Ruth has three ribbons, P, Q and R. The ratio of the length of Ribbon P to the length of Ribbon Q is 4 : 9. Ribbon Q is 56 as long as Ribbon R. What is the ratio of the length of Ribbon P to the length of Ribbon R?
- 10 : 27
- 4 : 6
- 4 : 30
- 27 : 10
Need a hint?
Make the number of units for Ribbon Q the same in both ratios before you combine them.
Worked answer
- Write P : Q = 4 : 9. Scale by 5 so that Q = 45 units: P : Q = 20 : 45.
- From Q is 56 of R, Q : R = 5 : 6. Scale by 9 so that Q = 45 units: Q : R = 45 : 54.
- Now Q is 45 units in both ratios, so P : Q : R = 20 : 45 : 54.
- Ratio of P to R = 20 : 54 = 10 : 27.
Answer: 10 : 27
The mistake this question tests
Habit
Stopped at one part in ratio
Pupils read the fraction 56 straight into the ratio as 5 : 6 for Q to R, then ignore the scaling of Q, which gives the wrong ratio 4 : 6.
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See the answer →Practise PSLE ratio until the mistakes stop.
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