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An inverse operation "reverses" another operation. Addition and subtraction are inverses of each other because adding and subtracting the same number does not change the original number. For example, 7 - 6 + 6 = 7 and 13 + 11 - 11 = 13.

Similarly, multiplication and division are inverses of each other because multiplying and dividing by the same number does not change the original number. For example, 11×5/5 = 11 and 6/2×2 = 6. Dividing by 2 and multiplying by 2 cancel each other out, and so 6 does not change.

Inverse Operations and the Commutative Property

Because addition and subtraction commute, two numbers need not be next to each other to cancel each other out. Observe the following example:

43 + 5 - 43 = 5

Be careful, however. Addition and subtraction do not commute if there is a multiplication or division sign between the two numbers being moved.

Because multiplication and division also commute, two numbers need not be next to each other to cancel each other out. For example:

6×4×5/4 = 6×5×4/4 = 30×4/4 = 30.

One must be careful here, too. Multiplication and division do not commute if there is an addition or subtraction sign between the two numbers being moved.

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