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

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