Two variables are in direct proportion if they have a constant multiplicative relationship.

The reciprocal is the multiplicative inverse of any non-zero number.  Any non-zero number multiplied by its reciprocal is equal to 1.

Abstract direct 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

Any non-zero number multiplied by its reciprocal is equal to {{ }}.

Which of the following tables show direct proportion?

The time taken to mow a lawn and the size of the lawn

The time taken to run a 5 k race and the speed at which its run

The number of metres of ribbon bought and the cost of the ribbon

The cost of hiring a coach and the cost per person

Decide which of the following would share a directly proportional relationship.

$$h$$ is directly proportional to $$g$$.  When $$g$$ = 12, $$h$$ = 7.2.  Find $$h$$ when $$g$$ = 28.

$$g$$ is directly proportional to $$h$$.  When $$g$$ = 17, $$h$$ = 93.5.  Find $$g$$ when $$h$$ = 45.1.

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

The number of cans of drink and the number of boxes bought

The time taken to fill a lorry and the number of people packing the lorry

The number of metres run and the number of kilometres run

The number of euros exchanged and the number of dollars

The amount of flour needed and the number of biscuits being made

Which of the following is an example of inverse proportion?

Which of the following is an equation representing inverse proportion?

A graph representing inverse proportion will appear in how many quadrants when plotted on a pair of axes?

The smaller the dividend, the {{ }} to the origin the graph will be. 

Which of the following is the graph of $$y={{{3.5}\over{x}}}$$?

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

Abstract direct proportion

Lesson outcome

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