Adding and Subtracting Integers Techniques

Jan 10, 2025

Math with Mr. J: Adding and Subtracting Integers

Introduction

  • Review focused on adding and subtracting integers, including both positive and negative integers.
  • Two main methods for solving integer problems.

Adding Integers

Example 1: 12 + (-7)

  • Method 1: Absolute Value Approach

    • Check the signs: Positive 12 and Negative 7.
    • Different signs: Take greater absolute value and subtract the lesser.
    • Absolute values: |12| = 12, |-7| = 7.
    • Subtract: 12 - 7 = 5.
    • Determine the sign: Larger absolute value is 12 (positive), so the answer is positive 5.

  • Method 2: Mental Math Approach

    • Start at positive 12 and add negative 7 (decrease by 7).
    • Think of it as 12 - 7 = 5.
    • Result: 12 decreased by 7 results in positive 5.

Example 2: (-8) + (-10)

  • Same signs: Add absolute values and use the same sign.
  • Absolute values: |-8| = 8, |-10| = 10.
  • Add: 8 + 10 = 18.
  • Use original sign: Both are negative, so answer is negative 18.
  • Mental Math Approach:
    • Start at negative 8 and add negative 10 (decrease by 10).
    • Result: End at negative 18.

Subtracting Integers

Principle

  • Subtracting integers involves adding the opposite.
  • If you can add integers, you can subtract them by using addition of the opposite value.

Example 1: 5 - (-9)

  • Add the opposite: 5 + 9.
  • Result: 5 + 9 = 14 (positive 14).
  • Conceptual Understanding:
    • Subtracting a negative increases value (think in terms of debt).

Example 2: (-3) - 20

  • Add the opposite: -3 + (-20).
  • Result: Decrease by 20 from -3 gives negative 23.

Conclusion

  • Strategies for adding and subtracting integers involve understanding the role of absolute values and signs.
  • For further help, additional resources and examples are provided.

Tips

  • Always determine whether the integers have the same or different signs.
  • Use absolute values to simplify calculations.
  • Think in terms of increasing or decreasing values when dealing with negatives in practical contexts.

Remember, practice makes perfect when mastering integer operations. Utilize provided examples and additional resources to strengthen your understanding!