Understanding the concept
Negative numbers are less than zero. They appear in temperatures below freezing, account balances, elevations and changes in value.
Start by identifying the quantities and units. Use a small example to understand the idea before attempting larger calculations.
Step-by-step method
On a number line, numbers increase to the right. Subtracting a positive number moves left; subtracting a negative number is equivalent to adding.
- Read the question and underline what you must find.
- Write down the given values and check their units.
- Apply the relevant method one step at a time.
- Estimate or reverse-check your answer before presenting it.
Quick-reference table
Use this reference to recognise common situations.
| Example | Meaning or method | Result |
|---|---|---|
| −5 | Five below zero | −5 < 0 |
| −2 versus −7 | −2 is further right | −2 > −7 |
| −3 + 8 | Move eight right from −3 | 5 |
| 4 − (−2) | Subtracting a negative adds | 6 |
Four worked examples
Compare the different types of questions and the steps used to answer them.
Example 1: Temperature
Question or method: Temperature moves from −3 °C to 4 °C.
Example 2: Bank balance
Question or method: A balance of −$20 receives $35.
Example 3: Number line
Question or method: Calculate −6 + 2.
Example 4: Two negatives
Question or method: Calculate −3 − (−5).
Common mistakes
These errors are easy to make. Read each one and check your working.
- Thinking −10 is greater than −2 because 10 is greater than 2.
- Missing the second negative sign in subtraction.
- Confusing a negative balance with money available.
Always ask whether your answer is reasonable for the original situation.
Practice questions
Try each question on paper before revealing the answer.
Question 1. Calculate −4 + 9.
Show answer and explanation
5.
Question 2. Calculate 3 − 8.
Show answer and explanation
−5.
Question 3. Which is colder, −7 °C or −2 °C?
Show answer and explanation
−7 °C.
Question 4. Calculate −5 − 3.
Show answer and explanation
−8.
Question 5. Calculate −2 − (−6).
Show answer and explanation
4.
Review checklist
- Can you explain the key idea in your own words?
- Can you complete a worked example without looking at the solution?
- Can you identify a common mistake and correct it?
- Can you estimate whether your result is sensible?