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What are the Rules of the Integer Model?

Published in Integer Arithmetic 2 mins read

The integer model operates under specific rules for addition, subtraction, multiplication, and division.

Integer Arithmetic Rules

Here's a breakdown of the rules governing integer operations, including information from the provided reference:

Addition Rules

  • Same Signs: If you are adding two integers that have the same sign (both positive or both negative), you add the numerical values of the integers and keep the same sign for the sum.

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

Subtraction Rules

  • Subtraction as Addition: Subtraction can be understood as adding the opposite (additive inverse) of the second number.

    • Example: (+5) - (+3) is the same as (+5) + (-3) = +2
    • Example: (+5) - (-3) is the same as (+5) + (+3) = +8
    • Example: (-5) - (+3) is the same as (-5) + (-3) = -8
    • Example: (-5) - (-3) is the same as (-5) + (+3) = -2

Multiplication and Division Rules

(The rules for multiplication and division are not provided in the reference and are provided here for completeness)

  • Multiplication:
    • Same signs result in a positive product.
      • Example: (+5) x (+3) = +15
      • Example: (-5) x (-3) = +15
    • Different signs result in a negative product.
      • Example: (+5) x (-3) = -15
      • Example: (-5) x (+3) = -15
  • Division:
    • Same signs result in a positive quotient.
      • Example: (+15) / (+3) = +5
      • Example: (-15) / (-3) = +5
    • Different signs result in a negative quotient.
      • Example: (+15) / (-3) = -5
      • Example: (-15) / (+3) = -5

Summary of Integer Rules

Operation Rule Example
Addition (Same Signs) Add values and keep the sign. (+3) + (+4) = +7
Addition (Same Signs) Add values and keep the sign. (-3) + (-4) = -7
Subtraction Add the opposite number. (+5) - (+2) = (+5) + (-2) = +3
Subtraction Add the opposite number. (+5) - (-2) = (+5) + (+2) = +7
Multiplication (Same Signs) Positive product. (+4) x (+2) = +8
Multiplication (Same Signs) Positive product. (-4) x (-2) = +8
Multiplication (Different Signs) Negative product. (+4) x (-2) = -8
Multiplication (Different Signs) Negative product. (-4) x (+2) = -8
Division (Same Signs) Positive quotient. (+8) / (+2) = +4
Division (Same Signs) Positive quotient. (-8) / (-2) = +4
Division (Different Signs) Negative quotient. (+8) / (-2) = -4
Division (Different Signs) Negative quotient. (-8) / (+2) = -4

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