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Primary 6 · Ratio · Question type 1.7

P6 Ratio: One Quantity Unchanged

With one quantity unchanged, scale both ratios until it has the same number of units in each.

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Primary 6, on the MOE Primary Mathematics syllabus.

In the Ratio chapter10 question types · see the chapter

The lesson · 2 minutes 21 seconds

How do you solve P6 ratio questions with one quantity unchanged?

Watch: 18 comic books are added and one quantity stays the same

Another worked example

A worked example

The ratio of comic books to storybooks on a shelf was 2 : 5. After 18 more comic books were added, the ratio became 4 : 5. How many storybooks are on the shelf?

The working · Four lines

The step-by-step working

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

  1. 2 units = 18
  2. 1 unit = 18 ÷ 2 = 9
  3. 5 units = 5 × 9 = 45 storybooks
  4. There are 45 storybooks.

There are 45 storybooks on the shelf.

Practise · Modelled on top school exam questions

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Count the cars that arrived

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40% of the vehicles in a car park were cars and the rest were vans. Some more cars then drove in, and no vans arrived or left. In the end, 55% of the vehicles in the car park were cars. There were 108 vans in the car park. How many cars drove in?

Show the step-by-step solution
  1. at first, cars : vans = 40% : 60%
  2. ÷ 20 = 2 : 3
  3. in the end, cars : vans = 55% : 45%
  4. ÷ 5 = 11 : 9
  5. no vans arrived or left, so the vans must read the same number in both ratios
  6. the vans read 3 at first and 9 in the end, and the lowest common multiple of 3 and 9 = 9
  7. at first, cars : vans = 2 : 3
  8. × 3 = 6 : 9
  9. cars that drove in = 11 units - 6 units = 5 units
  10. 9 units = 108
  11. 1 unit = 108 ÷ 9 = 12
  12. 5 units = 5 × 12 = 60 cars

Ans: 60

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Ratio Questions Where Neither Quantity Stays the Same →

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