Question

Integers are commutative under .............

Answer 1

Hint: In this particular type of question we need to check the commutative property for addition, subtraction, multiplication and division to get the desired answer.

Complete Step-by-step answer:
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:
The difference of two integers is not always the same
The following example 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 $ \ne $ b-a
Commutative Property of Multiplication:
Changing the order of the numbers we are multiplying, does not change the product. Thus multiplication is commutative i.e. $a \times b = b \times a$
Commutative Property of Division:
This property does not apply to divisions between integers. This means that $\dfrac{a}{b}$ $ \ne $ $\dfrac{b}{a}$
Thus multiplication and addition of integers are commutative.

Note: Remember to recall that the word "commutative" comes from "commute" or "move around", so the Commutative Property is the one that refers to moving stuff around. Note that addition and multiplication are the only ones who satisfy commutative property of integers but it does not mean that subtraction and division are never commutative.