We are asked to find the quotient of [tex]\frac{2}{3}[/tex] divides by [tex]\frac{4}{5}[/tex].
Let us divide [tex]\frac{2}{3}[/tex] by [tex]\frac{4}{5}[/tex] as:
[tex]\frac{2}{3}\div\frac{4}{5}[/tex]
Now we will convert our division problem into multiplication problem by flipping the 2nd fraction as:
[tex]\frac{2}{3}\times\frac{5}{4}[/tex]
Let us cancel out common factors.
[tex]\frac{1}{3}\times\frac{5}{2}[/tex]
[tex]\frac{1\times5}{3\times2}[/tex]
[tex]\frac{5}{6}[/tex]
Therefore, our required quotient is [tex]\frac{5}{6}[/tex].
