Notes on Adding and Subtracting Integers

Introduction

• Review of adding and subtracting integers (positive and negative integers).

Adding Integers

Example 1: 12 + (-7)

• Signs: Positive 12 and Negative 7 (different signs).
• Steps:
  1. Absolute Values:
     • |12| = 12
     • |-7| = 7
  2. Subtract:
     • Greater absolute value (12) - Lesser absolute value (7) = 12 - 7 = 5
  3. Determine Sign:
     • Larger absolute value from original problem is positive 12.
     • Final answer = +5.
• Mental Math Approach:
  • Think of it as starting at +12 and decreasing by 7.
  • 12 + (-7) = 12 - 7 = 5.

Example 2: -8 + (-10)

• Signs: Both are negative (same signs).
• Steps:
  1. Absolute Values:
     • |-8| = 8
     • |-10| = 10
  2. Add Absolute Values:
     • 8 + 10 = 18
  3. Determine Sign:
     • Same sign as original, hence final answer = -18.
• Interpretation:
  • Starting at -8 and adding -10 means decreasing value, resulting in -18.

Subtracting Integers

Example 1: 5 - (-9)

• Method: Convert subtraction into addition of the opposite.
• Steps:
  1. Addition of the Opposite:
     • 5 + 9 (since opposite of -9 is +9)
  2. Final Calculation:
     • 5 + 9 = 14 (positive value).
• Conceptual Understanding:
  • Subtracting a negative is akin to taking away a debt, increasing value (like money).

Example 2: -3 - 20

• Method: Convert subtraction into addition of the opposite.
• Steps:
  1. Addition of the Opposite:
     • -3 + (-20)
  2. Final Calculation:
     • Start at -3 and decrease by 20, resulting in -23.

Conclusion

• Summary of adding and subtracting integers.
• For more examples and help, additional resources are available in the description.