# Solve Problems Using Inverse Proportion

In this worksheet, students will solve problems using inverse proportion.

Key stage:  KS 3

Curriculum topic:   Ratio, Proportion and Rates of Change

Curriculum subtopic:   Solve Problems Involving Direct and Inverse Proportion

Difficulty level:

#### Worksheet Overview

In this activity, we are going to look at inverse proportion.

When we buy one of something, we expect the price to go up 'proportionally' if we want to buy more.

We call this direct proportion - as one value rises so does the other!

For example:

1 ice cream = £1

2 ice creams = 2 x £1 = £2

5 ice creams = 5 x £1 = £5 etc ......

Inverse proportion means the opposite.

As one value rises the other one drops proportionally.

For example, when driving a car, the more miles we travel, the less petrol we have left - inverse proportion.

Let's look at a typical question!

Example

It takes 3 plumbers 6 days to complete a job.

How long would it take 2 plumbers to complete the same job?

We are tempted to say

'If 3 plumbers can do it in 6 days then 2 plumbers can do it in 4 days', but of course that is not true! It will take longer the fewer plumbers you have!!

3 plumbers x 6 days = 18 days for 1 plumber to complete the job.

Now we know how long it would take 1 plumber, we divide by 2 to find out how long it would take 2 plumbers.

18 days ÷  2 = 9 days for 2 plumbers.

We can get some practise on this by trying some questions!

Let's go!

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