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Primary 6 · Fractions · Question type 2.4

P6 Fractions: Equal Fractions of Two Wholes

If a fraction of one group equals a fraction of another, that shared amount represents one unit in both bars.

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Primary 6, on the MOE Primary Mathematics syllabus.

In the Fractions chapter7 question types · see the chapter

The lesson · 1 minute 48 seconds

How do you compare equal fractions of two wholes in P6?

Watch: 1/3 of the boys equal to 1/5 of the girls, 48 children in all

Another worked example

A worked example

Wei Ling had twice as many stamps as Priya. Wei Ling used 1/4 of her stamps and Priya used 1/3 of hers. Wei Ling then had 45 more stamps than Priya. How many stamps did Wei Ling have at first?

The working · Ten lines

The step-by-step working

Written out in full, the way it should appear on paper.

  1. Priya: 3 parts
  2. Wei Ling: 2 × 3 = 6 parts
  3. we cannot do 1/4 × 6; it is not a whole number
  4. but we can do 1/4 × 12, so cut each part in half: Priya 6 units, Wei Ling 12 units
  5. fraction Wei Ling had left = 1 - 1/4 = 3/4 of 12 units, so 9 units
  6. fraction Priya had left = 1 - 1/3 = 2/3 of 6 units, so 4 units
  7. Wei Ling had 9 - 4 = 5 units more than Priya
  8. 5 units = 45
  9. 1 unit = 45 ÷ 5 = 9
  10. 12 units = 12 × 9 = 108

The answer is 108 stamps.

Practise · Modelled on top school exam questions

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Try it yourself

Compare the two tanks

Show how the same amount links the two wholes.

The same amount of water fills 1/4 of tank P and 2/3 of tank Q. Tank P and tank Q hold 550 litres altogether. How many litres does tank P hold?

Show the step-by-step solution
  1. 1/4 of tank P = 2/3 of tank Q
  2. cut tank P into 4 equal parts and tank Q into 3 equal parts
  3. 1/4 of tank P is 1 of its 4 parts, and 2/3 of tank Q is 2 of its 3 parts
  4. 1 part of tank P = 2 parts of tank Q
  5. 1 part of tank Q is 1 unit, so 1 part of tank P is 2 units
  6. tank P is 4 × 2 = 8 units
  7. tank Q is 3 units
  8. 8 + 3 = 11 units
  9. 11 units = 550
  10. 1 unit = 550 ÷ 11 = 50
  11. 8 units = 8 × 50 = 400

Ans: 400

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