$$\frac{23}{4}+5\frac{1}{2}$$
$\frac{45}{4}=11.25$
$$\frac{23}{4}+\frac{10+1}{2}$$
$$\frac{23}{4}+\frac{11}{2}$$
$$\frac{23}{4}+\frac{22}{4}$$
$$\frac{23+22}{4}$$
$$\frac{45}{4}$$
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$\frac{3 ^ {2} \cdot 5}{2 ^ {2}} = 11\frac{1}{4} = 11.25$