## Sign Rules and Properties of Integers

Subject: Compulsory Maths

#### Overview

This note gives information about the rule and properties of addition and subtractions.

#### Rules of 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

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)
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).
##### Things to remember
• Commutative property states that the sum of any two integers remains unchanged if their places are interchanged.
• It includes every relationship which established among the people.
• There can be more than one community in a society. Community smaller than society.
• It is a network of social relationships which cannot see or touched.
• common interests and common objectives are not necessary for society.
##### Properties of Integers

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.)