Developing math vocabulary
Ratio
Pronunciation: RAY-shee-oh
A ratio compares the relative sizes of two quantities by division while preserving the order of the comparison.
a:ba/bDeveloping
Plain language
What it means
A ratio compares the relative sizes of two quantities by division while preserving the order of the comparison.
Formal meaning
Mathematical definition
For quantities a and b with b not zero, the ratio a to b can be written a:b or a/b.
Where it fits
Its place in mathematics
Ratios describe mixtures, maps, scale drawings, rates, probability, geometry, and trigonometry.
Why it matters
The practical reason to learn it
They reveal relative size even when the original quantities use different totals.
| Blue | White |
|---|---|
| 2 | 3 |
| 4 | 6 |
| 8 | 12 |
Worked example
Scale a ratio
A paint mix uses 2 parts blue to 3 parts white. How much white is needed for 8 parts blue?
- The blue amount is multiplied by 4.
- Multiply the white amount by the same factor.
12 parts white are needed.
Real-life example
Where this appears
A cook maintains ingredient ratios when changing a recipe yield.
Common mistake
What to watch for
Comparing quantities with incompatible units without stating a rate or converting units first.
Memory tip
Keep this in mind
Keep the order of the comparison consistent from start to finish.
Little-known fact
Keep curiosity alive
The golden ratio is one famous ratio, but most practical ratios are ordinary comparisons chosen for a task.
A profession that uses this idea
Proportion shapes creative work
Artists and musicians compare dimensions, timing, intervals, mixtures, and repeated patterns with ratios.
Explore Artists & MusiciansFollow the learning trail
Prerequisites, related ideas and next concepts
People behind the ideas
Related Math Heroes
Eudoxus of Cnidus
Eudoxus of Cnidus was Greek mathematician and astronomer. His theory of proportion handled incommensurable magnitudes, and his method of exhaustion anticipated integral reasoning.
Euclid
The author traditionally associated with the Elements, a systematic presentation of definitions, postulates, proofs, geometry, and number theory.
Put the idea to work