📘 Class 7 - Mathematics Homework
Topic: Integers
🎯 Objective
Understand the concept of Integers, their representation on a number line, rules of operations, and application in real-life situations.
📚 Vocabulary
Integer, Negative, Positive, Zero, Number Line, Add, Subtract, Multiply, Opposite, Absolute Value
📝 Definitions
| Term | Definition |
|---|---|
| Integer | Whole numbers including negative numbers, zero, and positive numbers. (..., -3, -2, -1, 0, 1, 2, 3, ...) |
| Positive Integers | Integers greater than 0 (e.g., 1, 2, 3) |
| Negative Integers | Integers less than 0 (e.g., -1, -2, -3) |
| Zero | Neutral number. Neither positive nor negative. |
| Number Line | A straight line where integers are represented at equal distances. |
| Absolute Value | The distance of a number from 0. Always positive. Example: |-4| = 4 |
📐 Rules of Operations
- Addition:
- Same sign → Add and keep the same sign.
Example: (-3) + (-5) = -8 - Different signs → Subtract and keep sign of bigger number.
Example: (-6) + 9 = 3
- Same sign → Add and keep the same sign.
- Subtraction: Change to addition of opposite.
Example: 5 - (-3) = 5 + 3 = 8 - Multiplication:
- Same sign → Positive result.
Example: (-2) × (-3) = 6 - Different signs → Negative result.
Example: (-4) × 5 = -20
- Same sign → Positive result.
- Division: Same rule as multiplication.
Example: 12 ÷ (-4) = -3
🔍 Solved Examples
| Operation | Example |
|---|---|
| Addition | (-7) + 10 = 3 |
| Subtraction | 6 - (-4) = 6 + 4 = 10 |
| Multiplication | (-3) × 4 = -12 |
| Division | (-20) ÷ (-5) = 4 |
| Absolute Value | |-5| = 5 |
📊 Number Line
- Left side of 0: Negative numbers
- Right side of 0: Positive numbers
- Zero is at the center
Example: -3, -2, -1, 0, 1, 2, 3
🌍 Real Life Applications
- Thermometer readings: Example –10°C shows negative temperature.
- Bank transactions: Deposit (+), Withdrawal (–)
- Elevator floors: Basement floors are shown as –1, –2, etc.