Solve for n 1/(3/(5/12))=3/(5/n)

Multiply the numerator by the reciprocal of the denominator.

Combine ${\displaystyle 3}$ and ${\displaystyle \frac{n}{5}}$.

Multiply the numerator by the reciprocal of the denominator.

Multiply ${\displaystyle \frac{\frac{5}{12}}{3}}$ by ${\displaystyle 1}$.

Multiply the numerator by the reciprocal of the denominator.

Multiply ${\displaystyle \frac{5}{12}\cdot \frac{1}{3}}$.

Multiply each term by a factor of ${\displaystyle 1}$ that will equate all the denominators. In this case, all terms need a denominator of ${\displaystyle 180}$. The ${\displaystyle \frac{3n}{5}}$ expression needs to be multiplied by ${\displaystyle \frac{36}{36}}$ to make the denominator ${\displaystyle 180}$. The ${\displaystyle \frac{5}{36}}$ expression needs to be multiplied by ${\displaystyle \frac{5}{5}}$ to make the denominator ${\displaystyle 180}$.

Multiply the expression by a factor of ${\displaystyle 1}$ to create the least common denominator (LCD) of ${\displaystyle 180}$.

Multiply ${\displaystyle 36}$ by ${\displaystyle 3}$.

Multiply the expression by a factor of ${\displaystyle 1}$ to create the least common denominator (LCD) of ${\displaystyle 180}$.

Multiply ${\displaystyle 5}$ by ${\displaystyle 5}$.

Divide each term in ${\displaystyle 108n=25}$ by ${\displaystyle 108}$.

Cancel the common factor of ${\displaystyle 108}$.