📖Definition
Integers are whole numbers that can be positive, negative, or zero. They do not include fractions or decimals. The set of integers is written as {..., -3, -2, -1, 0, 1, 2, 3, ...} and extends infinitely in both directions.
📐Formula
The symbol ℤ (from German "Zahlen" meaning numbers) represents the set of all integers. Positive integers are greater than zero, negative integers are less than zero, and zero is neither positive nor negative.
📝Step-by-Step Guide
Adding Integers
Same signs: Add absolute values, keep the sign. Different signs: Subtract absolute values, use the sign of the larger absolute value.
Subtracting Integers
Change subtraction to addition of the opposite (add the additive inverse).
Multiplying Integers
Same signs give positive result. Different signs give negative result.
Dividing Integers
Same rules as multiplication: same signs = positive, different signs = negative.
⚠️Common Mistakes to Avoid
- Confusing the rules for adding and multiplying integers
- Forgetting that subtracting a negative becomes addition
- Including fractions or decimals as integers
- Making sign errors when working with multiple operations
- Thinking zero is a positive number
✏️Practice Problems
Calculate (-7) + 4
Answer: -3
Calculate (-6) × (-8)
Answer: 48
Calculate (-24) ÷ 6 + (-3) × (-2)
Answer: 2
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