Simplifying Ratios With Different Units
Learn how to simplify ratios safely when quantities use different units, with conversion steps, GCF shortcuts and checks.
Before you simplify, make the units match
You can only simplify a ratio directly when both quantities are expressed in the same unit. A ratio of 2 m : 50 cm is not 2 : 50, because metres and centimetres represent different scales.
Convert first
2 m : 50 cm.- Convert 2 m to 200 cm.
- Write the ratio as
200 : 50. - Divide both parts by 50.
Simplified ratio: 4 : 1.
Use the greatest common factor
For 84 : 126, the greatest common factor is 42, so the simplest ratio is 2 : 3. If the GCF is not obvious, divide by small common factors in stages; the final result is the same.
Three-part ratios
Every part must be divided by the same factor. For 36 : 60 : 84, divide all three numbers by 12 to get 3 : 5 : 7.
Three ways a ratio can look simplified when it is not
- Mixing units in the final ratio.
- Dividing only two parts of a three-part ratio.
- Stopping at a ratio that still has a common factor.
Read the ratio back in words
Ratios compare proportions. 4 : 1 means the first quantity is four times the second. In the example, 2 m is 200 cm, which is indeed four times 50 cm.
Simplify 1.5 m : 30 cm. Enter the first number in the ratio when the second is 1.
Keep going
For another problem using related ideas, return to the Fractions, Ratios & Percentages page.