$$\frac{1}{5}\times[\frac{2}{7}+\frac{3}{8}]=\frac{1}{5}\times\frac{2}{7}+\frac{}{}$$
$\text{false}$
$$\frac{1}{5}\left(\frac{2}{7}+\frac{3}{8}\right)=\frac{1}{5}\times \frac{2}{7}+1$$
$$\frac{1}{5}\left(\frac{16}{56}+\frac{21}{56}\right)=\frac{1}{5}\times \frac{2}{7}+1$$
$$\frac{1}{5}\times \frac{16+21}{56}=\frac{1}{5}\times \frac{2}{7}+1$$
$$\frac{1}{5}\times \frac{37}{56}=\frac{1}{5}\times \frac{2}{7}+1$$
$$\frac{1\times 37}{5\times 56}=\frac{1}{5}\times \frac{2}{7}+1$$
$$\frac{37}{280}=\frac{1}{5}\times \frac{2}{7}+1$$
$$\frac{37}{280}=\frac{1\times 2}{5\times 7}+1$$
$$\frac{37}{280}=\frac{2}{35}+1$$
$$\frac{37}{280}=\frac{2}{35}+\frac{35}{35}$$
$$\frac{37}{280}=\frac{2+35}{35}$$
$$\frac{37}{280}=\frac{37}{35}$$
$$\frac{37}{280}=\frac{296}{280}$$
$$\text{false}$$
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