# Direct proportion

Two amounts are in direct proportion when doubling one also doubles the other.

Maths (school) · Part 01: Number and ratio · Card 6 of 9 · Last updated 2026-10-19

## Analogy

Like buying apples: twice as many apples cost twice as much.

## Example

**3 pens cost 4.50**

1 pen = 4.50 / 3 = 1.50
7 pens = 7 x 1.50
= 10.50

## In practice

Scaling a recipe from 4 people to 8 people means doubling every ingredient.

## Practice

### Flashcards

- **3 pens cost 4.50. What do 7 cost?** 10.50. One pen costs 1.50, so 7 cost 7 x 1.50.

## Questions people ask

### What is the unitary method?

It means finding the value of one item first, then scaling up. If 3 pens cost 4.50, one pen costs 1.50. Then 7 pens cost 7 x 1.50 = 10.50. It works for any direct proportion problem and is easy to check.

### How can you tell if two things are in direct proportion?

Divide one amount by the other for each pair. If you always get the same answer, they are in direct proportion. Pens at 1.50 each always give a cost per pen of 1.50. Plotted on a graph, they form a straight line through zero.

## Related concepts

- [Ratio](https://studyvisually.com/learn/science/maths-school/maths-school-part-1/maths-school-part-1-concept-5)

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