$$34\frac{1}{2}+\frac{2}{3}=$$
$\frac{211}{6}\approx 35.166666667$
$$\frac{68+1}{2}+\frac{2}{3}$$
$$\frac{69}{2}+\frac{2}{3}$$
$$\frac{207}{6}+\frac{4}{6}$$
$$\frac{207+4}{6}$$
$$\frac{211}{6}$$
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$\frac{211}{2 \cdot 3} = 35\frac{1}{6} = 35.166666666666664$