$$6 \frac { 9 } { 14 } 7 \frac { 1 } { 6 } 5 \frac { 1 } { 21 }$$
$\frac{70649}{294}\approx 240.302721088$
$$\frac{84+9}{14}\times \frac{7\times 6+1}{6}\times \frac{5\times 21+1}{21}$$
$$\frac{93}{14}\times \frac{7\times 6+1}{6}\times \frac{5\times 21+1}{21}$$
$$\frac{93}{14}\times \frac{42+1}{6}\times \frac{5\times 21+1}{21}$$
$$\frac{93}{14}\times \frac{43}{6}\times \frac{5\times 21+1}{21}$$
$$\frac{93\times 43}{14\times 6}\times \frac{5\times 21+1}{21}$$
$$\frac{3999}{84}\times \frac{5\times 21+1}{21}$$
$$\frac{1333}{28}\times \frac{5\times 21+1}{21}$$
$$\frac{1333}{28}\times \frac{105+1}{21}$$
$$\frac{1333}{28}\times \frac{106}{21}$$
$$\frac{1333\times 106}{28\times 21}$$
$$\frac{141298}{588}$$
$$\frac{70649}{294}$$
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$\frac{31 \cdot 43 \cdot 53}{2 \cdot 3 \cdot 7 ^ {2}} = 240\frac{89}{294} = 240.30272108843536$
