Properties Of Addition And Subtraction Of Integers

Properties of Addition and Subtraction of Integers

1. Closure under Addition

For the closure property the sum of two integers must be an integer then it will be closed under addition.

Example

2 + 3 = 5

2+ (-3) = -1

(-2) + 3 = 1

(-2) + (-3) = -5

Hence, integers are closed under addition.

If we have two integers p and q, p + q is an integer.

2. Closure under Subtraction

If the difference between two integers is also an integer then it is said to be closed under subtraction.

Example

7 – 2 = 5

7 – (- 2) = 9

– 7 – 2 = – 9

– 7 – (- 2) = – 5

Hence, integers are closed under subtraction.

3. Commutative Property

a. If we change the order of the integers while adding then also the result is the same then it is said that addition is commutative for integers.

For any two integers p and q

p + q = q + p

Example

23 + (-30) = – 7

(-30) + 23 = – 7

b. If we change the order of the integers while subtracting then the result is not the same so subtraction is not commutative for integers.

For any two integers p and q

p – q ≠ q – p will not always equal. 

Example

23 – (-30) = 53

(-30) – 23 = -53

4. Associative Property

If we change the grouping of the integers while adding in case of more than two integers and the result is same then we will call it that addition is associative for integers.

For any three integers, p, q and r

p + (q + r) = (p + q) + r

5. Additive Identity

If we add zero to an integer, we get the same integer as the answer. So zero is an additive identity for integers.

For any integer p,

p + 0 = 0 + p =p

Example

2 + 0 = 2

(-7) + 0 = (-7)

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