Addition moves in the direction of the second number
Starting at -3 and adding 8 means moving 8 steps to the right.
A positive addend moves right on the number line, even when you begin below zero.
Year 7
Operations with negative numbers
Add, subtract, multiply and divide negative numbers accurately, and explain changes that move through zero.
Lesson overview
Number - directed number
Negative numbers describe positions below zero, debts, temperatures and directed change. A number line helps us picture addition and subtraction, while multiplication and division follow sign rules that keep patterns consistent. The key is to think about direction as well as size.
Subtracting a negative reverses the direction
Take away -7 from -4. This is the same as adding 7.
Subtracting a negative removes a loss, so the value increases.
Sign rules for multiplication and division
A negative and a positive give a negative result. Two negatives give a positive result.
| Calculation | Result |
|---|---|
| (-3) x 4 | -12 |
| 12 / (-3) | -4 |
| (-5) x (-2) | 10 |
The signs tell you the direction of the result before you work out its size.
Worked example
Work out -6 - (-9).
- Notice that the calculation subtracts a negative number.
- Change subtract negative into add positive.
- Now work out -6 + 9.
- Moving 9 to the right from -6 lands on 3.
Try it
Picture the direction of change first, then calculate the result.
Question 1
What is -3 + 8?
Question 2
What is 6 - 11?
Question 3
What is -7 - (-2)?
Question 4
The temperature rises from -4 C to 3 C. What is the change?
Question 5
Which statement is correct?
| Dividend | Divisor | Quotient |
|---|---|---|
| -18 | 6 | ? |
Common mistakes
Watch for these when working through the lesson.
- Treating subtract negative as though it means move further left.
- Forgetting that a negative multiplied by a positive is negative.
- Ignoring zero when interpreting a temperature or balance change.
Related topics
These ideas fit closely with this lesson.
- Mental and written arithmetic with integers, decimals and fractions.
- Prime factorisation and factor pairs.
- Construct bar charts, pictograms and frequency tables.