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Fractions and decimals

Fractions and decimals for A Level Design and Technology AQA: what it means, how to set the working out, and the questions it is asked in.
  • A Level
  • AQA
  • Design and Technology
  • Spec N7 · N17
  • 8 min read
  • 7 revision boxes

Introduction

2 boxes
3 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.
This idea appears again in the higher-mark questions, so it is worth over-learning.
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: 49=7\sqrt{49} = 7.
3 rows

The fractions and decimals reference table

The examiner marks the working, so a correct answer with no method still drops marks.
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
34×25\frac{3}{4} \times \frac{2}{5}
Row 3 column 4

Learning

3 boxes
5 steps

How to work with 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: ×10\times 10 moves every digit one column left.
  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: 34×25\frac{3}{4} \times \frac{2}{5}.
Answer: a2+b2=c2a^2 + b^2 = c^2
3 rules

Key facts: Fractions and decimals

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
Worth knowing: 34×25\frac{3}{4} \times \frac{2}{5}.

  • Rule 1

    How fractions and decimals behaves in the 1st of the cases the specification names.
    49=7\sqrt{49} = 7

  • Rule 2

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

How to work with fractions and decimals

This idea appears again in the higher-mark questions, so it is worth over-learning.
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: ×10\times 10 moves every digit one column left.
  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: ≈160\approx 160

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Examples

2 boxes
1 marks · worked

Worked example: fractions and decimals

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

Practice question 7: 34×25\frac{3}{4} \times \frac{2}{5}

Work through the method one line at a time and write down what changes at each step.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.

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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 A Level Design and Technology AQA paper?
Yes — it sits in the Geometry and measures strand.