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Primary 6 · Ratio · Question type 1.9

P6 Ratio: Two Ratios with One Shared Quantity

Use the lowest common multiple to give the shared quantity the same number of units in both ratios.

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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 8 seconds

How do you solve two ratios with one shared quantity in P6?

Watch: two ratios, one shared quantity, joined on the milk

Another worked example

A worked example

In a canteen fridge, the number of bottles of water to the number of cartons of milk is 3 : 4. The number of cartons of milk to the number of cans of juice is 6 : 5. There are 45 bottles of water in the fridge. How many drinks are there in the fridge altogether?

The working · Four lines

The step-by-step working

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

  1. water : milk : juice = 9 : 12 : 10
  2. 9 units = 45
  3. 1 unit = 45 ÷ 9 = 5
  4. 31 units = 31 × 5 = 155 drinks

There are 155 drinks in the fridge.

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Find the boxes of nails

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A hardware shop stocks boxes of nails, boxes of screws and boxes of bolts. The number of boxes of nails to the total number of boxes of screws and boxes of bolts is 1 : 3. The number of boxes of screws to the number of boxes of bolts is 3 : 5. There are 45 boxes of bolts. How many boxes of nails are there?

Show the step-by-step solution
  1. nailsscrews and boltsscrewsbolts:::1:3× 8× 88:248:3:5× 3× 324:9:15
  2. screws : bolts = 3 : 5
  3. the shared quantity is screws + bolts, and neither ratio states it as a term
  4. the compound reads 3 in the first ratio and 8 in the second, and the lowest common multiple of 3 and 8 = 24
  5. nails : screws : bolts = 8 : 9 : 15
  6. 15 units = 45
  7. 1 unit = 45 ÷ 15 = 3
  8. 8 units = 8 × 3 = 24 boxes

Ans: 24

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