we first off convert the mixed fractions to improper fractions, and then do the division,
[tex] \bf \stackrel{mixed}{2\frac{3}{4}}\implies \cfrac{2\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{11}{4}}
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\stackrel{mixed}{4\frac{1}{2}}\implies \cfrac{4\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{9}{2}}\\\\
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\cfrac{11}{4}\div \cfrac{9}{2}\implies \cfrac{11}{4}\cdot \cfrac{2}{9}\implies \cfrac{22}{36}\implies \stackrel{simplified}{\cfrac{11}{18}} [/tex]
