Negative numbers are useful for temperatures, balances, and many puzzles. This summary follows the same ideas as standard school explanations (for example step‑wise work on a number line).
What are negative numbers?
Negative numbers are less than zero. We write them with a minus sign in front: −1, −5, −10, and so on. Numbers greater than zero are positive: 1, 2, 3, …
Negative numbers in everyday life
You see them outside math class too. For example:
- Temperature: −5 °C means five degrees below freezing on the Celsius scale; a very cold night might be −20 °C. In Fahrenheit, cold winter days can be below 0 °F in some places.
- Money and bank balances: “−20” on an account can mean you owe 20 (euros, dollars, etc.); a statement may show negative amounts when spending exceeds what you had.
- Height and depth: places below sea level are often written with negative metres (for example the shores of the Dead Sea). Mines, wells, and submarine depths use negative numbers for “down”.
- Buildings: basement floors are often labelled −1, −2 or B−1, B−2 — “below” the ground floor.
The number line
A number line shows how numbers line up. Zero is the middle; negatives are on the left, positives on the right. Further left means smaller; further right means larger.
- Move to the right → you add (take steps upward).
- Move to the left → you subtract (take steps downward).
Examples
Subtracting. Start at 8 and take away 6: walk 6 steps left → 8 − 6 = 2. From 2, take away 6 again → 2 − 6 = −4.
Starting below zero. Start at −8 and add 6: walk 6 steps right → −8 + 6 = −2.
A longer sum. −8 + 10: from −8, 8 steps to the right reach 0, then 2 more → 2.
Several operations in a row
Work in order, step by step. Example: −7 − 3 + 5 − 2 → −7 − 3 = −10, then −10 + 5 = −5, then −5 − 2 = −7.
Parentheses and two minus signs
−8 + (−2) means the same as −8 − 2: adding a negative is like subtracting a positive. For −8 − (−2), subtracting a negative turns into addition: −8 − (−2) = −8 + 2.
Rules in short
- Subtracting a negative flips to a plus: a − (−b) = a + b (example: 5 − (−3) = 5 + 3).
- Adding a negative is like subtracting: a + (−b) = a − b.
- Two “subtract” steps in a row make the total more negative when you keep going left: −5 − 6 = −11.
Comparing negative numbers (and fractions)
On the line, the number further left is smaller. So −9 < −8. We write < for “less than”, > for “greater than”, and = for “equal”.
The same order works for fractions and mixed numbers on the line: −3⅓ lies to the left of −1½, so −3⅓ < −1½. For a sum like −4 + 3, you can start at −4 on the line and take 3 steps to the right; you land at −1.