$$\frac{ -3 }{ 4 } \times ( \frac{ 2 }{ 3 } + \frac{ -5 }{ 6 } )= \frac{ -3 }{ 4 } \times \frac{ 2 }{ 3 } + \frac{ -3 }{ 4 } \times \frac{ -5 }{ 6 }$$
$\text{true}$
$$-\frac{3}{4}\left(\frac{2}{3}+\frac{-5}{6}\right)=\frac{-3}{4}\times \frac{2}{3}+\frac{-3}{4}\times \frac{-5}{6}$$
$$-\frac{3}{4}\left(\frac{2}{3}-\frac{5}{6}\right)=\frac{-3}{4}\times \frac{2}{3}+\frac{-3}{4}\times \frac{-5}{6}$$
$$-\frac{3}{4}\left(\frac{4}{6}-\frac{5}{6}\right)=\frac{-3}{4}\times \frac{2}{3}+\frac{-3}{4}\times \frac{-5}{6}$$
$$-\frac{3}{4}\times \frac{4-5}{6}=\frac{-3}{4}\times \frac{2}{3}+\frac{-3}{4}\times \frac{-5}{6}$$
$$-\frac{3}{4}\left(-\frac{1}{6}\right)=\frac{-3}{4}\times \frac{2}{3}+\frac{-3}{4}\times \frac{-5}{6}$$
$$\frac{-3\left(-1\right)}{4\times 6}=\frac{-3}{4}\times \frac{2}{3}+\frac{-3}{4}\times \frac{-5}{6}$$
$$\frac{3}{24}=\frac{-3}{4}\times \frac{2}{3}+\frac{-3}{4}\times \frac{-5}{6}$$
$$\frac{1}{8}=\frac{-3}{4}\times \frac{2}{3}+\frac{-3}{4}\times \frac{-5}{6}$$
$$\frac{1}{8}=-\frac{3}{4}\times \frac{2}{3}+\frac{-3}{4}\times \frac{-5}{6}$$
$$\frac{1}{8}=\frac{-3\times 2}{4\times 3}+\frac{-3}{4}\times \frac{-5}{6}$$
$$\frac{1}{8}=\frac{-6}{12}+\frac{-3}{4}\times \frac{-5}{6}$$
$$\frac{1}{8}=-\frac{1}{2}+\frac{-3}{4}\times \frac{-5}{6}$$
$$\frac{1}{8}=-\frac{1}{2}-\frac{3}{4}\times \frac{-5}{6}$$
$$\frac{1}{8}=-\frac{1}{2}-\frac{3}{4}\left(-\frac{5}{6}\right)$$
$$\frac{1}{8}=-\frac{1}{2}+\frac{-3\left(-5\right)}{4\times 6}$$
$$\frac{1}{8}=-\frac{1}{2}+\frac{15}{24}$$
$$\frac{1}{8}=-\frac{1}{2}+\frac{5}{8}$$
$$\frac{1}{8}=-\frac{4}{8}+\frac{5}{8}$$
$$\frac{1}{8}=\frac{-4+5}{8}$$
$$\frac{1}{8}=\frac{1}{8}$$
$$\text{true}$$
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