Question

Solve the equation: \frac{2}{3}t=\frac{5}{9} (hint: reciprocal)

Answer 1

Given:

$\frac{2}{3}t=\frac{5}{9}$$\text{ We know that the reciprocal of }\frac{2}{3}\text{ is }\frac{3}{2}\text{.}$

Multiply both sides by 3/2, we get

$\frac{3}{2}\times\frac{2}{3}t=\frac{3}{2}\times\frac{5}{9}$

Cancel out the common multiples, we get

$t=\frac{1}{2}\times\frac{5}{3}$

$t=\frac{1\times5}{2\times3}$

$t=\frac{5}{6}$

The solution of the given equation is

$t=\frac{5}{6}$

or

$t=0.8333.$