Integers & the Number Line
Integers are whole numbers that can be positive, negative, or zero. Understanding them unlocks algebra, temperature, debt, and elevation problems.
What Are Integers?
The set of integers is: … −3, −2, −1, 0, 1, 2, 3 … Positive integers are to the right of zero on the number line; negative integers are to the left.
Key rules:
• Absolute value |n| = distance from zero (always ≥ 0)
• Opposite of n = −n
Adding & Subtracting Integers
Same signs → add and keep the sign.
Different signs → subtract the smaller absolute value and keep the sign of the larger.
Examples
−5 + (−3) = −8 (both negative, add)
−8 + 3 = −5 (subtract 3 from 8, keep negative)
6 − (−2) = 6 + 2 = 8 (subtracting a negative = adding)
Multiplying & Dividing Integers
Simple sign rules:
- Positive × Positive = Positive
- Negative × Negative = Positive
- Positive × Negative = Negative
Same rules apply to division.
(−4) × (−3) = 12 | (−12) ÷ 3 = −4
Real-World Uses
Integers appear everywhere: temperature below zero (−10°C), sea level elevation, bank balances, football yardage. Any situation with opposites needs integers.
FAQ
Is zero positive or negative? Neither. Zero is its own category.
What is the absolute value of −7? 7 — it is simply the distance from zero.
Quick Quiz
Test what you just learned. Choose the best answer for each question.