🔢 Integers (Negative Numbers)

What are Integers?
Integers are whole numbers and their opposites. They include:
• Positive integers: 1, 2, 3, 4... (to the right of zero)
• Zero: 0 (neither positive nor negative)
• Negative integers: -1, -2, -3, -4... (to the left of zero)

The Number Line:
<----|----|----|----|----|----|----|----|----|----|---->
-5 -4 -3 -2 -1 0 1 2 3 4 5

Negative ← → PositiveAbsolute Value:
• Distance from zero (always positive)
• Written as |−5| = 5
• |3| = 3

Comparing Integers Rules:
RuleExampleWhy?Positive > Negative5 > -3Positive on rightLarger positive > Smaller positive8 > 38 is further rightSmaller negative > Larger negative-2 > -7-2 is right of -7Any negative < 0-4 < 0Negative left of zeroNumber Line Shortcut:
More Negative ← → More Positive
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3

The farther LEFT, the SMALLER
The farther RIGHT, the LARGERComparing Trick:
• For negatives, the number with the smaller absolute value is larger!
• Example: -3 vs -7 → |−3|=3, |−7|=7 → 3 < 7 → -3 > -7

Adding Integers Using Number Line:
Adding a positive = move RIGHT
Adding a negative = move LEFTRules for Adding Integers:
First NumberOperationSecond NumberResultPositive+PositivePositive (add)Positive+NegativeSubtract, sign of largerNegative+PositiveSubtract, sign of largerNegative+NegativeNegative (add absolute values)Subtracting Integers:
Rule: Subtracting a number = adding its opposite
a - b = a + (-b)
a - (-b) = a + bExamples:
• 5 - 3 = 5 + (-3) = 2
• 5 - (-3) = 5 + 3 = 8
• -5 - 3 = -5 + (-3) = -8
• -5 - (-3) = -5 + 3 = -2