What is x when 81 divided by x equals 9?

To find the answer, just divide the dividend by the quotient: 81 ÷ 9 = 9

To prove this, let's compute 81 divided by 9: $\frac{81}{9} = 9$

How does it work?

Asking what the value of x could be when 81 divided by x gives a result of 9, is equivalent to solving the following equation:

$\frac{81}{x} = 9$

Multiply both sides by x: $\frac{81 x}{x} = 9 x$
$\frac{81 x}{x}$ is equivalent to $\frac{x}{x} \times 81$ , which simplifies to $1 \times 81$ (or just $81$ ).
Thus, the equation becomes: $81 = 9 x$
To find x, divide both sides by 9: $\frac{81}{9} = \frac{9 x}{9}$
Which gives, after simplification: $9 = x$ (or $x = 9$ )

So, if the dividend is 81 and the quotient is 9, the divisor is 9.