What is x when 61 divided by x equals 7?

To find the answer, just divide the dividend by the quotient: 61 ÷ 7 = 8.7142857142857

To prove this, let's compute 61 divided by 8.7142857142857: $\frac{61}{8.7142857142857} = 7$

How does it work?

Asking what the value of x could be when 61 divided by x gives a result of 7, is equivalent to solving the following equation:

$\frac{61}{x} = 7$

Multiply both sides by x: $\frac{61 x}{x} = 7 x$
$\frac{61 x}{x}$ is equivalent to $\frac{x}{x} \times 61$ , which simplifies to $1 \times 61$ (or just $61$ ).
Thus, the equation becomes: $61 = 7 x$
To find x, divide both sides by 7: $\frac{61}{7} = \frac{7 x}{7}$
Which gives, after simplification: $8.7142857142857 = x$ (or $x = 8.7142857142857$ )

So, if the dividend is 61 and the quotient is 7, the divisor is 8.7142857142857.