Ratios and Proportions: From Mixing Drinks to Reading Maps
How do you dilute a 1:4 concentrate? What does a 1:10000 map mean? Ratios are the most practical — and most misread — math in daily life.
A ratio expresses the relationship between two quantities. It's simple enough to be overlooked, yet misusing it has real consequences, from undrinkable cordial to a wrong dose.
Two common notations
- a:b — a relationship between two amounts, e.g. concentrate:water = 1:4.
- a:b:c — a continued ratio across three or more amounts, e.g. concrete at 1:2:3.
The key point: 1:4 means 1 part concentrate to 4 parts water — a total of 5 parts, not 4. That is the most common mistake.
Everyday examples
- Mixing drinks: for 500 mL at 1:4, concentrate = 500 ÷ 5 × 1 = 100 mL and water = 400 mL.
- Map scale: 1:10000 means 1 cm on the map equals 10,000 cm — i.e. 100 m — on the ground.
- Aspect ratio: 16:9 means the width is 16/9 of the height.
- Diluting cleaner: 1:10 means 1 part product plus 10 parts water, giving 11 parts total.
Converting ratios to percentages
A ratio converts to a percentage: in a:b, a's share is a ÷ (a + b). With a male-to-female ratio of 3:2, men are 3/5 = 60%. Conversely, 60% can be written as 3:2 or 60:40.
For complex cases, let the Ratio Calculator handle the arithmetic, especially with three or more terms or when solving backwards.
One thing people mix up
A ratio is not the same as a rate. A ratio compares two quantities of the same kind and has no unit; a rate usually compares different kinds and carries a unit, like speed (km/h) or population density (people/km²). Confusing them produces dimensional errors.