Sign Rules and Properties of Integers

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)
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).

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.

• It includes every relationship which established among the people.
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• common interests and common objectives are not necessary for society.

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