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.
Quick Practice
- Order from smallest: 4, −3, 0, −7, 2.
- Calculate −8 + 5.
- Calculate −3 × −6.
- What is |−15|?
- The temperature drops from 3°C to −4°C. By how many degrees did it drop?
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.