$$3\frac{1}{2}+\frac{1}{6}+3\frac{3}{4}=$$
$\frac{89}{12}\approx 7.416666667$
$$\frac{6+1}{2}+\frac{1}{6}+\frac{3\times 4+3}{4}$$
$$\frac{7}{2}+\frac{1}{6}+\frac{3\times 4+3}{4}$$
$$\frac{21}{6}+\frac{1}{6}+\frac{3\times 4+3}{4}$$
$$\frac{21+1}{6}+\frac{3\times 4+3}{4}$$
$$\frac{22}{6}+\frac{3\times 4+3}{4}$$
$$\frac{11}{3}+\frac{3\times 4+3}{4}$$
$$\frac{11}{3}+\frac{12+3}{4}$$
$$\frac{11}{3}+\frac{15}{4}$$
$$\frac{44}{12}+\frac{45}{12}$$
$$\frac{44+45}{12}$$
$$\frac{89}{12}$$
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$\frac{89}{2 ^ {2} \cdot 3} = 7\frac{5}{12} = 7.416666666666667$
