Ratio and Proportion Explained Simply (2026)

Ratio and proportion are the foundation of so many real-world calculations " scaling recipes, map reading, currency exchange, percentage problems, and even engineering design. This guide explains both concepts clearly with easy examples, so you can solve any proportion problem confidently.

What is a Ratio?

A ratio compares two or more quantities. It is written as a : b or a/b. Ratios have no units " they are pure numbers. Example: A class has 30 boys and 20 girls → ratio of boys to girls = 30:20 = 3:2 (simplified by dividing both by 10).

What is Proportion?

Proportion states that two ratios are equal. If a/b = c/d, then a, b, c, and d are said to be in proportion. This is useful for scaling quantities and solving "if X then Y" problems.

The Golden Rule " Cross Multiplication

Worked Examples

Example 1 " Recipe Scaling:
A recipe for 4 people needs 200g of flour. How much for 10 people?
200/4 = x/10 → 4x = 2000 → x = 500g

Example 2 " Currency Exchange:
If $1 = 84, how much is $350?
1/84 = 350/x → x = 350 — 84 = 29,400

Example 3 " Map Scale:
Scale 1:50,000. On map: 3 cm. Actual distance?
1/50,000 = 3/x → x = 3 — 50,000 = 150,000 cm = 1.5 km

Direct vs Inverse Proportion

Direct Proportion: As one quantity increases, the other increases proportionally. (y = kx)
Example: More workers → more output.

Inverse Proportion: As one quantity increases, the other decreases. (y = k/x)
Example: More workers → job done faster (fewer days).

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Also see our Percentage Formula Guide which closely relates to ratio calculations.

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