$$4\frac{1}{2}+1\frac{5}{7}$$
$\frac{87}{14}\approx 6.214285714$
$$\frac{8+1}{2}+\frac{1\times 7+5}{7}$$
$$\frac{9}{2}+\frac{1\times 7+5}{7}$$
$$\frac{9}{2}+\frac{7+5}{7}$$
$$\frac{9}{2}+\frac{12}{7}$$
$$\frac{63}{14}+\frac{24}{14}$$
$$\frac{63+24}{14}$$
$$\frac{87}{14}$$
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$\frac{3 \cdot 29}{2 \cdot 7} = 6\frac{3}{14} = 6.214285714285714$
