Pass Functional Skills logo

Fractions and decimals

Fractions and decimals for A Level Philosophy OCR Foundation: what it means, how to set the working out, and the questions it is asked in.
  • A Level
  • OCR
  • Philosophy
  • Foundation
  • Spec R19
  • 14 min read
  • 10 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.
Work through the method one line at a time and write down what changes at each step.
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.
6 rows

The fractions and decimals 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 fractions and decimals 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
x2+5x+6=0x^2 + 5x + 6 = 0
Row 2 column 1
Row 2 column 2
49=7\sqrt{49} = 7
Row 3 column 1
Row 3 column 2
×10\times 10 moves every digit one column left

Learning

6 boxes
4 steps

How to work with fractions and decimals

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 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: ×10\times 10 moves every digit one column left
3 rules

Key facts: Fractions and decimals

The specification wording is precise here, and the mark scheme follows that wording exactly.

  • Rule 1

    How fractions and decimals behaves in the 1st of the cases the specification names.
    ≈160\approx 160

  • Rule 2

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

  • Rule 3

    How fractions and decimals behaves in the 3rd of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2
3 steps

How to work with fractions and decimals

Work through the method one line at a time and write down what changes at each step.
  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: ≈160\approx 160
2 rules

Key facts: Fractions and decimals

Check the answer against an estimate before you move on, so a place-value slip is caught here.
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.
    49=7\sqrt{49} = 7

  • 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}

  • Rule 3

    How fractions and decimals behaves in the 3rd of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0
3 steps

How to work with fractions and decimals

Read the units in the question before you start; a converted unit is the most common slip.
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
3 rules

Key facts: Fractions and decimals

The specification wording is precise here, and the mark scheme follows that wording exactly.
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.
    ≈160\approx 160

  • Rule 2

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

20 minutes

Get your predicted grade

Twenty questions gives you a predicted grade, your target, and the gap between them — plus the topics that close it fastest.
Get my predicted grade

Examples

2 boxes
3 marks · worked

Worked example: fractions and decimals

This idea appears again in the higher-mark questions, so it is worth over-learning.
Worth knowing: x2+5x+6=0x^2 + 5x + 6 = 0.
1 marks · worked

Practice question 10: 49=7\sqrt{49} = 7

Read the units in the question before you start; a converted unit is the most common slip.
Worth knowing: x2+5x+6=0x^2 + 5x + 6 = 0.

Practice bank

Thousands of revision questions

Every topic is backed by graded practice with instant marking and full solutions.
Try it now
Practice questions
3,000+
Topics
10
Marking and solutions
Instant

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 Philosophy OCR Foundation paper?
Yes — it sits in the Geometry and measures strand.