The Rules


A number with no sign is considered to be POSITIVE. For example:
    3 = +3
8 + 2 = ( + 8) + ( + 2)
8 - 3 = ( + 8) - ( + 3)
Sometimes you find the '+' sign in front of a positive number, other times it is omitted, especially in higher level classes. In the first time I recommend you to use it (rewrite the problem with '+' signs), but as you proceed you should try to solve the problems without it. I show you examples here for both ways.
NOTE: Signed numbers should always be in parantheses. As a general rule, we can never write two signes next to each other:
Instead of   5 + -3  you should write:  5 + (- 3 ). Or instead of    4 + +2  you should write:  4 + (+ 2 ).



First ask yourself: Do the numbers have the same sign?
Based on your answer choose rule #1 or rule #2.

Rule 1. If the nubers have same signs

  • Ignore the signs of the numbers
  • Add the unsigned numbers together
  • Include the original sign of the numbers to the answer
  • Examples:
    (+5)+(+4) (-3)+(-7) 2 + 4 = (+2)+(+4)
    Add the UNSIGNED numbers
    5 + 4 = 9 3 + 7 = 10 2 + 4 = 6
    Include the original sign to your answer
    + 9 - 10 + 6

    Rule 2. If the nubers have different signs

  • Ignore the signs of the numbers
  • Subtract the smaller number from the larger one
  • Include the original sign of the LARGER number to the answer
  • Examples:
    (-5)+(+4) (+3)+(-7) -2 + 4 = (-2)+(+4)
    Subtract the UNSIGNED numbers:
    5 - 4 = 1 7 - 3 = 4 4 - 2 = 2
    Include the original sign of the LARGER number to your answer:
    - 1 - 4 + 2





    Turn your subtraction into addition as follows:
  • Change the operation sign from subtraction to addition
  • AND change the sign of the second number at the same time
  • Follow the rules for addition above

  • Examples:
    (-6)-(+4) (+4)-(-7) -3 - 4 = (-3)-(+4)
    Change to addition:
    (-6) + (-4) (+4)+(+7) (-3)+(-4)
    Follow the rules of addition:
    - 10 + 11 - 7



    Believe or not, the hard part is over. Multiplication and division are far easier than addition and subtraction.
    They even have the same rules:
  • Ignore the signs and do the operation (multiply or divide)
  • If the original signs were the same, your answer is POSITIVE
  • If the original signs were different, your answer is NEGATIVE


  • Examples:
    (-6) (+4) (+4) (-7) (-12) (-4)
    Ignore the sign and do the operation:
    6 4 = 24 4 7 = 28 12 4 = 3
    Follow the rule of signes:
    - 24 - 28 + 3







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