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Fractions and decimals

Fractions and decimals for GCSE Sociology AQA: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • AQA
  • Sociology
  • Spec A6 · A18 · A10
  • 13 min read
  • 8 revision boxes

Introduction

2 boxes
4 min read

What is fractions and decimals?

Listen to this box

Transcript

A short spoken summary of fractions and decimals and where it is used.

A spoken walk-through of fractions and decimals before you read the notes.
Sketch the shape even when the question does not ask for one — it makes the next step obvious.
5 rows

The fractions and decimals reference table

Practise the routine version until it is automatic, then move to the multi-step questions.
The layout below is the one the mark scheme expects.

Diagram showing fractions and decimals laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: x2+5x+6=0x^2 + 5x + 6 = 0.
Term
Meaning
Example
Common slip
Row 1 column 1
Row 1 column 2
≈160\approx 160
Row 1 column 4
Row 2 column 1
Row 2 column 2
a2+b2=c2a^2 + b^2 = c^2
Row 2 column 4
Row 3 column 1
Row 3 column 2
≈160\approx 160
Row 3 column 4

Learning

4 boxes
5 steps

How to work with fractions and decimals

The examiner marks the working, so a correct answer with no method still drops marks.
  1. Read the question and write down what is being asked for.
  2. Set out the working for fractions and decimals in the order the method gives.
  3. Substitute the values and simplify.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: x2+5x+6=0x^2 + 5x + 6 = 0.
Answer: ×10\times 10 moves every digit one column left
2 rules

Key facts: Fractions and decimals

This idea appears again in the higher-mark questions, so it is worth over-learning.

  • Rule 1

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

  • Rule 2

    How fractions and decimals behaves in the 2nd of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}
5 steps

How to work with fractions and decimals

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
  1. Read the question and write down what is being asked for.
  2. Set out the working for fractions and decimals in the order the method gives.
  3. Substitute the values and simplify.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: x2+5x+6=0x^2 + 5x + 6 = 0.
Answer: 34×25\frac{3}{4} \times \frac{2}{5}
3 rules

Key facts: Fractions and decimals

Practise the routine version until it is automatic, then move to the multi-step questions.
The layout below is the one the mark scheme expects.

Diagram showing fractions and decimals laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: x2+5x+6=0x^2 + 5x + 6 = 0.

  • Rule 1

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

  • Rule 2

    How fractions and decimals behaves in the 2nd of the cases the specification names.
    49=7\sqrt{49} = 7

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Examples

2 boxes
1 marks · worked

Worked example: fractions and decimals

This idea appears again in the higher-mark questions, so it is worth over-learning.
Worth knowing: ≈160\approx 160.
2 marks · worked

Practice question 8: ×10\times 10 moves every digit one column left

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 fractions and decimals laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: 34×25\frac{3}{4} \times \frac{2}{5}.

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Common questions

How many marks is fractions and decimals usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the GCSE Sociology AQA paper?
Yes — it sits in the Geometry and measures strand.