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Direct and inverse proportion

Direct and inverse proportion for ESOL Accounting: what it means, how to set the working out, and the questions it is asked in.
  • ESOL
  • Accounting
  • Spec P14 · P8
  • 10 min read
  • 8 revision boxes

Introduction

2 boxes
1 min read

What is direct and inverse proportion?

Listen to this box

Transcript

A short spoken summary of direct and inverse proportion and where it is used.

A spoken walk-through of direct and inverse proportion before you read the notes.
Work through the method one line at a time and write down what changes at each step.
Worth knowing: ×10\times 10 moves every digit one column left.
4 rows

The direct and inverse proportion reference table

Check the answer against an estimate before you move on, so a place-value slip is caught here.
The layout below is the one the mark scheme expects.

Diagram showing direct and inverse proportion laid out step by step

The same idea drawn out, so the method is visible.
Term
Meaning
Example
Row 1 column 1
Row 1 column 2
a2+b2=c2a^2 + b^2 = c^2
Row 2 column 1
Row 2 column 2
34×25\frac{3}{4} \times \frac{2}{5}

Learning

4 boxes
5 steps

How to work with direct and inverse proportion

Read the units in the question before you start; a converted unit is the most common slip.
  1. Read the question and write down what is being asked for.
  2. Set out the working for direct and inverse proportion in the order the method gives.
  3. Substitute the values and simplify.
  4. Check the answer against an estimate before writing it down.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: ×10\times 10 moves every digit one column left.
Answer: ≈160\approx 160
3 rules

Key facts: Direct and inverse proportion

The specification wording is precise here, and the mark scheme follows that wording exactly.
The layout below is the one the mark scheme expects.

Diagram showing direct and inverse proportion laid out step by step

The same idea drawn out, so the method is visible.

  • Rule 1

    How direct and inverse proportion behaves in the 1st of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0

  • Rule 2

    How direct and inverse proportion behaves in the 2nd of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0

  • Rule 3

    How direct and inverse proportion behaves in the 3rd of the cases the specification names.
    ×10\times 10 moves every digit one column left
5 steps

How to work with direct and inverse proportion

Work through the method one line at a time and write down what changes at each step.
Worth knowing: 49=7\sqrt{49} = 7.
  1. Read the question and write down what is being asked for.
  2. Set out the working for direct and inverse proportion in the order the method gives.
  3. Substitute the values and simplify.
  4. Check the answer against an estimate before writing it down.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: 49=7\sqrt{49} = 7.
Answer: a2+b2=c2a^2 + b^2 = c^2
2 rules

Key facts: Direct and inverse proportion

Check the answer against an estimate before you move on, so a place-value slip is caught here.

  • Rule 1

    How direct and inverse proportion behaves in the 1st of the cases the specification names.
    49=7\sqrt{49} = 7

  • Rule 2

    How direct and inverse proportion behaves in the 2nd of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}

  • Rule 3

    How direct and inverse proportion behaves in the 3rd of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0

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Examples

2 boxes
4 marks · worked

Worked example: direct and inverse proportion

Practise the routine version until it is automatic, then move to the multi-step questions.
3 marks · worked

Practice question 8: a2+b2=c2a^2 + b^2 = c^2

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
The layout below is the one the mark scheme expects.

Diagram showing direct and inverse proportion laid out step by step

The same idea drawn out, so the method is visible.

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Common questions

How many marks is direct and inverse proportion usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the ESOL Accounting paper?
Yes — it sits in the Chemical change strand.