$$4\frac{4}{4}-9\frac{6}{9}+6\frac{9}{8}$$
$\frac{59}{24}\approx 2.458333333$
$$\frac{16+4}{4}-\frac{9\times 9+6}{9}+\frac{6\times 8+9}{8}$$
$$\frac{20}{4}-\frac{9\times 9+6}{9}+\frac{6\times 8+9}{8}$$
$$5-\frac{9\times 9+6}{9}+\frac{6\times 8+9}{8}$$
$$5-\frac{81+6}{9}+\frac{6\times 8+9}{8}$$
$$5-\frac{87}{9}+\frac{6\times 8+9}{8}$$
$$5-\frac{29}{3}+\frac{6\times 8+9}{8}$$
$$\frac{15}{3}-\frac{29}{3}+\frac{6\times 8+9}{8}$$
$$\frac{15-29}{3}+\frac{6\times 8+9}{8}$$
$$-\frac{14}{3}+\frac{6\times 8+9}{8}$$
$$-\frac{14}{3}+\frac{48+9}{8}$$
$$-\frac{14}{3}+\frac{57}{8}$$
$$-\frac{112}{24}+\frac{171}{24}$$
$$\frac{-112+171}{24}$$
$$\frac{59}{24}$$
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$\frac{59}{2 ^ {3} \cdot 3} = 2\frac{11}{24} = 2.4583333333333335$
