Question : Simplify the following expression.
$\frac{7}{10} \div \frac{3}{7}$ of $\left(2 \frac{3}{10}+2 \frac{3}{5}\right)+\frac{1}{5} \div 1 \frac{2}{5}-\frac{2}{7}$
Option 1: $-\frac{4}{21}$
Option 2: $\frac{5}{21}$
Option 3: $\frac{4}{21}$
Option 4: $-\frac{5}{21}$
Correct Answer: $\frac{4}{21}$
Solution :
$\frac{7}{10} \div \frac{3}{7}$ of $\left(2 \frac{3}{10}+2 \frac{3}{5}\right)+\frac{1}{5} \div 1 \frac{2}{5}-\frac{2}{7}$
Converting mixed fractions to fractions,
= $\frac{7}{10} \div \frac{3}{7}$ of $\left(\frac{23}{10}+\frac{13}{5}\right)+\frac{1}{5} \div \frac{7}{5}-\frac{2}{7}$
Applying BODMAS, we get
= $\frac{7}{10} \div \frac{3}{7}\ $ of $ (\frac{49}{10})+\frac{1}{5} \div \frac{7}{5}-\frac{2}{7}$
= $\frac{7}{10} \div (\frac{21}{10})+\frac{1}{7}-\frac{2}{7}$
= $\frac{1}{3}-\frac{1}{7}$
= $\frac{4}{21}$
Hence, the correct answer is $\frac{4}{21}$.
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