Evaluate. Write your answer as a fraction in simplest form. \( \frac{3}{8}-\frac{1}{6}+\frac{5}{12} \)

To evaluate the expression \( \frac{3}{8}-\frac{1}{6}+\frac{5}{12} \), we first need to find a common denominator for the fractions involved. The denominators are 8, 6, and 12. The least common multiple (LCM) of these numbers is 24. Now we can convert each fraction: 1. Convert \( \frac{3}{8} \) to twenty-fourths: \( \frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24} \) 2. Convert \( \frac{1}{6} \) to twenty-fourths: \( \frac{1}{6} = \frac{1 \times 4}{6 \times 4} = \frac{4}{24} \) 3. Convert \( \frac{5}{12} \) to twenty-fourths: \( \frac{5}{12} = \frac{5 \times 2}{12 \times 2} = \frac{10}{24} \) Now, substitute these back into the expression: \[ \frac{9}{24} - \frac{4}{24} + \frac{10}{24} \] Simplifying this: First, perform the subtraction: \[ \frac{9}{24} - \frac{4}{24} = \frac{5}{24} \] Then, add the \( \frac{10}{24} \): \[ \frac{5}{24} + \frac{10}{24} = \frac{15}{24} \] Next, we simplify \( \frac{15}{24} \). The greatest common divisor of 15 and 24 is 3, so we divide both the numerator and denominator by 3: \[ \frac{15 \div 3}{24 \div 3} = \frac{5}{8} \] Thus, the answer in simplest form is: \[ \boxed{\frac{5}{8}} \]