Simplify: \(\left\{\frac{16}{36} \div \frac{16}{4}\right\} \div \left(\frac{2}{7} \times \frac{14}{6} + \frac{5}{12}\right) + \frac{4}{7} \div \frac{39}{12} \text{ of } \frac{12}{7}\)
\(\frac{8}{39}\)
Apply BODMAS, resolving of before division. First bracket: \(\frac{16}{36} \div \frac{16}{4} = \frac{16}{36} \times \frac{4}{16} = \frac{4}{36} = \frac{1}{9}\).
Second bracket: \(\frac{2}{7} \times \frac{14}{6} + \frac{5}{12} = \frac{2}{3} + \frac{5}{12} = \frac{8}{12} + \frac{5}{12} = \frac{13}{12}\).
Resolve the of term: \(\frac{39}{12} \text{ of } \frac{12}{7} = \frac{39}{12} \times \frac{12}{7} = \frac{39}{7}\), so \(\frac{4}{7} \div \frac{39}{7} = \frac{4}{7} \times \frac{7}{39} = \frac{4}{39}\).
Now the first division: \(\frac{1}{9} \div \frac{13}{12} = \frac{1}{9} \times \frac{12}{13} = \frac{12}{117} = \frac{4}{39}\).
Add: \(\frac{4}{39} + \frac{4}{39} = \frac{8}{39}\).
Hence, the value of the expression is \(\frac{8}{39}\).
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