What is x when 97 divided by x equals 11?

To find the answer, just divide the dividend by the quotient: 97 ÷ 11 = 8.8181818181818

To prove this, let's compute 97 divided by 8.8181818181818: $\frac{97}{8.8181818181818} = 11$

How does it work?

Asking what the value of x could be when 97 divided by x gives a result of 11, is equivalent to solving the following equation:

$\frac{97}{x} = 11$

Multiply both sides by x: $\frac{97 x}{x} = 11 x$
$\frac{97 x}{x}$ is equivalent to $\frac{x}{x} \times 97$ , which simplifies to $1 \times 97$ (or just $97$ ).
Thus, the equation becomes: $97 = 11 x$
To find x, divide both sides by 11: $\frac{97}{11} = \frac{11 x}{11}$
Which gives, after simplification: $8.8181818181818 = x$ (or $x = 8.8181818181818$ )

So, if the dividend is 97 and the quotient is 11, the divisor is 8.8181818181818.