[tex]\[\begin{array}{l}1.)\frac{1}{2} \div \frac{2}{5}\\\\ = \frac{1}{2}(\frac{5}{2})\\\\ = \frac{5}{4}\end{array}\][/tex]
[tex]\[\begin{array}{l}2.)5 \div \frac{1}{3}\\\\ = 5(\frac{3}{1})\\\\ = 15\end{array}\][/tex]
[tex]\[\begin{array}{l}3.)\frac{3}{5} \div 4\\\\ = \frac{3}{5}(\frac{1}{4})\\\\ = \frac{3}{{20}}\end{array}\][/tex]
[tex]\[\begin{array}{l}4.)\frac{9}{{10}} \div \frac{1}{2}\\\\ = \frac{9}{{10}}(\frac{2}{1})\\\\ = \frac{{18}}{{10}}\\\\ = \frac{9}{5}\end{array}\][/tex]
[tex]\[\begin{array}{l}5.)\frac{3}{4} \div \frac{2}{5}\\\\ = \frac{3}{4}(\frac{5}{2})\\\\ = \frac{{15}}{8}\end{array}\][/tex]
[tex]\[\begin{array}{l}6.)\frac{1}{5} \div \frac{2}{6}\\\\ = \frac{1}{5}(\frac{6}{2})\\\\ = \frac{6}{{10}}\\\\ = \frac{3}{5}\end{array}\][/tex]
[tex]\[\begin{array}{l}7.)\frac{1}{4} \div \frac{3}{{10}}\\\\ = \frac{1}{4}(\frac{{10}}{3})\\\\ = \frac{{10}}{{12}}\\\\ = \frac{5}{6}\end{array}\][/tex]
[tex]\[\begin{array}{l}8.)\frac{1}{2} \div \frac{2}{3}\\\\ = \frac{1}{2}(\frac{3}{2})\\\\ = \frac{3}{4}\end{array}\][/tex]
[tex]\[\begin{array}{l}9.)\frac{8}{9} \div 4\\\\ = \frac{8}{9}(\frac{1}{4})\\\\ = \frac{8}{{36}}\\\\ = \frac{2}{9}\end{array}\][/tex]
[tex]\[\begin{array}{l}10.)\frac{{31}}{5} \div \frac{2}{3}\\\\ = \frac{{31}}{5}(\frac{3}{2})\\\\ = \frac{{93}}{{10}}\end{array}\][/tex]
[tex]\[\begin{array}{l}11.)\frac{5}{6} \div \frac{1}{4}\\\\ = \frac{5}{6}(\frac{4}{1})\\\\ = \frac{{20}}{6}\\\\ = \frac{{10}}{3}\end{array}\][/tex]
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