(i) . (2frac (1)/(4)-1(3)/(5))(3)

To solve the expression \(\frac{2\frac{1}{4} - 1\frac{3}{5}}{3}\), follow these steps:<br /><br />1. Convert the mixed numbers to improper fractions:<br /> - \(2\frac{1}{4} = \frac{9}{4}\)<br /> - \(1\frac{3}{5} = \frac{8}{5}\)<br /><br />2. Subtract the improper fractions:<br /> - Find a common denominator for \(\frac{9}{4}\) and \(\frac{8}{5}\). The least common multiple of 4 and 5 is 20.<br /> - Convert \(\frac{9}{4}\) to \(\frac{45}{20}\) and \(\frac{8}{5}\) to \(\frac{32}{20}\).<br /> - Subtract the fractions: \(\frac{45}{20} - \frac{32}{20} = \frac{13}{20}\).<br /><br />3. Divide the result by 3:<br /> - \(\frac{\frac{13}{20}}{3} = \frac{13}{20} \times \frac{1}{3} = \frac{13}{60}\).<br /><br />So, the final answer is \(\frac{13}{60}\).