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Four operations

Four operations for A Level German AQA Foundation: what it means, how to set the working out, and the questions it is asked in.
  • A Level
  • AQA
  • German
  • Foundation
  • Spec G11 · G9
  • 7 min read
  • 9 revision boxes

Introduction

2 boxes
4 min read

What is four operations?

Listen to this box

Transcript

A short spoken summary of four operations and where it is used.

A spoken walk-through of four operations before you read the notes.
Work through the method one line at a time and write down what changes at each step.
Worth knowing: ×10\times 10 moves every digit one column left.
2 rows

The four operations 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 four operations laid out step by step

The same idea drawn out, so the method is visible.
Term
Meaning
Example
Common slip
Row 1 column 1
Row 1 column 2
x2+5x+6=0x^2 + 5x + 6 = 0
Row 1 column 4
Row 2 column 1
Row 2 column 2
49=7\sqrt{49} = 7
Row 2 column 4

Learning

5 boxes
5 steps

How to work with four operations

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 four operations 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: ≈160\approx 160.
Answer: 49=7\sqrt{49} = 7
2 rules

Key facts: Four operations

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 four operations laid out step by step

The same idea drawn out, so the method is visible.

  • Rule 1

    How four operations behaves in the 1st of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 2

    How four operations behaves in the 2nd of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}

  • Rule 3

    How four operations 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 four operations

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 four operations 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
3 rules

Key facts: Four operations

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}.

  • Rule 1

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

  • Rule 2

    How four operations behaves in the 2nd of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 3

    How four operations behaves in the 3rd of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2
5 steps

How to work with four operations

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 four operations 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: ×10\times 10 moves every digit one column left.
Answer: 49=7\sqrt{49} = 7

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Examples

2 boxes
1 marks · worked

Worked example: four operations

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
The layout below is the one the mark scheme expects.

Diagram showing four operations laid out step by step

The same idea drawn out, so the method is visible.
1 marks · worked

Practice question 9: ≈160\approx 160

The examiner marks the working, so a correct answer with no method still drops marks.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.

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Common questions

How many marks is four operations usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the A Level German AQA Foundation paper?
Yes — it sits in the Number strand.