[tex]\boxed{\dfrac{a}{b}\div\dfrac{c}{d}=\dfrac{a}{b}\cdot\dfrac{d}{c}}\\\\10\dfrac{1}{2}\div3\dfrac{1}{5}\\\\\text{convert mixed numbers to an improper fractions}\\\\10\dfrac{1}{2}=\dfrac{10\cdot2+1}{2}=\dfrac{21}{2}\\\\3\dfrac{1}{5}=\dfrac{3\cdot5+1}{5}=\dfrac{16}{5}\\\\10\dfrac{1}{2}\div3\dfrac{1}{5}=\dfrac{21}{2}\div\dfrac{16}{5}=\dfrac{21}{2}\cdot\dfrac{5}{16}=\dfrac{21\cdot5}{2\cdot16}=\dfrac{105}{32}=3\dfrac{9}{32}\to\boxed{B}[/tex]
