Theory:

A set of numbers is said to be commutative for a specific mathematical operation if the result obtained when changing the order of the operands does not change the result.
Whole Numbers:
i) Addition: Changing the order of operands in addition to whole numbers does not change the result. Hence, whole numbers under addition are commutative.
 
2+3 = 3 + 20 + 6 = 6 + 0

ii) Subtraction: Changing the order of operands in the subtraction of whole numbers changes the result. Hence, whole numbers under subtraction are not commutative.

53 ≠3 − 50 − 6 ≠ 6 − 0

iii) Multiplication: Changing the order of operands in the multiplication of whole numbers does not change the result. Hence, whole numbers under multiplication are commutative.

5 × 3 = 3 × 52 × 0 = 0 × 2

iv) Division: Changing the order of operands in the division of whole numbers changes the result. Hence, whole numbers under division are not commutative.

4 ÷ 2  2÷ 410 ÷ 4 4 ÷ 10
Integers:
i) Addition: Changing the order of operands in addition to integers, does not change the result. Hence integers under addition are commutative.
 
2 + (−3) = (−3) + 2(−1) + 6 = 6 + (−1)

ii) Subtraction: Changing the order of operands in the subtraction of integers changes the result. Hence, integers under subtraction are not commutative.
 
5 −(−3) ≠ (−3) − 5(−1) − 6 ≠ 6 − (−1)

iii) Multiplication: Changing the order of operands in the multiplication of integers does not change the result. Hence, integers under multiplication are commutative.

5 × (−3) = (−3× 5(−2× 0 = 0 × (−2)

iv) Division: Changing the order of operands in the division of integers changes the result. Hence, integers under division are not commutative.
 
4 ÷ (−2)(−2)÷ 4(−10) ÷ 4 ≠4 ÷ (−10)
Rational Numbers:
i) Addition: Changing the order of operands in addition to rational numbers, does not change the result. Hence, rational numbers under addition are commutative.
 
ab+cd=cd+ab.
 
85 + (2)5= (2)5+85.

ii) Subtraction: Changing the order of operands in the subtraction of rational numbers changes the result. Hence, rational numbers under subtraction are not commutative.
 
abcdcdab.
 
85  (2)5 (2)5  85.

iii) Multiplication: Changing the order of operands in the multiplication of rational numbers does not change the result. Hence, rational numbers under multiplication are commutative.
 
ab×cd=cd×ab.
 
85× (2)5 (2)5×85.

iv) Division: Changing the order of operands in the division of rational numbers changes the result. Hence, rational numbers under division are not commutative.
 
ab÷cdcd÷ab.
 
4 3÷ (2)7 (2)7÷4 3.