---
title: "Inverse Proportion"
description: "Use y = k/x when one quantity falls as the other rises, find k from a given pair, and recognise the curve it produces."
canonical: https://lightmysky.com/learn/mathematics/inverse-proportion-mt_ZbbN2x6tcL
source: https://lightmysky.com/learn/mathematics/inverse-proportion-mt_ZbbN2x6tcL.md
retrieved: 2026-09-12
---

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# Inverse Proportion

Use y = k/x when one quantity falls as the other rises, find k from a given pair, and recognise the curve it produces.

Subject: Mathematics · Area: Ratio & Proportion · Ages 14 to 15
Page: https://lightmysky.com/learn/mathematics/inverse-proportion-mt_ZbbN2x6tcL

## Ready when they can

- Tell direct from inverse proportion in a word problem
- Find k and use it, for example with workers and the time a job takes
- Describe the shape of an inverse proportion graph

## Lesson: When more means less

Direct proportion grows together, while inverse proportion trades off. More taps fill the tank faster, and more workers finish the job sooner. When one quantity doubles while the other halves, the product stays fixed, and that fixed product is the signature of inverse proportion.

**Example.** Four taps fill a tank in 6 hours. Double the taps to 8 and the time halves to 3 hours. The job itself never changes: 5 workers for 8 days is 40 worker-days, and 4 workers need 40 divided by 4, which is 10 days. Find the fixed total first, then divide.

The constant k pins the rule down through y equals k over x. With x equal to 3 and y equal to 10, multiply to find k equal to 30. Every other pair must multiply to 30 as well, so y is 6 when x is 5. One pair buys the whole rule.

**Tip.** Graphs tell the two apart at a glance. Direct proportion draws a straight line through the origin, while inverse proportion draws a curve that falls steeply near zero then flattens, never touching either axis. In words, splitting money by ratio grows together, while sharing a fixed job trades off.

**Recap.** Spot the trade-off, find the fixed product, then divide.

## Practice

17 questions on this page, each with its working shown.

## Needs first

- [Direct Proportion as a Formula](https://lightmysky.com/learn/mathematics/direct-proportion-as-a-formula-mt_nhSf9I7Bjz)