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Writing and simplifying ratio Quiz

Grade 3 • 3D • 10 Questions (31 Marks)

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Score: 0 / 10
Writing and simplifying ratio — Notes & Worked Examples Show / Hide

Explanation:

A ratio compares the sizes of parts to each other. Write the numbers in the exact order stated in the question, separated by a colon (:). If quantities have different units (such as cm and m, or g and kg), convert them into the same unit before simplifying.

To simplify a ratio to its simplest form, divide all parts by their highest common factor (HCF) until the parts are whole numbers with no common factor. To write a ratio in the form 1 : n or n : 1, divide both sides by the number that needs to become 1.

Example 1: Simplify the ratio 45 minutes : 2 hours fully.

Solution:

Convert 2 hours into minutes: 2 × 60 = 120 minutes
Ratio in same units = 45 : 120
Divide both sides by HCF (15):
45 ÷ 15 = 3  and  120 ÷ 15 = 8
Answer: 3 : 8

Example 2: Write the ratio 5 : 18 in the form 1 : n.

Solution:

To make the left-hand side equal to 1, divide both parts by 5:
Left side: 5 ÷ 5 = 1
Right side: 18 ÷ 5 = 3.6
Answer: 1 : 3.6
Question 1
[2 marks]
There are 24 cows and 36 sheep on a farm.
Write as a ratio the number of cows to the number of sheep.
Give your ratio in its simplest form.
Worked Solution & Answer
24 : 36 ÷ 12 = 2 : 3 M1 A1
Answer: 2 : 3
Question Paper (PDF) • Mark Scheme (PDF)
Question 2
[2 marks]
There are 24 red counters and 40 blue counters in a bag.
Write down the ratio of the number of red counters to the number of blue counters in the bag.
Give your ratio in its simplest form.
Worked Solution & Answer
24 : 40 = 3 : 5 (dividing by 8) M1 A1
Answer: 3 : 5
Question Paper (PDF) • Mark Scheme (PDF)
Question 3 AQA Nov 2020 1F Q5
[2 marks]
The diagram shows Shape A and Shape B on a centimetre grid.
Shape AShape B
Work out area of Shape A : area of Shape B
Give your answer in its simplest form.
Answer
Worked Solution & Answer
Area of Shape A = 4 × 6 = 24 cm2 M1
Area of Shape B = (4 × 2) + (3 × 4) = 8 + 12 = 20 cm2
Ratio = 24 : 20 = 6 : 5 A1
Shape AShape BArea A = 24 squares, Area B = 8 + 12 = 20 squares → 24 : 20 = 6 : 5
Answer: Answer 6 : 5
Question Paper (PDF) • Mark Scheme (PDF)
Question 4
[2 marks]
Here is a solid sphere and a solid cone.
rrhVolume of sphere =43πr3Volume of cone =13πr2h
All measurements are in cm.
The volume of the sphere is equal to the volume of the cone.
(a) Find r : h
Give your answer in its simplest form. [2 marks]
Worked Solution & Answer
(a)
(4/3)πr³ = (1/3)πr²h M1
⇒ 4r = h
⇒ r : h = 1 : 4 A1
Answer (a): 1 : 4
Question Paper (PDF) • Mark Scheme (PDF)
Question 5 Specimen Set 2 2F Q18
[3 marks]
There are 64 cards in a pack.
Each card is either red or black.
The ratio of the number of red cards to the number of black cards is 1 : 1
8 red cards are removed from the pack.
Find the ratio of the number of red cards now in the pack to the number of black cards now in the pack.
Give your answer in its simplest form.
Worked Solution & Answer
Initially 32 red and 32 black cards M1
After removing 8 red cards: 32 – 8 = 24 red cards M1
Ratio = 24 : 32 = 3 : 4 A1
Answer: 3 : 4
Question Paper (PDF) • Mark Scheme (PDF)
Question 6
[3 marks]
The table shows a cricket club’s income in 2016 from a fete, a quiz and membership fees.
IncomeFete£250QuizEntry fees13 at £5 eachRefreshments£35Membership fees25 at £20 each
Express as a ratio
the income from the fete to the income from the quiz to the income from membership fees.
Give your ratio in its simplest form.
Worked Solution & Answer
Fete = £250 M1
Quiz = 13 × 5 + 35 = £100 M1
Membership = 25 × 20 = £500
Ratio = 250 : 100 : 500 = 5 : 2 : 10 A1
Answer: 5 : 2 : 10
Question Paper (PDF) • Mark Scheme (PDF)
Question 7 AQA Nov 2021 3H Q9
[4 marks]
Rectangle ABCD is split into four smaller rectangles.
Two of the smaller rectangles are shaded.
Not drawnaccuratelyADBC4 cmx cm12 cm²56 cm²
4 : x = 1 : 2
For rectangle ABCD, work out the ratio shaded area : unshaded area
Give your answer in its simplest form.
Answer
Worked Solution & Answer
(The area of a rectangle is length × width)
From 4 : x = 1 : 2, x = 8 cm M1
Top-left height = 12 ÷ 4 = 3 cm
Top-right (shaded) area = 8 × 3 = 24 cm2 M1
Bottom-right height = 56 ÷ 8 = 7 cm
Bottom-left (shaded) area = 4 × 7 = 28 cm2 M1
Total shaded area = 24 + 28 = 52 cm2
Total unshaded area = 12 + 56 = 68 cm2
Ratio = 52 : 68 = 13 : 17. A1
Answer: Answer 13 : 17
Question Paper (PDF) • Mark Scheme (PDF)
Question 8 OCR Jun 2025 3F Q12
[4 marks]
The diagram shows a large rectangle made from 10 smaller rectangles of equal area.
The large rectangle is divided into two unequal parts, A and B.
AB
(a) Tick (✓) all the correct statements.
@@TABULAR0@@ [2 marks]
(b) The area of Part A is 18k.
Write an expression, in terms of k, for the area of Part B.
Give your answer in its simplest form. [2 marks]
Worked Solution & Answer
(a)
(The area of a rectangle is length × width)
Part A has 3 small rectangles and Part B has 7 small rectangles out of 10 M1
So A : B = 3 : 7 and A is 3/10 of the large rectangle. A1
Answer (a): Tick 2nd row (A : B = 3 : 7) and 3rd row (A is 3/10 of the large rectangle)
(b)
(The area of a rectangle is length × width)
1 small rectangle = 18k ÷ 3 = 6k M1
Area of Part B (7 small rectangles) = 7 × 6k = 42k. A1
Answer (b): 42k
Question Paper (PDF) • Mark Scheme (PDF)
Question 9 AQA Jun 2025 1F Q9
[4 marks]
Numbered discs are in two boxes.
Box A22439Box B11123449
(a) Work out the ratio
total value of the numbers in **Box A** : total value of the numbers in **Box B**
Give your answer in its simplest form. [3 marks]
Answer
(b) One disc is picked at random from Box A.
Write down the probability that the number on the disc is greater than 6 [1 mark]
Answer
Worked Solution & Answer
(a)
Total Box A = 2 + 2 + 3 + 4 + 9 = 20 M1
Total Box B = 1 + 1 + 1 + 2 + 3 + 4 + 4 + 9 = 25 M1
Ratio = 20 : 25 = 4 : 5 A1
Answer (a): Answer 4 : 5
(b)
Box A has 5 discs
Only the disc with '9' is > 6, so probability = 1/5 B1
Answer (b): Answer 15
Question Paper (PDF) • Mark Scheme (PDF)
Question 10
[5 marks]
Scott wants to make orange juice.
He is going to buy boxes of oranges.
There are 24 oranges in each box of oranges.30 oranges make 2 litres of orange juice.
(a) Work out the number of boxes of oranges that Scott needs to buy.
You must show all your working. [3 marks]
(b) Write down the ratio of the number of apples that Scott buys to the number of bananas that he buys.
Give your ratio in its simplest form. [2 marks]
Worked Solution & Answer
(a)
8 ÷ 2 = 4 M1
4 × 30 = 120 oranges needed M1
120 ÷ 24 = 5 boxes A1
Answer (a): 5
(b)
1260 : 280 = 126 : 28 = 9 : 2 (dividing by 140) M1 A1
Answer (b): 9 : 2
Question Paper (PDF) • Mark Scheme (PDF)
Score: 0 / 10 (0 / 31 marks)
Writing and simplifying ratio Worksheets Next: Ratio →

Grade 3 Quizzes

24 Topics
3A - Error intervals3B - Operations with fractions
3C - Estimation3D - Writing and simplifying ratio
3E - Ratio3F - Proportion recipes
3G - Percentages3H - Percentage change
3J - Exchange rates3K - Conversions and units
3L - Scale drawings3M - Best buy questions
3N - Substitution3P - Solving linear equations
3Q - Straight line graphs3R - Area and circumference
3S - Rotations3T - Reflections
3U - Enlargements3V - Translations
3W - Mixed transformations3X - Area of compound shapes
3Y - Frequency trees3Z - Two way tables