What is x when 27 divided by x equals 40?

To find the answer, just divide the dividend by the quotient: 27 ÷ 40 = 0.675

To prove this, let's compute 27 divided by 0.675: $\frac{27}{0.675} = 40$

How does it work?

Asking what the value of x could be when 27 divided by x gives a result of 40, is equivalent to solving the following equation:

$\frac{27}{x} = 40$

Multiply both sides by x: $\frac{27 x}{x} = 40 x$
$\frac{27 x}{x}$ is equivalent to $\frac{x}{x} \times 27$ , which simplifies to $1 \times 27$ (or just $27$ ).
Thus, the equation becomes: $27 = 40 x$
To find x, divide both sides by 40: $\frac{27}{40} = \frac{40 x}{40}$
Which gives, after simplification: $0.675 = x$ (or $x = 0.675$ )

So, if the dividend is 27 and the quotient is 40, the divisor is 0.675.