What is the result of \(\frac{2}{3} \div \frac{4}{5}\)?

Step 1 ：Firstly, convert the division operation into multiplication by finding the reciprocal of the second fraction. The reciprocal of \(\frac{4}{5}\) is \(\frac{5}{4}\). So, the operation becomes \(\frac{2}{3} \times \frac{5}{4}\).

Step 2 ：Then, multiply the numerators together to get the new numerator and the denominators together to get the new denominator. \(2 \times 5\) gives the new numerator 10, and \(3 \times 4\) gives the new denominator 12. The result is \(\frac{10}{12}\).

Step 3 ：Finally, simplify the fraction \(\frac{10}{12}\) to its lowest terms. Both 10 and 12 can be divided by 2. So, the simplest form of the fraction is \(\frac{5}{6}\).