What is x when 82 divided by x equals 9?

How does it work?

Asking what the value of x could be when 82 divided by x gives a result of 9, is equivalent to solving the following equation:

$\frac{82}{x}=9$

1. Multiply both sides by x: $\frac{82x}{x}=9x$
2. $\frac{82x}{x}$ is equivalent to $\frac{x}{x}\times 82$, which simplifies to $1\times 82$ (or just $82$).
3. Thus, the equation becomes: $82=9x$
4. To find x, divide both sides by 9: $\frac{82}{9}=\frac{9x}{9}$
5. Which gives, after simplification: $9.1111111111111=x$ (or $x=9.1111111111111$)

So, if the dividend is 82 and the quotient is 9, the divisor is 9.1111111111111.