PAss Functional Skills

Fractions and decimals

Fractions and decimals for GCSE English Literature AQA Foundation: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • AQA
  • English Literature
  • Foundation
  • Spec S2 · S1 · S18
  • 8 min read
  • 10 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.
The examiner marks the working, so a correct answer with no method still drops marks.
6 rows

The fractions and decimals reference table

This idea appears again in the higher-mark questions, so it is worth over-learning.
Term
Meaning
Example
Row 1 column 1
Row 1 column 2
x2+5x+6=0x^2 + 5x + 6 = 0
Row 2 column 1
Row 2 column 2
34×25\frac{3}{4} \times \frac{2}{5}
Row 3 column 1
Row 3 column 2
34×25\frac{3}{4} \times \frac{2}{5}

Learning

6 boxes
3 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.
  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: 34×25\frac{3}{4} \times \frac{2}{5}.
Answer: 49=7\sqrt{49} = 7
2 rules

Key facts: Fractions and decimals

Practise the routine version until it is automatic, then move to the multi-step questions.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.

  • Rule 1

    How fractions and decimals behaves in the 1st of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}

  • Rule 2

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

  • Rule 3

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

How to work with fractions and decimals

The examiner marks the working, so a correct answer with no method still drops marks.
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.
  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: a2+b2=c2a^2 + b^2 = c^2.
Answer: 34×25\frac{3}{4} \times \frac{2}{5}
3 rules

Key facts: Fractions and decimals

This idea appears again in the higher-mark questions, so it is worth over-learning.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.

  • 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

  • Rule 3

    How fractions and decimals behaves in the 3rd 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.
  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: 49=7\sqrt{49} = 7
2 rules

Key facts: Fractions and decimals

Practise the routine version until it is automatic, then move to the multi-step questions.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.

  • Rule 1

    How fractions and decimals behaves in the 1st of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}

  • Rule 2

    How fractions and decimals behaves in the 2nd of the cases the specification names.
    ≈160\approx 160

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Examples

2 boxes
4 marks · worked

Worked example: fractions and decimals

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.
2 marks · worked

Practice question 10: ≈160\approx 160

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 fractions and decimals 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 fractions and decimals usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the GCSE English Literature AQA Foundation paper?
Yes — it sits in the Ratio and proportion strand.