Question

The value of \(\frac{2}{5} \div \frac{3}{{10}}\) of \(\frac{4}{9} - \frac{4}{5} \times 1\frac{1}{9} \div \frac{8}{{15}} - \frac{3}{4} + \frac{3}{4} \div \frac{1}{2}\) is:
1. \(\frac{7}{9}\)
2. \(\frac{23}{6}\)
3. \(\frac{4}{3}\)
4. \(\frac{25}{12}\)

Answer 1

Correct Answer - Option 4 : \(\frac{25}{12}\)

Concept:

Use BODMAS rule.

Calculation:

∵  \(\frac{2}{5} \div \frac{3}{{10}}\) of \(\frac{4}{9} - \frac{4}{5} \times 1\frac{1}{9} \div \frac{8}{{15}} - \frac{3}{4} + \frac{3}{4} \div \frac{1}{2}\)

= \(\frac{2}{5} \div (\frac{3}{{10}} \times \frac{4}{{9}} )\) \( - (\frac{4}{5} \times \frac{10}{9} \times \frac{15}{{8}}) - \frac{3}{4} + \frac{3}{4} \times{2}\) 

= \((\frac{2}{5} \div \frac{2}{{15}})\) \( - \frac{5}{3} - \frac{3}{4} + \frac{3}{2}\)

= \((\frac{2}{5} \times \frac{15}{{2}})\) \( - \frac{5}{3} - \frac{3}{4} + \frac{3}{2}\)

= 3 \( - \frac{5}{3} - \frac{3}{4} + \frac{3}{2}\)

= (36 -20 -9 +18)/12

= 25/12