$$3 \frac { 1 } { 2 } + 4 \frac { 1 } { 3 } =$$
$\frac{47}{6}\approx 7.833333333$
$$\frac{6+1}{2}+\frac{4\times 3+1}{3}$$
$$\frac{7}{2}+\frac{4\times 3+1}{3}$$
$$\frac{7}{2}+\frac{12+1}{3}$$
$$\frac{7}{2}+\frac{13}{3}$$
$$\frac{21}{6}+\frac{26}{6}$$
$$\frac{21+26}{6}$$
$$\frac{47}{6}$$
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$\frac{47}{2 \cdot 3} = 7\frac{5}{6} = 7.833333333333333$
