Evaluate the expression \( a+b \) when \( a=\frac{2}{3} \) and \( b=\frac{4}{5} \). Write in simplest form.

To evaluate the expression \( a+b \) when \( a=\frac{2}{3} \) and \( b=\frac{4}{5} \), we first need to find a common denominator for the two fractions. The denominators are 3 and 5, and the least common multiple of these two numbers is 15. Now, we will convert each fraction to have a denominator of 15: 1. For \( a = \frac{2}{3} \): \[ a = \frac{2 \times 5}{3 \times 5} = \frac{10}{15} \] 2. For \( b = \frac{4}{5} \): \[ b = \frac{4 \times 3}{5 \times 3} = \frac{12}{15} \] Now, we can add the two fractions: \[ a + b = \frac{10}{15} + \frac{12}{15} = \frac{10 + 12}{15} = \frac{22}{15} \] The fraction \( \frac{22}{15} \) is already in simplest form. Thus, the final answer is: \[ \frac{22}{15} \]