# How do you solve (10h)/108=5/9?

Dec 26, 2016

$\frac{10}{108} h = \frac{5}{9}$

Multiply each side by the reciprocal of the coefficient of h. The coefficient of h is $\frac{10}{108}$, so the reciprocal is $\frac{108}{10}$

$h = \left(\frac{5}{9}\right) \cdot \left(\frac{108}{10}\right)$

$h = \left(\frac{1}{1}\right) \cdot \left(\frac{12}{2}\right)$

$h = 6$

Dec 26, 2016

$h = 6$

#### Explanation:

$\frac{10 h}{108} = \frac{5}{9} \text{ } \leftarrow$ isolate $h$ by $\times \frac{108}{10}$ on both sides

$\frac{108}{10} \times \frac{10 h}{108} = \frac{108}{10} \times \frac{5}{9}$

$h = {\cancel{108}}^{12} / {\cancel{10}}^{2} \times \frac{\cancel{5}}{\cancel{9}}$

$h = 6$

Notice that cancelling first avoids ending up with

$h = \frac{540}{90}$