# How do you find the unknown value of 32divy=4?

Apr 2, 2018

$\frac{32}{y} \left(\frac{y}{32}\right) = 4 \left(\frac{y}{32}\right)$
$1 = \frac{y}{8}$
$8 \left(1\right) = 8 \left(\frac{y}{8}\right)$
$y = 8$

#### Explanation:

Multiply the 32/y fraction by its reciprocal, to obtain 1, which removes y from the denominator. In order to not affect the equality, you must also multiply the other side - the 4, by the reciprocal of the 32/y fraction.
On the left, we now have 1, and, on the right, the 4 cancels a 4 out of the 32 on the denominator, leaving us with a denominator of 8.
To clear the denominator 8 on the right, multiply both sides of the equation by 8, this leaves us with the solution, y equals 8.