Adding (and subtracting) signed numbers:

• Same signs (either both positive or both negative) - Add the numbers and keep the same sign.
  • (+) + (+) = +                      5 + 3 = 8
  • (-) + (-) = -                       -2 + (-4) = -6
  • same as (-) – (+) = -         -2 – 4 = -6 (both numbers are considered negative)
    
• Opposite signs - Take the difference between the two numbers and the sign of the higher of the two.
  • (+) + (-) =   or   (+) – (+) =          3 + (-7) = -4
                                                        5 + (-2) = 3
                                                        4 – 5 = 4 + (-5) = -1
                                                       11 – 2 = 11 + (-2) = 9
  • (-) + (+) =                                  -3 + 14 = 11
                                                      -9 + 5 = -4
• Subtracting a negative
  • -(-) = +       like (-1) times a negative number
    • -1 times –3 equals positive 3
    • (-1)(-3) = -(-3) = 3

Multiplying signed numbers:

• Two numbers with the same sign - Answer will be positive
  • (+)(+) = +                    3 (4) = 12
  • (-)(-) = +                      (-2)(-1) = 2
• Two numbers with opposite signs - Answer will be negative
  • (+)(-) = -                      (2)(-5) = -10
  • (-)(+) = -                      (-3)(6) = -18
• More than two numbers multiplied by each other:
  • If an even number of negative multiples, answer will be positive
    • (-)(-)(-)(-) = +              (-3)(-1)(-2)(-1) = 6
  • If an odd number of negatives multiples, answer is negative
    • (-)(-)(-)(-)(-) = -          (-1)(-2)(-3)(-2)(-2) = -2

Dividing signed numbers:

• Same sign - Answer will be positive
  •                      Â
    
  •                      Â         Because (-6)(4) = -24
    
• Opposite signs - Answer will be negative
  •                                Because (-6)(-3) = 18
    
  •                              Because (3)(-4) = -12