Answer:
The quotient of the given expression is;
[tex]3\frac{2}{3}\div3\frac{4}{5}=\frac{55}{57}[/tex]
Explanation:
Given the expression;
[tex]3\frac{2}{3}\div3\frac{4}{5}[/tex]
To solve, let us convert the mixed fraction to improper fraction.
[tex]\begin{gathered} 3\frac{2}{3}\div3\frac{4}{5} \\ \frac{3(3)+2}{3}\div\frac{5(3)+4}{5} \\ \frac{11}{3}\div\frac{19}{5} \end{gathered}[/tex]
Then we can now divide the fractions to get the quotient;
[tex]\begin{gathered} \frac{11}{3}\div\frac{19}{5} \\ \frac{11}{3}\times\frac{5}{19} \\ \frac{11\times5}{3\times19} \\ =\frac{55}{57} \end{gathered}[/tex]
Therefore, the quotient of the given expression is;
[tex]3\frac{2}{3}\div3\frac{4}{5}=\frac{55}{57}[/tex]
