# How do you determine whether the proportion is true or false: (3/2)/(21/5)=(1/3)/(14/15)?

Nov 22, 2016

The proportion is true. Both sides are equal to $\frac{5}{14}$.

#### Explanation:

$\frac{\frac{3}{2}}{\frac{21}{5}} = \frac{\frac{1}{3}}{\frac{14}{15}}$

There are 2 fractions on each side. Make it so that there is only one fraction on each side by dividing. Dividing is the same as multiplying by the reciprocal.

Left Side:
$\frac{\frac{3}{2}}{\frac{21}{5}}$
$= \left(\frac{3}{2}\right) \cdot \left(\frac{5}{21}\right)$
$= \left(\frac{5}{14}\right) \cdot \left(\frac{3}{3}\right)$
$= \frac{5}{14}$

Right Side:
$\frac{\frac{1}{3}}{\frac{14}{15}}$
$= \left(\frac{1}{3}\right) \cdot \left(\frac{15}{14}\right)$
$= \frac{5}{14} \cdot \frac{3}{3}$
$= \frac{5}{14}$