# Difference between associative and commutative property of addition.

Dear student,

The commutative property states that the factors in an equation can be rearranged freely without affecting the outcome of the equation. The operation is commutative because the order of the elements does not affect the result of the operation.
This can be shown by the equation a + b = b + a.
For example, the numbers 2, 3, and 5 can be added together in any order without affecting the final result:
2 + 3 + 5 = 10 , 3 + 2 + 5 = 10

The associative property states that the grouping of factors in an operation can be changed without affecting the outcome of the equation.
The associative property, on the other hand, concerns the grouping of elements in an operation.
This can be shown by the equation (a + b) + c = a + (b + c).
For example, take the equation 2 + 3 + 5. No matter how the values are grouped, the result of the equation will be 10:
(2 + 3) + 5 = (5) + 5 = 10 , 2 + (3 + 5) = 2 + (8) = 10

When the commutative property is used, elements in an equation are rearranged. When the associative property is used, elements are merely regrouped.

Regards

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