$$\frac{3}{4}\times(\frac{4}{5}+\frac{2}{3})=\frac{3}{4}\times\frac{4}{5}+\frac{3}{4}\times\frac{2}{3}$$
$\text{true}$
$$\frac{3}{4}\left(\frac{12}{15}+\frac{10}{15}\right)=\frac{3}{4}\times \frac{4}{5}+\frac{3}{4}\times \frac{2}{3}$$
$$\frac{3}{4}\times \frac{12+10}{15}=\frac{3}{4}\times \frac{4}{5}+\frac{3}{4}\times \frac{2}{3}$$
$$\frac{3}{4}\times \frac{22}{15}=\frac{3}{4}\times \frac{4}{5}+\frac{3}{4}\times \frac{2}{3}$$
$$\frac{3\times 22}{4\times 15}=\frac{3}{4}\times \frac{4}{5}+\frac{3}{4}\times \frac{2}{3}$$
$$\frac{66}{60}=\frac{3}{4}\times \frac{4}{5}+\frac{3}{4}\times \frac{2}{3}$$
$$\frac{11}{10}=\frac{3}{4}\times \frac{4}{5}+\frac{3}{4}\times \frac{2}{3}$$
$$\frac{11}{10}=\frac{3\times 4}{4\times 5}+\frac{3}{4}\times \frac{2}{3}$$
$$\frac{11}{10}=\frac{3}{5}+\frac{3}{4}\times \frac{2}{3}$$
$$\frac{11}{10}=\frac{3}{5}+\frac{3\times 2}{4\times 3}$$
$$\frac{11}{10}=\frac{3}{5}+\frac{2}{4}$$
$$\frac{11}{10}=\frac{3}{5}+\frac{1}{2}$$
$$\frac{11}{10}=\frac{6}{10}+\frac{5}{10}$$
$$\frac{11}{10}=\frac{6+5}{10}$$
$$\frac{11}{10}=\frac{11}{10}$$
$$\text{true}$$
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