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Fractions and decimals

Fractions and decimals for Access to HE Law: what it means, how to set the working out, and the questions it is asked in.
  • Access to HE
  • Law
  • Spec R1 · R6
  • 10 min read
  • 10 revision boxes

Introduction

2 boxes
2 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 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.
5 rows

The fractions and decimals reference table

Read the units in the question before you start; a converted unit is the most common slip.
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
a2+b2=c2a^2 + b^2 = c^2

Learning

6 boxes
5 steps

How to work with fractions and decimals

Check the answer against an estimate before you move on, so a place-value slip is caught here.
Worth knowing: 34×25\frac{3}{4} \times \frac{2}{5}.
  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: 34×25\frac{3}{4} \times \frac{2}{5}
2 rules

Key facts: Fractions and decimals

Work through the method one line at a time and write down what changes at each step.

  • 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
5 steps

How to work with fractions and decimals

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

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

  • 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.
    a2+b2=c2a^2 + b^2 = c^2
5 steps

How to work with fractions and decimals

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

Key facts: Fractions and decimals

Work through the method one line at a time and write down what changes at each step.

  • 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.
    x2+5x+6=0x^2 + 5x + 6 = 0

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Examples

2 boxes
2 marks · worked

Worked example: 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.
3 marks · worked

Practice question 10: a2+b2=c2a^2 + b^2 = c^2

The examiner marks the working, so a correct answer with no method still drops marks.

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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 Access to HE Law paper?
Yes — it sits in the Ratio and proportion strand.