Same units, always
Convert first, then compare or complete the proportion.
A car and a clock
A car travels 90 km in 150 minutes. If it keeps the same speed, how far does it go in 4 hours? Priya writes 150 : 90 :: 4 : ? and cross-multiplies.
Will Priya's answer be right?
What this lesson covers
The idea
Corresponding quantities in the two ratios of a proportion must be in the same units, so units are converted before the ratios are compared or a term is found.
A car and a clock
A car travels 90 km in 150 minutes. If it keeps the same speed, how far does it go in 4 hours? Priya writes 150 : 90 :: 4 : ? and cross-multiplies.
Will Priya's answer be right?
- Yes, numbers are just numbers
- No, something is wrong
- Cannot tell
Fix the units
The car story starts with the wrong unit. See the answer and the bars. Then write the quantity in the same unit as the first ratio. Do all three stories.
Convert first
Corresponding quantities in the two ratios of a proportion must be in the same units, so units are converted before the ratios are compared or a term is found.
4 hours = 240 minutes, so 150 : 90 :: 240 : x and x = 90 × 240 ÷ 150 = 144. The car covers 144 km.
With 4 hours left unconverted, Priya got 2.4 km: less than 90 km in more time. A quick check shows something is wrong.
Notes
Corresponding quantities in the two ratios of a proportion must be in the same units, so units are converted before the ratios are compared or a term is found.
Check yourself
A tap fills 12 litres in 90 seconds. How much in 3 minutes? Which proportion is right?
A cyclist rides 12 km in 90 minutes. How many km in 2 hours at the same speed?
Answer: 16 km
2 hours = 120 minutes. 90 : 12 :: 120 : d, so d = 12 × 120 ÷ 90 = 16 km.
A ribbon of 2 m costs ₹60. What is the cost of 150 cm of the same ribbon? (in ₹)
Answer: 45
2 m = 200 cm. 200 : 60 :: 150 : d, so d = 60 × 150 ÷ 200 = ₹45.
Himachal tea is 200 g for ₹200. Meghalaya tea is 1 kg for ₹800. To check whether the weight-to-price ratios are in proportion, what must you do first?
- 90 : 12 :: 3 : ?. The first ratio uses seconds but 3 is in minutes.
- 90 : 12 :: 30 : ?. 3 minutes is 180 seconds, not 30 seconds.
- 90 : 12 :: 180 : ? — correct. Yes! 3 minutes = 180 seconds, the same unit as 90 seconds.
- 12 : 90 :: 3 : ?. The litres and seconds have swapped places, and 3 is still in minutes.
- Nothing: a weight is a weight. The numbers 200 and 1 are in different units. Compared directly they give nonsense.
- Write both weights in the same unit, such as 1 kg = 1000 g — correct. Yes! Then compare 200 : 200 with 1000 : 800.
- Change the rupees into paise on one side only. Both prices are already in rupees. It is the weights that differ.