Integer Operations: Addition
Master adding positive and negative numbers! Integers are whole numbers that can be positive, negative, or zero. Understanding integer addition is essential for algebra, temperature changes, bank accounts, and so much more.
Do this: Read the concept below, then try the quiz or activity.
Concept
Integer addition follows clear rules that make sense once you understand them!
WHAT ARE INTEGERS? Integers: {..., -3, -2, -1, 0, 1, 2, 3, ...} - Positive integers: 1, 2, 3, 4, ... (above zero) - Negative integers: -1, -2, -3, -4, ... (below zero) - Zero: neither positive nor negative
INTEGER ADDITION RULES:
Rule 1: Same Signs When adding integers with the same sign: - ADD the absolute values - KEEP the common sign
Examples: - 5 + 3 = 8 (both positive → add → positive result) - (-5) + (-3) = -8 (both negative → add → negative result)
Think: Moving in the same direction on a number line!
Rule 2: Different Signs When adding integers with different signs: - SUBTRACT the smaller absolute value from the larger - TAKE the sign of the number with the larger absolute value
Examples: - 7 + (-3) = 4 (|7| > |-3|, so subtract: 7 - 3 = 4, keep positive) - (-10) + 6 = -4 (|-10| > |6|, so subtract: 10 - 6 = 4, keep negative)
Think: Opposites cancel each other out!
NUMBER LINE METHOD: Visualize on a number line: - Start at the first number - Positive = move RIGHT - Negative = move LEFT - Where you land = answer
Example: -3 + 5 Start at -3, move 5 spaces right → land on 2
REAL-WORLD CONNECTIONS: - Temperature: 5°F + (-8°F) = -3°F (temperature drops) - Money: Earn $20, spend $12 → 20 + (-12) = $8 left - Elevation: Climb 100 ft, descend 60 ft → 100 + (-60) = 40 ft gain - Football: Gain 7 yards, lose 4 yards → 7 + (-4) = 3 yards net
Try it
Practice adding integers with confidence!
SAME SIGNS: 1. 12 + 8 = ? 2. (-6) + (-9) = ? 3. 15 + 23 = ? 4. (-18) + (-7) = ?
DIFFERENT SIGNS: 5. 10 + (-4) = ? 6. (-15) + 9 = ? 7. 25 + (-30) = ? 8. (-8) + 20 = ?
MIXED PRACTICE: 9. (-14) + (-6) = ? 10. 17 + (-17) = ? 11. (-9) + 15 = ? 12. 0 + (-23) = ?
WORD PROBLEMS: 13. The temperature was -5°F in the morning. It rose 12°F by afternoon. What is the afternoon temperature?
14. A submarine at -250 feet descends another 175 feet. What is its new depth? (Write as a negative integer)
15. Your bank account has -$45 (overdrawn). You deposit $60. What's your new balance?
CHALLENGE:
16. Evaluate: (-8) + 12 + (-15) + 3
(Hint: Add positives together, add negatives together, then combine!)17. The sum of two integers is -5. One integer is 8. What's the other integer?