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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.
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.
Example:
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.
Example:
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.
Example:
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.
Example:
4 3÷ (2)7 (2)7÷4 3.
Important!
Therefore for rational number addition, and multiplication operations only satisfy the commutative property, not the subtraction and division operations.