Use the given digits so each expression has the greatest possible value. Express the answer as a mixed number in simplest form. (a) \( 4,5,6 \)

To find the greatest possible value using the digits \(4\), \(5\), and \(6\) in an expression, we can consider different operations such as addition, subtraction, multiplication, and division. Let's explore the possible combinations: 1. **Addition**: \[ 4 + 5 + 6 = 15 \] 2. **Multiplication**: \[ 4 \times 5 \times 6 = 120 \] 3. **Division**: - If we divide, we can try different combinations, but generally, division will yield a smaller result compared to multiplication. - For example: \[ \frac{6}{4} + 5 = 1.5 + 5 = 6.5 \] - Other combinations will yield even smaller results. 4. **Mixed Operations**: - We can also try combinations of operations: \[ 6 \times (5 - 4) = 6 \times 1 = 6 \] \[ (6 + 5) \times 4 = 11 \times 4 = 44 \] From the calculations above, the maximum value is obtained through multiplication: \[ 4 \times 5 \times 6 = 120 \] Since the problem asks for the answer as a mixed number in simplest form, we can express \(120\) as: \[ 120 = 120 \frac{0}{1} \] Thus, the final answer is: \[ \boxed{120} \]