Integers
Positive and negative integers, number line, and operations with signs.
Chapter Overview
On the number line, moving right increases value; moving left decreases value.
Integers include all whole numbers and their negatives: ..., −3, −2, −1, 0, 1, 2, 3, ... They represent opposite directions — profit/loss, above/below sea level, temperature rise/fall.
What Are Integers?
Zero is neither positive nor negative. Integers extend whole numbers to include negatives, essential for representing losses, depths below sea level, and temperatures below freezing.
- Positive integers: 1, 2, 3, ...
- Negative integers: −1, −2, −3, ...
- Zero: 0 (neutral)
Number Line
- Moving right increases value; moving left decreases value
- −5 is less than −2 (farther left on the number line)
- Adding a negative means moving left; subtracting a negative means moving right
Rules for Operations
- Addition: (−a) + (−b) = −(a+b)
- Subtraction: a − (−b) = a + b
- Multiplication: negative × negative = positive; negative × positive = negative
- Division follows same sign rules as multiplication
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Temperature on Number Line
Morning temperature was −3°C. It rose by 5°C by afternoon. Find the afternoon temperature.
- 1Start at −3 on the number line.
- 2Rise of 5°C means move 5 steps right.
- 3−3 + 5 = 2.
Answer
2°C
Example 2: Depth Below Sea Level
A submarine is at −120 m (below sea level). It rises 85 m. Find its new depth.
- 1Rising means adding a positive: −120 + 85.
- 2On number line: move 85 steps right from −120.
- 3−120 + 85 = −35.
Answer
−35 m (still 35 m below sea level)
Key Points to Remember
- ✓ Use number line until rules feel natural
- ✓ Sign rules are critical for algebra in higher classes
- ✓ Real-life word problems often use integers
- ✓ Absolute value is distance from zero, always non-negative
Exam Tips
- • Draw number line for addition/subtraction in exams
- • Double-check signs in multiplication problems
- • State whether answer is above or below zero in word problems
Practice MCQs — Integers
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Which integer is greater: −7 or −4?