Question Video: Simplifying Ratios between Three Quantities Involving Distance Unit Conversion Mathematics

Express the ratio 4.7 km : 2,350 m : 18.8 km in its simplest form.


Video Transcript

Express the ratio 4.7 kilometers to 2,350 meters to 18.8 kilometers in its simplest form.

We notice here that our units are not the same. We have kilometers and meters. 1,000 meters is equal to one kilometer. We could therefore convert the middle value to kilometers or the first and third values to meters. A ratio in its simplest form must have integer or whole number values. As a result, we will convert 4.7 kilometers and 18.8 kilometers into meters. To do this, we will multiply our values by 1,000. This moves all our digits three places to the left. So 4.7 kilometers is 4,700 meters. In the same way, 18.8 kilometers is equal to 18,800 meters.

As our three numbers are large, it is not immediately clear what the highest common factor is. We might notice, however, that 4,700 is twice as big as 2,350. 18,800 is four times as big as 4,700. This means that all three of our values are divisible by 2,350. Our ratio simplifies to two to one to eight. The ratio 4.7 kilometers, 2,350 meters, 18.8 kilometers written in its simplest form is two, one, eight.

If we hadn’t spotted this pattern, we could’ve divided all three of our numbers by 10 or 50. We could then continue to simplify this until we reached two, one, eight.

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