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Unitary method Quiz

Grade 2 • 2Q • 10 Questions (16 Marks)

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Score: 0 / 10
Unitary method — Notes & Worked Examples Show / Hide

Explanation:

The unitary method solves direct proportion problems in two clear steps: first divide to find the value of 1 unit (one item, 1 g, or 1 ml), and then multiply by the number of units you need.

Writing down the value of 1 item clearly in the middle of your working guarantees method marks and avoids mistakes when scaling recipes, weights, or costs.

Example 1: 5 identical notebooks cost £6.75.
Work out the total cost of 8 of these notebooks.

Solution:

Step 1: Divide by 5 to find the cost of 1 notebook:
• £6.75 ÷ 5 = £1.35
Step 2: Multiply by 8 to find the cost of 8 notebooks:
• £1.35 × 8 = £10.80
Answer: £10.80

Example 2: A recipe for 6 flapjacks uses 150 g of oats.
How many grams of oats are needed to make 15 flapjacks?

Solution:

Step 1: Divide by 6 to find oats for 1 flapjack:
• 150 g ÷ 6 = 25 g per flapjack
Step 2: Multiply by 15 for 15 flapjacks:
• 25 g × 15 = 375 g
Answer: 375 g
Question 1
[1 mark]
Sarah wants to make 15 cookies using this recipe:
@@TABULAR0@@
How much of each ingredient does she need?
Worked Solution & Answer
1) Divide to find the value for 1 unit (the unitary method)
2) Multiply by the number of units needed
450g chocolate chips 600ml milk
Answer: 450g chocolate chips 600ml milk
Question 2
[1 mark]
@@TABULAR0@@
How much of each ingredient is needed for 15 people?
Worked Solution & Answer
1) Divide to find the value for 1 unit (the unitary method)
2) Multiply by the number of units needed
450g flour 450g sugar 450g butter
Answer: 450g flour 450g sugar 450g butter
Question 3
[1 mark]
3 identical pens cost £0.45
Calculate the cost of 9 of these pens
£
Worked Solution & Answer
1) Divide to find the value for 1 unit (the unitary method)
2) Multiply by the number of units needed
£1.35
Answer: £ £1.35
Question 4
[1 mark]
Work out
4 identical apples weigh 440g
Calculate the weight of 9 of these apples
g
Worked Solution & Answer
1) Divide to find the value for 1 unit (the unitary method)
2) Multiply by the number of units needed
990g
Answer: 990g g
Question 5
[1 mark]
4 cups of coffee cost £5.60
You pay for 7 cups of coffee with a £20 note
How much change should you get?
£
Worked Solution & Answer
1) Divide to find the value for 1 unit (the unitary method)
2) Multiply by the number of units needed
£10.20
Answer: £ £10.20
Question 6
[1 mark]
Sarah wants to make 30 cookies using this recipe:
@@TABULAR0@@
How much of each ingredient does she need?
Worked Solution & Answer
1) Divide to find the value for 1 unit (the unitary method)
2) Multiply by the number of units needed
900g chocolate chips 2400ml milk
Answer: 900g chocolate chips 2400ml milk
Question 7
[2 marks]
3 pens cost £9.
How much do 6 pens cost?
£
Worked Solution & Answer
1 pen = £3, 6 pens = £18 B1
Answer: £ £18
Question 8
[2 marks]
4 pens cost £16.
How much do 8 pens cost?
£
Worked Solution & Answer
1 pen = £4, 8 pens = £32 B1
Answer: £ £32
Question 9
[3 marks]
Batteries are sold in packs of 4, in packs of 8 and in packs of 12
£1.80£3.20£6.00
A pack of 4 batteries costs £1.80
A pack of 8 batteries costs £3.20
A pack of 12 batteries costs £6.00
Which pack gives the best value for money?
You must show how you get your answer.
Worked Solution & Answer
Pack of 4: £1.80 ÷ 4 = 45p per battery M1
Pack of 8: £3.20 ÷ 8 = 40p per battery M1
Pack of 12: £6.00 ÷ 12 = 50p per battery → Pack of 8 gives the best value for money A1
Answer: Pack of 8 (40p per battery vs 45p and 50p)
Question Paper (PDF) • Mark Scheme (PDF)
Question 10
[3 marks]
Choci bar200 g£3.50LondonChoci bar360 g7.20 Swiss francsZurich
In London, a 200 g Choci bar costs £3.50. In Zurich, a 360 g Choci bar costs 7.20 Swiss francs. £1 = 1.25 Swiss francs. In which city is the Choci bar better value for money?
In London, a 200 g Choci bar costs £3.50
In Zurich, a 360 g Choci bar costs 7.20 Swiss francs.
The exchange rate is £1 = 1.25 Swiss francs.
In which city is the Choci bar the better value for money, in London or in Zurich?
You must show how you get your answer.
Worked Solution & Answer
7.20 ÷ 1.25 = £5.76 M2
£5.76 ÷ 360 = 1.6p per gram vs £3.50 ÷ 200 = 1.75p per gram ⇒ Zurich A1
Answer: Zurich (London = 1.75p/g; Zurich = £5.76 for 360 g = 1.6p/g)
Question Paper (PDF) • Mark Scheme (PDF)
Score: 0 / 10 (0 / 16 marks)
Unitary method Worksheets Next: Bar charts →

Grade 2 Quizzes

19 Topics
2A - Calculation problems2B - Using a calculator
2C - Systematic listing2D - Fraction of an amount
2E - FDP2F - Simplifying algebra
2G - Writing an expression2H - Function machines
2J - Solving one step equations2K - Angles
2L - Area and perimeter2M - Reading scales
2N - Probability & Probability Scale2P - Frequency polygons
2Q - Unitary method2R - Bar charts
2S - Pie charts2T - Averages
2U - Stem and leaf diagrams