Developing math vocabulary
Proportion
Pronunciation: pruh-POR-shun
A proportion is an equation stating that two ratios are equal.
a/b = c/dDeveloping
Plain language
What it means
A proportion is an equation stating that two ratios are equal.
Formal meaning
Mathematical definition
For nonzero b and d, a/b = c/d is a proportion and implies ad = bc.
Where it fits
Its place in mathematics
Proportions connect scaling to similar figures, unit rates, conversions, percentages, and algebra.
Why it matters
The practical reason to learn it
They let a known relationship predict an unknown value while preserving relative size.
| Blue | White |
|---|---|
| 2 | 3 |
| 4 | 6 |
| 8 | 12 |
Worked example
Solve a proportion
Solve 3/5 = x/20.
- Recognize that 5 is multiplied by 4 to reach 20.
- Multiply 3 by the same factor.
x = 12.
Real-life example
Where this appears
A map reader uses scale proportions to estimate real distance from a printed distance.
Common mistake
What to watch for
Cross-multiplying before checking that corresponding quantities are placed in matching positions.
Memory tip
Keep this in mind
Label units and keep like quantities in the same numerator or denominator position.
Little-known fact
Keep curiosity alive
Proportional relationships graph as straight lines through the origin when both variables begin at zero.
A profession that uses this idea
Maps depend on proportional scale
Navigators convert map distances to real distances using a consistent scale ratio.
Explore Navigators & PilotsFollow 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.
Pedro Nunes
Pedro Nunes was mathematician and royal cosmographer. He studied navigation, spherical geometry, map projections, and the path of constant bearing called a rhumb line.
Put the idea to work