Operations on Integers
Operations that can be performed on integers:
- Addition
- Subtraction
- Multiplication
- Division.
Addition of Integers
1. Addition of Two Positive Integers
If you have to add two positive integers then simply add them as natural numbers.
(+6) + (+7) = 6 + 7 = 13
(+5) + (+2) = +7
2. Addition of Two Negative Integers
If we have to add two negative integers then simply add them as natural numbers and then put a negative sign on the answer.
(-6) + (-7) = - (6+7) = -13
(-5) + (-2) = -7
3. Addition of One Negative and One Positive Integer
If we have to add one negative and one positive integer then simply subtract the numbers and put the sign of the bigger integer.
We will decide the bigger integer ignoring the sign of the integers.
(-6) + (7) = 1 (bigger integer 7 is positive integer)
(6) + (-7) = -1 (bigger integer 7 is negative integer)
Additive Inverse
If we add numbers like (-7) and 7 then we get the result as zero. So these are called the Additive inverse of each other.
If we add (-2) + (2), then first we move 2 steps to the left of zero then we move two steps to the right of (-2).so finally we reached to zero.
Hence, if we add the positive and negative of the same number then we get the zero.
Example
What is the additive inverse of 4 and (-8)?
Solution
The additive inverse of 4 is (-4).
The additive inverse of (-8) is 8.
Subtraction of Integers
Example:
(-3) – (+2) = (-3) + (-2) = -5
Properties of Addition and Subtraction of Integers
Closure under Addition
- a + b and a – b are integers, where a and b are any integers.
Commutativity Property
- a + b = b + a for all integers a and b.
Associativity of Addition
- (a + b) + c = a + (b + c) for all integers a, b and c.
Additive Identity
- Additive Identity is 0, because adding 0 to a number leaves it unchanged.