[tex]\displaystyle\sf~1 \frac{1}{3} \times \frac{1}{2} \div \frac{3}{5} = \frac{4}{3} \times \frac{1}{2} \div \frac{3}{5} \\ \\ \displaystyle\sf~ = \frac{4}{6} \div \frac{3}{5} \\ \\ \displaystyle\sf~ = \frac{4}{6} \times \frac{5}{3} \\ \\ \displaystyle\sf~ = \frac{20}{18} \\ \\ \displaystyle\sf~ = \frac{10}{9} \\ \\ \displaystyle\sf~ = 1 \frac{1}{9} [/tex]
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[tex]\displaystyle\sf~1 \frac{1}{3} \times \frac{1}{2} \div \frac{3}{5} = \frac{4}{3} \times \frac{1}{2} \div \frac{3}{5} \\ \\ \displaystyle\sf~ = \frac{4}{6} \div \frac{3}{5} \\ \\ \displaystyle\sf~ = \frac{4}{6} \times \frac{5}{3} \\ \\ \displaystyle\sf~ = \frac{20}{18} \\ \\ \displaystyle\sf~ = \frac{10}{9} \\ \\ \displaystyle\sf~ = 1 \frac{1}{9} [/tex]