Proportionality Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Proportionality.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

A relationship where two quantities maintain a constant ratio: doubling one always doubles the other, giving y = kx.

If you double one, you double the other. Triple one, triple the other.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Proportional quantities have a constant ratio: \frac{y}{x} = k, or y = kx.

Common stuck point: Not all linear relationships are proportional (y = 2x + 3 is not).

Sense of Study hint: Compute y/x for several data pairs. If you always get the same number, the relationship is proportional and that number is k.

Worked Examples

Example 1

easy
A car travels 150 miles in 3 hours at constant speed. How far will it travel in 5 hours?

Solution

  1. 1
    Find the unit rate (speed): \dfrac{150 \text{ miles}}{3 \text{ hours}} = 50 mph.
  2. 2
    Distance in 5 hours: 50 \times 5 = 250 miles.
  3. 3
    Alternatively, set up a proportion: \dfrac{150}{3} = \dfrac{d}{5}, so d = \dfrac{150 \times 5}{3} = 250 miles.

Answer

The car travels 250 miles in 5 hours.
Two quantities are proportional when their ratio is constant. Here, distance and time have a constant ratio (speed). Setting up a proportion or multiplying by the unit rate both give the same result.

Example 2

medium
The table shows: x = 2, y = 8; x = 5, y = 20; x = 9, y = 36. Determine whether y is proportional to x, and if so write the proportionality equation.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
If 12 apples cost \3.60, how much do 20$ apples cost?

Example 2

medium
Is the relationship y = 3x + 2 proportional? Is y = 5x proportional? Explain.
← Back to Proportionality Formula Explained Practice Mode

Background Knowledge

These ideas may be useful before you work through the harder examples.

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