What Is a Ratio?
A ratio compares two quantities by showing how much of one thing there is relative to another.
"For every 2 red marbles, there are 3 blue marbles." That relationship, 2 to 3, is a ratio.
Three ways to write a ratio
The ratio "2 to 3" can be written:
- With words: 2 to 3
- With a colon: 2:3
- As a fraction: 2/3
All three mean the same thing: for every 2 of the first quantity, there are 3 of the second.
Ratio vs. fraction
Ratios and fractions look similar but mean different things:
- Fraction: 2/5 means "2 out of 5 total." It is a part-to-whole comparison.
- Ratio: 2:3 means "2 of this for every 3 of that." It can be part-to-part or part-to-whole.
In a bag with 2 red and 3 blue marbles:
- The fraction of red marbles = 2/5 (2 red out of 5 total)
- The ratio of red to blue = 2:3 (2 red for every 3 blue)
Equivalent ratios
Just like equivalent fractions, ratios can be scaled:
2:3 = 4:6 = 6:9 = 10:15
Multiply (or divide) both sides by the same number, and the ratio stays the same. A recipe that calls for 2 cups flour to 3 cups water can be doubled to 4:6 or tripled to 6:9.
Where ratios appear
- Recipes: "1 part vinegar to 3 parts oil"
- Maps: "1 inch represents 10 miles" (ratio of 1:10)
- Speed: "60 miles per hour" is a ratio of distance to time
- Prices: "$3 per pound" is a ratio of cost to weight
Related concepts
- Ratios and proportions: full teaching guide
- Fractions: ratios use fraction notation
- Percents: a percent is a ratio with denominator 100