All About Numbers
Negative Numbers
Negative numbers are numbers less than zero. They appear on the left side of zero on a number line and are written with a minus sign (−) in front. Together with positive numbers and zero, they form the set of integers.
What Are Negative Numbers?
When we count up from zero (1, 2, 3 …), we get positive numbers. When we count down past zero (−1, −2, −3 …), we get negative numbers.
Real-Life Contexts for Negative Numbers
| Context | Negative Meaning | Example |
|---|---|---|
| Temperature | Below zero (freezing) | −10°C in winter |
| Altitude | Below sea level | Dead Sea at −430 m |
| Finance | Debt / overdraft | −£200 in a bank account |
| Sport | Under par (golf) | −3 in a golf round |
| Floors | Below ground level | Basement = Floor −1 |
Ordering Integers
On the number line, numbers increase from left to right. So any number to the right is greater.
Absolute Value
The absolute value of a number is its distance from zero, always positive. Written as |n|.
Adding and Subtracting Negative Numbers
| Operation | Rule | Example |
|---|---|---|
| Adding a negative | Same as subtracting the positive | 5 + (−3) = 5 − 3 = 2 |
| Subtracting a negative | Same as adding the positive | 5 − (−3) = 5 + 3 = 8 |
| Negative + Negative | Add and keep the minus sign | −4 + (−2) = −6 |
Multiplying and Dividing
| Signs | Result | Example |
|---|---|---|
| Positive × Positive | Positive | 3 × 4 = 12 |
| Negative × Positive | Negative | −3 × 4 = −12 |
| Negative × Negative | Positive | −3 × −4 = 12 |
- Negative numbers are less than zero; positive numbers are greater than zero.
- On a number line, smaller numbers are always to the left.
- A larger absolute value does not mean a larger negative number (e.g., −10 < −2).
- Two negatives multiplied or divided give a positive result.
Practice: Calculate with Negative Numbers
Work out the result below. If you get it wrong (or leave it blank), we'll walk through the sign rules together.
Summary
Negative numbers extend our number system below zero and are essential for describing temperatures, debts, depths, and many other real-world measurements. They follow clear rules for arithmetic, and understanding them is a prerequisite for algebra, coordinate geometry, and beyond.