$$2\frac{1}{3}\times3\frac{2}{5}\div1\frac{3}{7}$$
$\frac{833}{150}\approx 5.553333333$
$$\frac{\frac{6+1}{3}\times \frac{3\times 5+2}{5}}{\frac{1\times 7+3}{7}}$$
$$\frac{\frac{7}{3}\times \frac{3\times 5+2}{5}}{\frac{1\times 7+3}{7}}$$
$$\frac{\frac{7}{3}\times \frac{15+2}{5}}{\frac{1\times 7+3}{7}}$$
$$\frac{\frac{7}{3}\times \frac{17}{5}}{\frac{1\times 7+3}{7}}$$
$$\frac{\frac{7\times 17}{3\times 5}}{\frac{1\times 7+3}{7}}$$
$$\frac{\frac{119}{15}}{\frac{1\times 7+3}{7}}$$
$$\frac{\frac{119}{15}}{\frac{7+3}{7}}$$
$$\frac{\frac{119}{15}}{\frac{10}{7}}$$
$$\frac{119}{15}\times \frac{7}{10}$$
$$\frac{119\times 7}{15\times 10}$$
$$\frac{833}{150}$$
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$\frac{7 ^ {2} \cdot 17}{2 \cdot 3 \cdot 5 ^ {2}} = 5\frac{83}{150} = 5.553333333333334$
