Simple Algebraic Equations Question 8

What value of $t$ is the solution to the equation below? $$ \frac{3}{4}t=\frac{5}{3} $$

$\dfrac{5}{4}$

$\dfrac{20}{9}$

$9$

$20$

Approach 1

Rewrite the fraction and cross multiply.

$$ \frac{3}{4}t=\frac{5}{3} $$ $$ \frac{3t}{4}\xcancel{=}\frac{5}{3} $$ $$ 3t(3)=4(5) $$ $$ 9t=20 $$ $$ \boxed{t=\frac{20}{9}} $$

Approach 2

Multiply both sides by the reciprocal of the $t$ coefficient. (Same as dividing each side by the coefficient)

$$ \frac{3}{4}t=\frac{5}{3} $$ $$ \left(\frac{4}{3}\right)\frac{3}{4}t=\frac{5}{3}\left(\frac{4}{3}\right) $$ $$ \left( \frac{\cancel{4}}{\bcancel{3}}\right)\frac{\bcancel{3}}{\cancel{4}}t=\frac{5}{3}\left(\frac{4}{3}\right) $$ $$ t=\frac{5\cdot4}{3\cdot3}$$ $$ \boxed{t=\frac{20}{9}} $$