Question

It took 12 gallons of gas to fill the tank of the family car. This is five sixths of the amount the tank can hold. How much gas does the tank hold?

Answer 1

We know 12 gallons is 5/6, so there was some in the car already, the whole tank will be 6/6 or one whole.

if 12 is 5/6, how much is 6/6, or the whole thing?

$\bf \begin{array}{ccll} gallons&tan\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 12&\frac{5}{6}\\\\ g&\frac{6}{6} \end{array}\implies \cfrac{12}{g}=\cfrac{\quad \frac{5}{6}\quad }{\frac{6}{6}}\implies \cfrac{12}{g}=\cfrac{5}{6}\cdot \cfrac{6}{6}\implies \cfrac{12}{g}=\cfrac{5}{6} \\\\\\ 72=5g\implies \cfrac{72}{5}=g\implies 14\frac{2}{5}=g$