What is x when 100 divided by x equals 9?

To find the answer, just divide the dividend by the quotient: 100 ÷ 9 = 11.111111111111

To prove this, let's compute 100 divided by 11.111111111111: $\frac{100}{11.111111111111} = 9$

How does it work?

Asking what the value of x could be when 100 divided by x gives a result of 9, is equivalent to solving the following equation:

$\frac{100}{x} = 9$

Multiply both sides by x: $\frac{100 x}{x} = 9 x$
$\frac{100 x}{x}$ is equivalent to $\frac{x}{x} \times 100$ , which simplifies to $1 \times 100$ (or just $100$ ).
Thus, the equation becomes: $100 = 9 x$
To find x, divide both sides by 9: $\frac{100}{9} = \frac{9 x}{9}$
Which gives, after simplification: $11.111111111111 = x$ (or $x = 11.111111111111$ )

So, if the dividend is 100 and the quotient is 9, the divisor is 11.111111111111.