Commutative Property Formula
The word "Commutative" originates from the word "commute," meaning "to move around". Hence, the commutative property formulas deal with moving the numbers around. So mathematically, we can define any binary operation as a commutative one, if changing the order of the operands does not change the result of the operation. Let's learn about the commutative property formula with a few solved examples in the end.
What Is the Commutative Property Formula?
The commutative property says that the order operands do not change the final result. The commutative property formulas for addition and multiplication are given as,
Commutative property of addition: The commutative property of addition says that changing the order of the addends will not change the value of summation.
A + B = B + A
Commutative property of multiplication: The commutative property of multiplication says that the order in which we multiply the numbers does not change the final product.
A × B = B × A
Let us have a look at a few solved examples to understand the commutative property formula better.

Example 1: Jacky's mother asked him whether x + y = y + x is an example of the commutative property formula. Can you help Jacky find out whether it is commutative or not?
Solution:
We know that the commutative property formula states that changing the order of the addends will not change the value of summation.
So, we see that changing the order will not alter the summation value.
Hence, the summation remains the same. So this is an example of the commutative property.
Answer: x + y = y + x is an example of the commutative property.

Example 2: Rinny walked 5 miles to the North, and then 3 miles to the East. Will she end up at the same place if she would have walked 3 miles to the East first, and then 5 miles to the North?
Solution:
We try to convert this on a coordinate plane. We assume the miles he walked to the North to be the ycoordinate, while miles in the East to be the xcoordinate. By simple rules of vector addition, we can say that the final position of Rinny can be calculated as:
Final position 1 = 5 miles to the North + 3 miles to the East = (3,5)
Therefore the final coordinate = (3,5)
Now, we can also say: Final position 2 = 3 miles to the East + 5 miles to the North = (3,5)
Therefore the final coordinate = (3,5)
Thus, in both cases, our answer for the final position coordinate is the same.
Answer: Rinny will end up in the same place.