An inverse operation are two operations, each of which "undoes" the other. In mathematics, the term inverse can generally be thought of as some kind of negation. The term inverse comes from the latin inversus which means "turned upside down" or "overturned."

One of the first types of inverses that students typically encounter involve the basic arithmetic operations: addition, subtraction, multiplication, and division.

Addition and subtraction

Addition and subtraction are inverses in that the sign is reversed between operations.


4 + 3 = 7
7 - 3 = 4

As can be seen, adding 3 to 4 and then subtracting 3 from the sum leaves us where we started, with 4. The figure below depicts this relationship.

Multiplication and division

The inverse operation of multiplication is division, where in either case, reciprocating results in the other operation.


6 × 5 = 30
30 ÷ 5 = 6

As shown above, multiplication and division essentially cancel each other out, which is why they are inverse operations; the product of a multiplication problem can be divided by one of its factors, and the result would be the other factor.

The concept of inverses is used in far more than just the basic arithmetic operations. You will encounter different types of inverses throughout your study of mathematics.