$$11 \frac { 2 } { 3 } \div 9 \frac { 3 } { 8 } \times 5 \frac { 3 } { 5 } = ?$$
$\frac{1568}{225}\approx 6.968888889$
$$\frac{\left(11\times 3+2\right)\times 8}{3\left(9\times 8+3\right)}\times \frac{5\times 5+3}{5}$$
$$\frac{\left(33+2\right)\times 8}{3\left(9\times 8+3\right)}\times \frac{5\times 5+3}{5}$$
$$\frac{35\times 8}{3\left(9\times 8+3\right)}\times \frac{5\times 5+3}{5}$$
$$\frac{280}{3\left(9\times 8+3\right)}\times \frac{5\times 5+3}{5}$$
$$\frac{280}{3\left(72+3\right)}\times \frac{5\times 5+3}{5}$$
$$\frac{280}{3\times 75}\times \frac{5\times 5+3}{5}$$
$$\frac{280}{225}\times \frac{5\times 5+3}{5}$$
$$\frac{56}{45}\times \frac{5\times 5+3}{5}$$
$$\frac{56}{45}\times \frac{25+3}{5}$$
$$\frac{56}{45}\times \frac{28}{5}$$
$$\frac{56\times 28}{45\times 5}$$
$$\frac{1568}{225}$$
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$\frac{2 ^ {5} \cdot 7 ^ {2}}{3 ^ {2} \cdot 5 ^ {2}} = 6\frac{218}{225} = 6.9688888888888885$
