What is x when 61 divided by x equals 9?

To find the answer, just divide the dividend by the quotient: 61 ÷ 9 = 6.7777777777778

To prove this, let's compute 61 divided by 6.7777777777778: $\frac{61}{6.7777777777778} = 9$

How does it work?

Asking what the value of x could be when 61 divided by x gives a result of 9, is equivalent to solving the following equation:

$\frac{61}{x} = 9$

Multiply both sides by x: $\frac{61 x}{x} = 9 x$
$\frac{61 x}{x}$ is equivalent to $\frac{x}{x} \times 61$ , which simplifies to $1 \times 61$ (or just $61$ ).
Thus, the equation becomes: $61 = 9 x$
To find x, divide both sides by 9: $\frac{61}{9} = \frac{9 x}{9}$
Which gives, after simplification: $6.7777777777778 = x$ (or $x = 6.7777777777778$ )

So, if the dividend is 61 and the quotient is 9, the divisor is 6.7777777777778.