first off, let's convert the mixed fraction to "improper", and divide from there,
[tex]\bf \stackrel{mixed}{10\frac{5}{8}}\implies \cfrac{10\cdot 8+5}{8}\implies \stackrel{improper}{\cfrac{85}{8}}
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\cfrac{85}{8}\div 2\implies \cfrac{85}{8}\div \cfrac{2}{1}\implies \cfrac{85}{8}\cdot \cfrac{1}{2}\implies \cfrac{85}{16}\implies 5\frac{5}{16}[/tex]
