# Understand Indirect Proportion Using Indices

In this worksheet, students will be asked to resolve problems related to indirect proportion with indices.

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

Direct proportion refers to the relationship between two variables where one goes up as the other goes up.

With indirect or inverse proportion one goes up as the other one goes down.

Recap from Direct Proportion

Given that A is directly proportional to B and that A = 19 when B = 133.

Find:
(i) a formula connecting A and B
(ii) the value of A when B = 13

A ∝ B

So, A = K B

(i) Given A = 19 when B = 133

133 = 19K

K = 133 ÷ 19

K = 7

Therefore, the formula is A = 7B

(ii) When B = 13

A = 7 x B

A = 7 x 13

A = 91

Indirect proportion is the same working but the start is different!

Let's look at a question to help with this!

Example

Given that A is indirectly proportional to B and that A = 4 when B = 5.

Find:

(i) a formula connecting A and B
(ii) the value of A when B = 2

A ∝ 1 ÷ B

So, A = K ÷ B

(i) Given A = 4 when B = 5

4 = K ÷ 5

Multiply through by 5

K = 4 x 5

K = 20

Therefore, the formula is A = 20 ÷ B

(ii) When B = 2,

A = 20 ÷ 2

A = 10

It's useful to have paper and a pencil in order to record your own workings.

These are not the kind of questions you can calculate mentally.

You can look back at this introduction at any point by clicking on the red help button on the screen.

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