Sign Rules and Properties of Integers

Subject: Compulsory Maths

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Overview

This note gives information about the rule and properties of addition and subtractions.
Sign Rules and Properties of Integers

Rules of Addition and Subtraction of Integers

source: www.slideshare.net Fig: Addition and Subtraction of Integers
source: www.slideshare.net
Fig: Addition and Subtraction of Integers
  1. The positive integers are always added holding the positive (+) sign in resulting value. For example,
    (+5) + (+6) = 11 or (+11)
  2. The negative integers are always added holding the negative (-) sign in the resulting value. For example,
    (-5) + (-6) = -11
  3. The positive and negative integers are always added holding the negative (-) sign in the resulting value. For example,
    (+6) + (-5) = 1 or (+1)
    (-6) + (+5) = -1

Properties of addition of Integers

source: www.slideshare.net Fig: Properties of Additional of Integers
source: www.slideshare.net
Fig: Properties of Additional of Integers
  1. Closure property
    Closure property states that the sum of any two integers is also integers. For example,
    (+2) + (+3) = +5, which is an integer
    (+3) + (-2) = +1, which is an integer
    (-3) + (+2) = -1, which is an integer
    Thus, if x and y be any two integers and z is the set of integers then x + y∈ z.
  2. Commutative property
    Commutative property states that thesum of any two integers remains unchanged if their places are interchanged. If x and y are two integers, then x + y = y + z
    For example,
    (+2) + (+3) = (+3) + (+2) = +5
    (-3) + (+2) = (+2) + (-3) = -1
  3. Associative property
    Associative property states that the sum of any three integers remains unchanged if the order in which they are grouped is altered. If x, y and z are three integers, then (x + y) + z = x + (y + z)
    For example,
    (+3) + (+4) + (+5) = (+3) + [(+4) + (+5)] = (+3) + (+9) = +12
    (+3) + (-4) + (+5) = (+3) + [(-4) + (+5)] = (+3) + (+1) = +4
  4. Additive property of zero (0)
    If zero (0) is added +0 any integers, the sum is equal to the integer itself. So, zero (0) is known as the identity element of addition. If a is any integer, then a + 0 = a
    For example,
    (+2) + 0 = (+2) or 2
    (-3) + 0 = (-3)
  5. Additive inverse
    Each integer is said to the additive inverse of the other if the sum of any two integer is zero (0). If a is any integer, then (+a) + (-a) = 0, where (+a) is the additive inverse of (-a) and (-a) is te additive inverse of (+a).

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Things to remember
  • The positive integers are always added holding the positive (+) sign in resulting value.
  • Commutative property states that the sum of any two integers remains unchanged if their places are interchanged.
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Videos for Sign Rules and Properties of Integers
Properties of Integers
Questions and Answers

The sign rules for the addition and subtraction of integers are:

  • The positive integers are always added.
  • The negative integers are always added.
  • The positive and negative integers are always subtracted.

Solution:

Here, (+2) + (+5)

 = +7 or 7 ans.

Solution: 

Here, (-3) + (-2)

 = -5 (The sum holds the negative (-) sign.)

Solution

Here, (+4) + (-1)

 = +3 or 3

Similarly, (+4) + (-7)

 = -7 (The difference holds the sign of the bigger integer.)

Solution:

Here,  (+4) + (+5) 

 = +9 or 9 (The sum holds the positive sign.)

Quiz

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