Adding, Subtracting, Multiplying, and Dividing Integers with Mr. J

Adding Integers

Different Signs

• Example: 12 + (-7)

  • Positive 12 and negative 7 (different signs)
  • Take absolute values:
    • |12| = 12, |-7| = 7
  • Subtract the smaller absolute value from the larger: 12 - 7 = 5
  • Sign of answer: Take the sign of the larger absolute value (positive)
  • Answer: +5

• Mental Math Approach

  • Start at 12, add -7 (decrease by 7)
  • Think of it as 12 - 7 = 5

Same Signs

• Example: -8 + (-10)

  • Both numbers are negative
  • Add absolute values: |8| + |10| = 18
  • Use sign from original problem (negative)
  • Answer: -18

• Mental Math Approach

  • Start at -8, add -10 (decrease further)
  • Final answer: -18

Subtracting Integers

General Rule

• Subtracting is adding the opposite
• Change subtraction to addition and take the opposite of the second number

Examples

• Example 1: 5 - (-9)

  • Change to addition: 5 + 9
  • Answer: 14
  • Interpretation: Subtracting a negative increases value

• Example 2: -3 - 20

  • Change to addition: -3 + (-20)
  • Start at -3, decrease by 20
  • Answer: -23

Multiplying Integers

Different Signs

• Example: -7 * 4
  • Negative times positive
  • Answer: -28
  • Rule: Different signs give a negative product*

Same Signs

• Example: -10 * -6
  • Both numbers negative
  • Answer: 60
  • Rule: Same signs give a positive product*

Dividing Integers

Same Signs

• Example: -48 ÷ -8
  • Negative divided by negative
  • Answer: +6
  • Rule: Same signs give a positive quotient

Different Signs

• Example: 36 ÷ -4
  • Positive divided by negative
  • Answer: -9
  • Rule: Different signs give a negative quotient

Mr. J wraps up the session by inviting viewers to access more resources via links provided in the video description for further practice.

End Note: Understanding the signs (positive or negative) and their interactions in integer operations is crucial for accurate calculations.