$$(3 \frac{ 1 }{ 2 } \times 5 \frac{ 1 }{ 3 } -10 \frac{ 2 }{ 5 } ) \times (3 \frac{ 1 }{ 8 } -6 \frac{ 1 }{ 2 } +2 \frac{ 1 }{ 6 } )$$
$-\frac{899}{90}\approx -9.988888889$
$$\left(\frac{6+1}{2}\times \frac{5\times 3+1}{3}-\frac{10\times 5+2}{5}\right)\left(\frac{3\times 8+1}{8}-\frac{6\times 2+1}{2}+\frac{2\times 6+1}{6}\right)$$
$$\left(\frac{7}{2}\times \frac{5\times 3+1}{3}-\frac{10\times 5+2}{5}\right)\left(\frac{3\times 8+1}{8}-\frac{6\times 2+1}{2}+\frac{2\times 6+1}{6}\right)$$
$$\left(\frac{7}{2}\times \frac{15+1}{3}-\frac{10\times 5+2}{5}\right)\left(\frac{3\times 8+1}{8}-\frac{6\times 2+1}{2}+\frac{2\times 6+1}{6}\right)$$
$$\left(\frac{7}{2}\times \frac{16}{3}-\frac{10\times 5+2}{5}\right)\left(\frac{3\times 8+1}{8}-\frac{6\times 2+1}{2}+\frac{2\times 6+1}{6}\right)$$
$$\left(\frac{7\times 16}{2\times 3}-\frac{10\times 5+2}{5}\right)\left(\frac{3\times 8+1}{8}-\frac{6\times 2+1}{2}+\frac{2\times 6+1}{6}\right)$$
$$\left(\frac{112}{6}-\frac{10\times 5+2}{5}\right)\left(\frac{3\times 8+1}{8}-\frac{6\times 2+1}{2}+\frac{2\times 6+1}{6}\right)$$
$$\left(\frac{56}{3}-\frac{10\times 5+2}{5}\right)\left(\frac{3\times 8+1}{8}-\frac{6\times 2+1}{2}+\frac{2\times 6+1}{6}\right)$$
$$\left(\frac{56}{3}-\frac{50+2}{5}\right)\left(\frac{3\times 8+1}{8}-\frac{6\times 2+1}{2}+\frac{2\times 6+1}{6}\right)$$
$$\left(\frac{56}{3}-\frac{52}{5}\right)\left(\frac{3\times 8+1}{8}-\frac{6\times 2+1}{2}+\frac{2\times 6+1}{6}\right)$$
$$\left(\frac{280}{15}-\frac{156}{15}\right)\left(\frac{3\times 8+1}{8}-\frac{6\times 2+1}{2}+\frac{2\times 6+1}{6}\right)$$
$$\frac{280-156}{15}\left(\frac{3\times 8+1}{8}-\frac{6\times 2+1}{2}+\frac{2\times 6+1}{6}\right)$$
$$\frac{124}{15}\left(\frac{3\times 8+1}{8}-\frac{6\times 2+1}{2}+\frac{2\times 6+1}{6}\right)$$
$$\frac{124}{15}\left(\frac{24+1}{8}-\frac{6\times 2+1}{2}+\frac{2\times 6+1}{6}\right)$$
$$\frac{124}{15}\left(\frac{25}{8}-\frac{6\times 2+1}{2}+\frac{2\times 6+1}{6}\right)$$
$$\frac{124}{15}\left(\frac{25}{8}-\frac{12+1}{2}+\frac{2\times 6+1}{6}\right)$$
$$\frac{124}{15}\left(\frac{25}{8}-\frac{13}{2}+\frac{2\times 6+1}{6}\right)$$
$$\frac{124}{15}\left(\frac{25}{8}-\frac{52}{8}+\frac{2\times 6+1}{6}\right)$$
$$\frac{124}{15}\left(\frac{25-52}{8}+\frac{2\times 6+1}{6}\right)$$
$$\frac{124}{15}\left(-\frac{27}{8}+\frac{2\times 6+1}{6}\right)$$
$$\frac{124}{15}\left(-\frac{27}{8}+\frac{12+1}{6}\right)$$
$$\frac{124}{15}\left(-\frac{27}{8}+\frac{13}{6}\right)$$
$$\frac{124}{15}\left(-\frac{81}{24}+\frac{52}{24}\right)$$
$$\frac{124}{15}\times \frac{-81+52}{24}$$
$$\frac{124}{15}\left(-\frac{29}{24}\right)$$
$$\frac{124\left(-29\right)}{15\times 24}$$
$$\frac{-3596}{360}$$
$$-\frac{899}{90}$$
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$-\frac{899}{90} = -9\frac{89}{90} = -9.988888888888889$
