Question

Simplify:

\[\left( \frac{2}{3} + \frac{4}{9} \right) \text{ of }\frac{3}{5} \div 1\frac{2}{3} \times 1\frac{1}{4} - \frac{1}{3}\]

Answer 1

Given expression:
\[= \left( \frac{2}{3} + \frac{4}{9} \right)\text{ of  }\frac{3}{5} \div 1\frac{2}{3} \times 1\frac{1}{4} - \frac{1}{3} \]
\[ = \left( \frac{6 + 4}{9} \right)\text{ of }\frac{3}{5} \div 1\frac{2}{3} \times 1\frac{1}{4} - \frac{1}{3} \left(\text{ Removing parentheses}\right)\]
\[ = \frac{10}{9} \times \frac{3}{5} \div 1\frac{2}{3} \times 1\frac{1}{4} - \frac{1}{3} \left(\text{Removing 'of ' }\right)\]
\[ = \frac{2}{3} \div \frac{5}{3} \times 1\frac{1}{4} - \frac{1}{3} \]
\[ = \frac{2}{3} \times \frac{3}{5} \times \frac{5}{4} - \frac{1}{3} (\text{Removing }'\div ' )\]
\[ = \frac{2}{5} \times \frac{5}{4} - \frac{1}{3} \]
\[ = \frac{1}{2} - \frac{1}{3} (\text{Removing }' \times ' )\]
\[ = \frac{\left( 3 - 2 \right)}{6} = \frac{1}{6}\]