for Question 12 is 3 marks)

Aisha is baking a cake. Her recipe uses flour, sugar and butter with masses 300 g flour, 150 g sugar and 100 g butter.

(a)Write the ratio flour : sugar : butter in its simplest form.(2)

(b)Aisha decides to make a bigger cake using 900 g of flour, keeping the same ratio. Work out the mass of sugar and the mass of butter she needs.(3)

(Total for Question 13 is 5 marks)

In a garden the ratio of flowers to shrubs is 3:7. Write down what fraction of the plants are flowers.

(Total for Question 14 is 2 marks)

A rectangular garden bed has length 24 m and width 18 m. Write the ratio of length to width in its simplest form.

(Total for Question 15 is 2 marks)

Chidi, Priya and Tom invest £120, £180 and £300 respectively in a business. Write the ratio of their investments, Chidi : Priya : Tom, in its simplest form.

(Total for Question 16 is 3 marks)

Simplify the ratio 0.5 : 1.25, giving your answer as a ratio of whole numbers in its simplest form.

(Total for Question 17 is 2 marks)

Simplify the ratio 3/4 : 1/2, giving your answer as a ratio of whole numbers in its simplest form.

(Total for Question 18 is 2 marks)

Leon mixes paint using 2 litres of white paint, 500 ml of blue paint and 1.5 litres of red paint. Write the ratio white : blue : red in its simplest form.

(Total for Question 19 is 3 marks)

Freya is drawing a scale plan of her bedroom.

(a)On the plan, one wall is drawn 8 cm long. The real wall is 20 m long. Find the scale of the drawing, giving your answer in the form 1 : n.(3)

(b)A different wall is drawn 11.4 cm long on the plan. Work out the real length of this wall, giving your answer in metres.(2)

(Total for Question 20 is 5 marks)

Mark scheme · 3.4 Writing and Simplifying Ratio

Question 1

B1 8:12 oe (simplifying is not required)
Answer: 8:12

Question 2

B1 9:5 oe (order must be cats then dogs)
Answer: 9:5

Question 3

B1 2:3 cao
Answer: 2:3

Question 4

B1 A cao
Answer: A) 4:10

Question 5

M1 identify a common factor of 24 and 36 (e.g. divide by 12) oe
A1 2:3 cao
Answer: 2:3

Question 6

M1 divide all three parts by a common factor (e.g. 3) oe
A1 2:3:5 cao
Answer: 2:3:5

Question 7

M1 convert 2 hours to 120 minutes oe
M1 form the ratio 40:120 (or equivalent) and begin to simplify
A1 1:3 cao
Answer: 1:3

Question 8

M1 convert 3 kg to 3000 g oe
M1 form the ratio 750:3000 and begin to simplify
A1 1:4 cao
Answer: 1:4

Question 9

M1 convert £2.25 to 225p oe
M1 form the ratio 45:225 and begin to simplify
A1 1:5 cao
Answer: 1:5

Question 10

M1 divide both parts by 9 oe
A1 1:4 cao
Answer: 1:4

Question 11

M1 divide both parts by 8 oe
A1 2.25:1 oe (accept 9/4 : 1)
Answer: 2.25:1

Question 12

M1 girls = 30 - 12 = 18 oe
M1 form the ratio 12:18
A1 2:3 cao
Answer: 2:3

Question 13

(a) M1 divide all three masses by a common factor (e.g. 50) oe
(a) A1 6:3:2 cao
(a) Answer: 6:3:2
(b) M1 find the scale factor, 900 / 300 = 3 oe
(b) M1 multiply the sugar and butter masses by 3 (or use ratio part = 150 g)
(b) A1 sugar = 450 g and butter = 300 g cao
(b) Answer: sugar = 450 g, butter = 300 g

Question 14

M1 total parts = 3 + 7 = 10 oe
A1 3/10 oe
Answer: 3/10

Question 15

M1 identify a common factor of 24 and 18 (e.g. 6) oe
A1 4:3 cao
Answer: 4:3

Question 16

M1 identify a common factor of 120, 180 and 300 (e.g. 60) oe
M1 divide all three amounts by the common factor
A1 2:3:5 cao
Answer: 2:3:5

Question 17

M1 multiply both parts by a suitable number (e.g. x4 or x100) to remove the decimals oe
A1 2:5 cao
Answer: 2:5

Question 18

M1 multiply both parts by a common denominator (e.g. x4) oe
A1 3:2 cao
Answer: 3:2

Question 19

M1 convert all amounts to the same unit, e.g. 2000 ml, 500 ml, 1500 ml oe
M1 form the ratio 2000:500:1500 and begin to simplify
A1 4:1:3 cao
Answer: 4:1:3

Question 20

(a) M1 convert 20 m to 2000 cm oe
(a) M1 form the ratio 8:2000 and simplify (e.g. divide by 8)
(a) A1 n = 250, i.e. 1:250 cao
(a) Answer: 1:250
(b) M1 11.4 x 250 (= 2850) oe, ft from part (a)
(b) A1 28.5 m cao
(b) Answer: 28.5 m

Writing and Simplifying Ratio - Worksheets, Questions and Revision