Reverse operation

In mathematics, the reverse operation is the rule with which one gets back the other operand for a specific two-digit arithmetic operation from its result and one of the two operands .

In the case of the basic arithmetic operations , the reverse operation of addition is subtraction and the reverse operation of multiplication is division.

For some operations, including multiplication, it is not possible to reverse them with every combination of operands (see below).

Reverse operations can also be viewed as special reverse functions .

Examples

addition

If the sum and the summand are known for the addition , the other summand is obtained by subtracting . So subtraction is the reverse of addition. Since the addition is commutative , if the sum and addend are known, the other addend is also obtained by subtraction, namely . ${\displaystyle c=a+b}$ ${\displaystyle c}$ ${\displaystyle a}$ ${\displaystyle b}$ ${\displaystyle b=c-a}$ ${\displaystyle c}$ ${\displaystyle b}$ ${\displaystyle a}$ ${\displaystyle a=c-b}$

multiplication

If the product and the factor are known for the multiplication , the other factor is obtained by dividing . So division is an inverse operation of multiplication. Since the multiplication is also commutative, if the product and factor are known, the other factor is also obtained by division, namely . ${\displaystyle c=a\cdot b}$ ${\displaystyle c}$ ${\displaystyle a}$ ${\displaystyle b}$ ${\displaystyle b=c/a}$ ${\displaystyle c}$ ${\displaystyle b}$ ${\displaystyle a}$ ${\displaystyle a=c/b}$

However, this method is no longer applicable as soon as one of the two factors and thus also their product becomes zero, since division by zero is fundamentally prohibited.

Potentiate

If the result and the exponent of the power are known, the base is obtained from the root . So the extraction of the root is a reverse operation of the exponentiation, with which the question of the basis used is answered. ${\displaystyle c=b^{a}}$ ${\displaystyle c}$ ${\displaystyle a}$ ${\displaystyle b}$ ${\displaystyle b={\sqrt[{a}]{c}}}$

But if the result and the base are known, the exponent is obtained from the logarithm . So taking the logarithm is another inverse operation of the exponentiation, with which the question about the exponent used is answered. ${\displaystyle c}$ ${\displaystyle b}$ ${\displaystyle a}$ ${\displaystyle a=\log _{b}{c}}$

In contrast to addition and multiplication, exponentiation has two inverse operations because the operation is not commutative.

See also

• Inverse element

literature

• E. Cramer, J. Neslehova: preliminary course in mathematics . 2nd Edition. Springer, Berlin, Heidelberg, New York 2005, ISBN 3-540-26186-9 , pp. 14, 19, 87.