$$(\frac{-3}{2}\times\frac{4}{5})+(\frac{9}{5}\times\frac{-10}{3})-(\frac{1}{2}\times\frac{3}{4}$$
$-\frac{303}{40}=-7.575$
$$-\frac{3}{2}\times \frac{4}{5}+\frac{9}{5}\times \frac{-10}{3}-\frac{1}{2}\times \frac{3}{4}$$
$$\frac{-3\times 4}{2\times 5}+\frac{9}{5}\times \frac{-10}{3}-\frac{1}{2}\times \frac{3}{4}$$
$$\frac{-12}{10}+\frac{9}{5}\times \frac{-10}{3}-\frac{1}{2}\times \frac{3}{4}$$
$$-\frac{6}{5}+\frac{9}{5}\times \frac{-10}{3}-\frac{1}{2}\times \frac{3}{4}$$
$$-\frac{6}{5}+\frac{9}{5}\left(-\frac{10}{3}\right)-\frac{1}{2}\times \frac{3}{4}$$
$$-\frac{6}{5}+\frac{9\left(-10\right)}{5\times 3}-\frac{1}{2}\times \frac{3}{4}$$
$$-\frac{6}{5}+\frac{-90}{15}-\frac{1}{2}\times \frac{3}{4}$$
$$-\frac{6}{5}-6-\frac{1}{2}\times \frac{3}{4}$$
$$-\frac{6}{5}-\frac{30}{5}-\frac{1}{2}\times \frac{3}{4}$$
$$\frac{-6-30}{5}-\frac{1}{2}\times \frac{3}{4}$$
$$-\frac{36}{5}-\frac{1}{2}\times \frac{3}{4}$$
$$-\frac{36}{5}-\frac{1\times 3}{2\times 4}$$
$$-\frac{36}{5}-\frac{3}{8}$$
$$-\frac{288}{40}-\frac{15}{40}$$
$$\frac{-288-15}{40}$$
$$-\frac{303}{40}$$
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$-\frac{303}{40} = -7\frac{23}{40} = -7.575$
