INTEGERS

Integer Laws

  1. Adding Integers

    • Same Sign: To add integers with the same sign, add their absolute values and keep the sign.

      • Example: (−3)+(−5)=−8(-3) + (-5) = -8

    • Different Signs: To add integers with different signs, subtract the smaller absolute value from the larger absolute value and keep the sign of the integer with the larger absolute value.

      • Example: (−7)+4=−3(-7) + 4 = -3

  2. Subtracting Integers

    • To subtract an integer, add its opposite (additive inverse).

      • Example: 5−(−2)=5+2=75 - (-2) = 5 + 2 = 7

      • Example: (−4)−3=(−4)+(−3)=−7(-4) - 3 = (-4) + (-3) = -7

  3. Multiplying Integers

    • Same Sign: The product of two integers with the same sign is positive.

      • Example: (−3)×(−4)=12(-3) \times (-4) = 12

      • Example: 2×6=122 \times 6 = 12

    • Different Signs: The product of two integers with different signs is negative.

      • Example: (−5)×2=−10(-5) \times 2 = -10

      • Example: 3×(−4)=−123 \times (-4) = -12

  4. Dividing Integers

    • Same Sign: The quotient of two integers with the same sign is positive.

      • Example: (−12)÷(−3)=4(-12) \div (-3) = 4

      • Example: 15÷3=515 \div 3 = 5

    • Different Signs: The quotient of two integers with different signs is negative.

      • Example: (−20)÷4=−5(-20) \div 4 = -5

      • Example: 18÷(−6)=−318 \div (-6) = -3

  5. Summary Table

Operation

Rule

Example

Addition (Same Sign)

Add absolute values and keep the sign.

(−2)+(−3)=−5(-2) + (-3) = -5

Addition (Diff. Sign)

Subtract smaller absolute value from larger and keep the sign of larger.

7+(−4)=37 + (-4) = 3

Subtraction

Add the opposite.

5−(−2)=75 - (-2) = 7

Multiplication (Same Sign)

Product is positive.

(−3)×(−5)=15(-3) \times (-5) = 15

Multiplication (Diff. Sign)

Product is negative.

4×(−2)=−84 \times (-2) = -8

Division (Same Sign)

Quotient is positive.

(−10)÷(−2)=5(-10) \div (-2) = 5

Division (Diff. Sign)

Quotient is negative.

8÷(−4)=−28 \div (-4) = -2