Writing and Simplifying Ratio - Worksheets, Questions and Revision

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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.

Revision notes: Writing and Simplifying Ratio

A ratio compares two or more quantities of the same type, written with a colon, e.g. 3:5. Simplifying a ratio means dividing every part by their highest common factor (HCF), the same idea as simplifying a fraction, so the ratio uses the smallest possible whole numbers.

Make sure all parts of the ratio are in the same units before simplifying (e.g. convert everything to cm, or everything to minutes).
Find the highest common factor (HCF) of all the numbers in the ratio.
Divide every part of the ratio by the HCF to write it in its simplest form.
If the ratio contains decimals or fractions, first multiply every part by the same number to clear them into whole numbers, then simplify as normal.

Worked example. Write 350 g : 2 kg as a ratio in its simplest form.

Convert to the same units: 2 kg = 2000 g, so the ratio is 350 : 2000.
Find the HCF of 350 and 2000: HCF = 50.
Divide both parts by 50: 350/50 = 7, and 2000/50 = 40.

Answer: 7 : 40.

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

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Writing and Simplifying Ratio - Worksheets, Questions and Revision

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3.4 Writing and Simplifying Ratio

Revision notes: Writing and Simplifying Ratio

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Question 20

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