Two variables are inversely proportional if there is a constant multiplicative relationship between one variable and the reciprocal of the other.

Abstract inverse proportion

Maths

In the linear graphs unit, pupils learnt to recognise and interpret graphs that illustrate direct and inverse proportion. In this unit, pupils learn how to represent these relationships algebraically.

Direct and inverse proportion

Match the equations with the correct proportions.

Converting euros to dollars or vice versa

The hours you work and the salary received

The taps to fill a water bucket and the time it takes to fill the bucket

The number of robots to complete a job and the time to complete the job

Which of the following are examples of inverse proportion?

$$p\propto \frac{1}{q}$$, match the correct values for A, B and C.

It takes 10 workers 6 hours to build a wall. They all work at the same rate. Firstly, all workers build for 2 hours, then 6 workers leave. How many hours will it take the 4 workers to finish the wall?

$$y\propto \frac{1}{\sqrt{x}}$$, when $$x=25, y=16$$. Work out the value of $$y$$ when $$x=400$$.

$$y\propto \frac{1}{\sqrt[3]{x}}$$, when $$x=125, y=0.15$$. Work out the value of $$y$$ when $$x=0.008$$.

Two variables are {{}} proportional if there is a constant multiplicative relationship between one variable and the reciprocal of the other. 

Pair up the reciprocals with the following numbers. 

What is the single multiplier that connects 9 to 54?

What is the single multiplier that connects 15 to 10?

What is the single multiplier that connects 24 to 9.6?

$$y\propto \sqrt{x}$$, when $$x=64, y=6$$. Work out the value of $$y$$ when $$x=400$$.

This lesson will be removed by end of Summer Term 2025.

Abstract inverse proportion

Lesson outcome

This lesson will be removed by end of Summer Term 2025.