Integer Operations: Subtraction
Subtracting integers is easier than you think - just add the opposite! This powerful shortcut transforms every subtraction problem into an addition problem you already know how to solve.
Do this: Read the concept below, then try the quiz or activity.
Concept
Subtraction of integers follows one golden rule that simplifies everything!
THE GOLDEN RULE OF INTEGER SUBTRACTION: To subtract an integer, ADD ITS OPPOSITE!
a - b = a + (-b)
WHAT IS THE OPPOSITE? The opposite of a number has the same distance from zero but different sign: - Opposite of 5 is -5 - Opposite of -3 is 3 - Opposite of 0 is 0
THE TWO-STEP METHOD:
Step 1: Keep-Change-Change (KCC) - KEEP the first number - CHANGE subtraction to addition - CHANGE the sign of the second number
Step 2: Use integer addition rules
EXAMPLES:
Example 1: 8 - 5 - Keep: 8 - Change - to + - Change 5 to -5 - Result: 8 + (-5) = 3
Example 2: 4 - 9 - Keep: 4 - Change - to + - Change 9 to -9 - Result: 4 + (-9) = -5
Example 3: -7 - 3 - Keep: -7 - Change - to + - Change 3 to -3 - Result: -7 + (-3) = -10
Example 4: -6 - (-10) - Keep: -6 - Change - to + - Change -10 to 10 (opposite of -10 is 10!) - Result: -6 + 10 = 4
IMPORTANT PATTERN: Subtracting a negative = Adding a positive! - 5 - (-3) = 5 + 3 = 8 - -2 - (-7) = -2 + 7 = 5
Two negatives make a positive in subtraction!
NUMBER LINE VISUALIZATION: For a - b: - Start at a - If b is positive, move LEFT (subtract means go left) - If b is negative, move RIGHT (subtracting negative = going right)
REAL-WORLD APPLICATIONS: - Temperature: -3°F - 5°F = -8°F (gets colder) - Elevation: Sea level (0) - underwater depth (-50) = 50 ft difference - Time zones: If it's 3 PM here and 5 hours earlier there → 3 - 5 = -2 (which means 2 PM yesterday... or use 15 - 5 = 10 AM) - Debt: Owing $20 and removing a debt of $30 → -20 - (-30) = $10 (you're $10 ahead!)
Try it
Master integer subtraction through practice!
BASIC SUBTRACTION: 1. 15 - 8 = ? 2. 7 - 12 = ? 3. 20 - 25 = ? 4. 3 - 15 = ?
SUBTRACTING NEGATIVES: 5. 10 - (-6) = ? 6. 5 - (-5) = ? 7. -3 - (-8) = ? 8. -12 - (-7) = ?
NEGATIVE MINUS POSITIVE: 9. -6 - 4 = ? 10. -15 - 9 = ? 11. -2 - 20 = ?
MIXED PRACTICE: 12. 0 - 8 = ? 13. 0 - (-8) = ? 14. -9 - 0 = ? 15. 14 - (-6) = ?
WORD PROBLEMS:
16. The temperature was 6°F. It dropped to -4°F. What was the change in temperature?
(Hint: Find -4 - 6 or calculate the difference)17. A hiker starts at elevation 200 feet and descends to -50 feet (below sea level). What is the total change in elevation?
18. Your checking account has $25. You make a payment of $40. What's your new balance? (Express as an integer)
CHALLENGE:
19. Evaluate: 15 - (-8) - 12 - (-5)
(Rewrite each subtraction as addition first!)20. If a - b = 10 and b = -3, what is a?
THINK DEEPER: 21. Why does subtracting a negative number give the same result as adding a positive number? Explain using a real-world example.