Short answer
Negative numbers appear whenever a quantity goes below a reference point: temperatures below 0 °C, bank accounts in overdraft, depths below sea level, or a lift going below ground floor. Recognising these contexts makes negative number arithmetic feel natural rather than abstract.
At a glance
- Key stage
- Key Stage 3
- Subject
- Number
- Type
- Guide
- For
- Students
- Read time
- 4 min
- Last updated
- 21 October 2026
Where this fits
- Key Stage 3Years 7–9This article
- GCSEYears 10–11
Where do negative numbers appear in everyday life?
Negative numbers arise whenever there is a zero reference point and values can fall below it. The word directed number is sometimes used to emphasise that the sign tells you a direction (above or below, credit or debit, east or west).
| Context | Positive means | Zero | Negative means |
|---|---|---|---|
| Temperature | Above 0 °C | Freezing point of water | Below 0 °C (frost/ice) |
| Bank balance | Money in account | Neither credit nor debt | Overdraft (debt) |
| Altitude / sea level | Above sea level | Sea level | Below sea level |
| Floors in a building | Above ground | Ground floor | Basement/underground |
| Golf scores | Over par | Par | Under par (good!) |
| Time | After a reference event | The event itself | Before the event |
How do you find the difference between two temperatures?
Difference = higher temperature − lower temperature (always positive).
Worked example 1: The temperature at noon was 8 °C. By midnight it had fallen to −3 °C. What was the temperature drop?
Temperature drop = 8 − (−3) = 8 + 3 = 11 °C
Worked example 2: In Moscow, the temperature was −12 °C. In Rome it was 9 °C. What is the difference?
Difference = 9 − (−12) = 9 + 12 = 21 °C
The key operation: subtracting a negative is the same as adding the positive.
How do you interpret bank balance problems?
A positive balance means you have money in the account. A negative balance (overdraft) means you owe the bank money.
| Operation | Meaning |
|---|---|
| Balance increases | Deposit or credit payment |
| Balance decreases | Withdrawal or direct debit |
| Balance goes negative | You've gone into overdraft |
Worked example: Priya's bank balance is −£45 (she is £45 overdrawn). She deposits £120. What is her new balance?
New balance = −45 + 120 = £75
Worked example: Jay has a balance of £30. He pays a bill of £75 by direct debit. What is his new balance?
New balance = 30 − 75 = −£45 (he is now £45 overdrawn)
How do you work with altitudes and depths?
Altitude above sea level is positive; depth below sea level is negative.
Worked example 1: A submarine is at −240 m (240 m below sea level). It rises 80 m. What is its new depth?
New depth = −240 + 80 = −160 m (still 160 m below sea level)
Worked example 2: A cliff is 85 m above sea level. The seabed directly below it is 30 m below sea level. What is the total height from the seabed to the cliff top?
Total = 85 − (−30) = 85 + 30 = 115 m
How do you use a number line with negative numbers?
A number line runs from negative values on the left to positive values on the right, with zero in the middle.
To find the difference between two values on a number line, count the steps between them (or subtract the smaller from the larger):
- From −5 to 3: count 5 steps right to reach 0, then 3 more = 8 steps apart.
- Calculation: 3 − (−5) = 8 ✓
To order negative numbers, remember: the further left on the number line, the smaller the value. −10 < −3 < −1 < 0 < 2.
How are negative numbers used in golf scores?
In golf, the target is to use as few shots as possible. Shooting under par (below the target) is good and is shown as a negative number; over par is shown as positive.
Example: A golfer is −4 after the first round and −7 after the second round. What is the change in score?
Change = −7 − (−4) = −7 + 4 = −3 (they improved by 3 under par in the second round)
Frequently asked questions
Why does subtracting a negative number give a bigger result?
Subtraction moves left on the number line; subtracting a negative is like "un-doing" the leftward move — so you go right instead. Picture it physically: if you owe someone £5 (−£5) and that debt is cancelled (subtract −5), you are £5 better off: 0 − (−5) = +5.
Does the sign of a temperature change which formula I use?
No. Addition and subtraction with temperatures follow exactly the same rules as with any directed numbers. The only thing to remember is that the zero point (0 °C) is arbitrary — it is the freezing point of water, not "nothing."
What does "overdrawn by £30" mean in maths?
It means the account balance is −£30. The word "overdrawn" signals a negative balance. Similarly, "in credit by £50" means the balance is +£50.
Are there contexts where negative numbers are unusual?
Yes — some quantities cannot be negative: number of people, a physical length, a mass, or a probability. In these contexts a negative result from a calculation signals an error. For example, if a "distance" calculation gives −3 metres, you have likely subtracted in the wrong order.
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Key terms
- zero reference point
- directed number
- positive balance
- negative balance
- −160 m
- number line
- order
- under par