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SATs practice · Year 6Chapter 3 · Ratio and proportion reasoning
Year 6 Maths reasoning (SATs) · Ratio and proportion reasoning · Lesson 3.4

Year 6 Maths reasoning (SATs): Best value and fair comparisons

Part of the Year 6 Maths reasoning (SATs) ratio and proportion reasoning chapter. Chapter overview · whole chapter on one page

3.4

Best value and fair comparisons

Year 6
Use proportional reasoning to compare prices and quantities, and explain why a comparison is or is not fair (Year 5-6)
Story. At the school shop, Pack A has 6 flapjacks for 240 pence, and Pack B has 4 flapjacks for 180 pence. The children argue about which is better value.

Rule

To compare prices, find the price of one item. The lower price for one item is the better value.

To compare results fairly, use the same basis. Compare percentages when the totals are different.

Key ideas

  • Price per item = total price / number of items.
  • A bigger pack is not always cheaper per item.
  • Compare percentages, not raw scores, when the number of tries is different.
Worked example 3.4.1
Pack A: 6 items cost 240p. Pack B: 4 items cost 180p. Which is better value for one item? Write the name.

Method. Work out the price of one item for each pack, then compare.

  1. Work out the price of one item in Pack A. 240p / 6 = 40p.
    40p
  2. Work out the price of one item in Pack B. 180p / 4 = 45p.
    45p
  3. Compare the prices of one item. The cheaper one for one item is the better value.
    Pack A is cheaper for one item
  4. Write the answer.
    Pack A

Check. Pack A costs less for each item. ✓

Watch out. Compare the price of ONE item. A bigger pack is not always cheaper for each item.

Worked example 3.4.2
Team A scored 24 from 30 shots, and Team B scored 30 from 40 shots. Which had the better success rate? Write the name.

Method. Write each result as a percentage, then compare.

  1. Work out the percentage for Team A. 24 out of 30 is 24 / 30 x 100.
    80%
  2. Work out the percentage for Team B. 30 out of 40 is 30 / 40 x 100.
    75%
  3. Compare the two percentages. The higher percentage is the better result.
    Team A is higher
  4. Write the answer.
    Team A

Check. 80% and 75% are compared fairly. ✓

Watch out. Comparing 30 with 24 is not fair when the numbers of shots are different.

Worked example 3.4.3
Box X: 3 items cost 90p. Box Y: 5 items cost 175p. Which is better value for one item? Write the name.

Method. Work out the price of one item for each pack, then compare.

  1. Work out the price of one item in Box X. 90p / 3 = 30p.
    30p
  2. Work out the price of one item in Box Y. 175p / 5 = 35p.
    35p
  3. Compare the prices of one item. The cheaper one for one item is the better value.
    Box X is cheaper for one item
  4. Write the answer.
    Box X

Check. Box X costs less for each item. ✓

Watch out. Compare the price of ONE item. A bigger pack is not always cheaper for each item.

Watch out

Watch out. Team B scored more goals in total, but they are not the better team if they had more attempts.

Exam tip

Practice guide. Put the same unit (pence per item, or percentage) on both sides before you compare.

Exercise 3D  Practice: best value and fair comparisons

Non-calculator
1
FBox X: 4 items cost 300p. Box Y: 6 items cost 390p. Which is better value for one item? Write the name.
2
FPacket A: 5 items cost 400p. Packet B: 8 items cost 600p. Which is better value for one item? Write the name.
3
FSam scored 18 from 20 shots, and Lou scored 21 from 30 shots. Which had the better success rate? Write the name.
4
FTeam Red scored 12 from 15 shots, and Team Blue scored 16 from 25 shots. Which had the better success rate? Write the name.
5
PSWhich is better value: 500 g of oats for 250 pence, or 750 g for 360 pence? Write the size of the better-value pack in grams.
6
PSA jar holds 1.5 litres for 2.10 pounds. Another jar holds 2 litres for 2.60 pounds. Which jar is cheaper per litre? Write 1.5 litres or 2 litres.
7
RWhich comparison is fair when two shops have different numbers of customers? Choose one: Compare the percentage of customers who bought something, Compare only the number of sales or Compare the number of shops.
8
RExplain why a bigger pack is not always better value.
9
PSRavi scored 15 from 20 shots, and Ben scored 36 from 50 shots. Which had the better success rate? Write the name.
10
RA cinema sold 180 tickets in one week, and 300 tickets in another week. Which week was the better week for sales, if the cinema had 300 seats in each week? Write the week, 1 or 2.
11
RBen says that 9 out of 10 is better than 19 out of 20, because 10 is less than 20. Explain why he is wrong.

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