Question

Proof that integers are commutative property under addition and multiplication,not under division and subtraction

Answer 1

Commutative property for addition:

Integers are commutative under addition when any two integers are added irrespective of their order, the sum remains the same.

a+b =b+a

The sum of two integer numbers is always the same. This means that integer numbers follow the commutative property.

Let’s see the following examples:

15 + 20 =35; 20 +15=35

-10 + (-5) = -15; -5 + (-10) = -15

The above examples prove that the addition of integers is commutative. 

The commutative property for Subtraction:

Is the case true with subtractions? Are subtractions also commutative? The following examples will let us know this:

5-(-3) = +8

-3-5 = -8

This brings us to the conclusion that subtractions of integers are not commutative. Therefore, a-b ≠ b-a

Commutative Property of Division

This property does not apply to divisions between integers. This means that a÷b ≠b÷a

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