1¾ of 5½ is simply the product of both, so, let's firstly change the mixed fractions to "improper", and then get the product.
[tex]\bf \stackrel{mixed}{1\frac{3}{4}}\implies \cfrac{1\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{7}{4}}
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\stackrel{mixed}{150\frac{1}{2}}\implies \cfrac{150\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{301}{2}}\\\\
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\cfrac{7}{4}\cdot \cfrac{301}{2}\implies \cfrac{2107}{8}\implies 263\frac{3}{8}[/tex]
