1. Introduction to Negative Numbers
Negative numbers help us describe values that are less than zero. They often appear in real-life situations like temperature below zero, money owed, or positions below sea level.
If a number has a minus sign (−) before it, it is a negative number.
2. Definition of Negative Numbers
Negative numbers are numbers that are less than zero.
They are written with a minus sign in front. Examples include:
- −1
- −5
- −12
- −100
3. Understanding Negative Numbers Using a Number Line
The number line is the easiest way to understand negative numbers.
All negative numbers appear to the left of zero.
3.1. Position on the Number Line
Example: ... −5, −4, −3, −2, −1, 0, 1, 2, 3 ...
Numbers get smaller as you move left.
3.2. Comparing Negative Numbers
Among negative numbers, the number closer to zero is larger.
- −3 is greater than −7
- −1 is greater than −9
4. Why Do We Need Negative Numbers?
Negative numbers appear naturally in many situations:
4.1. Temperature
Winter temperatures can fall below 0°C, such as −2°C or −10°C.
4.2. Bank Balance
If you owe money, your balance may show a negative number like −₹500.
4.3. Sea Level
Places below sea level, like −50 meters, use negative numbers.
5. Operations with Negative Numbers
You can add, subtract, multiply, and divide negative numbers using simple rules.
5.1. Addition
Adding a negative number means moving left on the number line.
Example: 5 + (−3) = 2
5.2. Subtraction
Subtracting a negative is the same as adding a positive.
Example: 6 − (−2) = 6 + 2 = 8
5.3. Multiplication Rules
- Positive × Negative = Negative
- Negative × Positive = Negative
- Negative × Negative = Positive
Example: (−3) × (−4) = 12
5.4. Division Rules
- Positive ÷ Negative = Negative
- Negative ÷ Positive = Negative
- Negative ÷ Negative = Positive
6. Examples of Negative Numbers
- −1
- −20
- −100
- −0.5
All these values are less than zero.
7. Properties of Negative Numbers
Negative numbers follow predictable mathematical patterns.
7.1. Opposite of a Number
The opposite of a positive number is a negative number.
Example: The opposite of 7 is −7.
7.2. Zero Is Neither Positive nor Negative
Zero is a neutral number in the number system.
7.3. Negative Numbers Always Less Than Zero
No negative number is greater than zero.
8. Difference Between Negative and Positive Numbers
Positive and negative numbers lie on opposite sides of zero.
8.1. Comparison Table
| Negative Numbers | Positive Numbers |
|---|---|
| Less than zero | Greater than zero |
| Examples: −3, −10 | Examples: 3, 10 |
| Left of zero on number line | Right of zero on number line |
9. Practice Questions
- Which is greater: −2 or −5?
- What is the opposite of −7?
- Solve: 8 + (−11)
- Solve: −4 × −6
- Is −0.5 a negative number?
10. Summary
Negative numbers are values less than zero, shown with a minus sign. They are used in real-life situations like temperature, money, and measurements. Negative numbers follow special rules for addition, subtraction, multiplication, and division.