What is x when 65 divided by x equals 10?

To find the answer, just divide the dividend by the quotient: 65 ÷ 10 = 6.5

To prove this, let's compute 65 divided by 6.5: $\frac{65}{6.5} = 10$

How does it work?

Asking what the value of x could be when 65 divided by x gives a result of 10, is equivalent to solving the following equation:

$\frac{65}{x} = 10$

Multiply both sides by x: $\frac{65 x}{x} = 10 x$
$\frac{65 x}{x}$ is equivalent to $\frac{x}{x} \times 65$ , which simplifies to $1 \times 65$ (or just $65$ ).
Thus, the equation becomes: $65 = 10 x$
To find x, divide both sides by 10: $\frac{65}{10} = \frac{10 x}{10}$
Which gives, after simplification: $6.5 = x$ (or $x = 6.5$ )

So, if the dividend is 65 and the quotient is 10, the divisor is 6.5.