Rules governing the operations on signed numbers?

Answer 1

WHAT ARE THE RULES TO GOVERNING THE OPERATING SIGNED NUMBERS?

• 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 signeds 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 numbers 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 numbers5 + 4 = 93 + 7 = 102 + 4 = 6Include the original sign to your answer+ 9- 10+ 6Rule 2. If the numbers 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 = 17 - 3 = 44 - 2 = 2Include 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 = 244 7 = 2812 4 = 3Follow the rule of signes:- 24- 28+ 3