Developing math vocabulary

Proportion

Pronunciation: pruh-POR-shun

A proportion is an equation stating that two ratios are equal.

Symbols and notationa/b = c/d
Subject
Grade bands
Difficulty

Developing

Profession trailNavigators & Pilots

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.

Equivalent ratios
BlueWhite
23
46
812
Two equivalent ratiosA proportion is valid only when both ratios describe the same multiplicative relationship.

Worked example

Solve a proportion

Solve 3/5 = x/20.

  1. Recognize that 5 is multiplied by 4 to reach 20.
  2. Multiply 3 by the same factor.
Answer

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.

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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.

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