$$6\frac{3}{2}+\frac{2}{7}$$
$\frac{109}{14}\approx 7.785714286$
$$\frac{12+3}{2}+\frac{2}{7}$$
$$\frac{15}{2}+\frac{2}{7}$$
$$\frac{105}{14}+\frac{4}{14}$$
$$\frac{105+4}{14}$$
$$\frac{109}{14}$$
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$\frac{109}{2 \cdot 7} = 7\frac{11}{14} = 7.785714285714286$