1. The problem is to simplify the expression $7 \frac{5}{12}$.\n2. This is a mixed number, which means it consists of a whole number and a fraction.\n3. To work with it more easily, convert the mixed number to an improper fraction using the formula: \n$$\text{Improper fraction} = \frac{\text{whole number} \times \text{denominator} + \text{numerator}}{\text{denominator}}$$\n4. Substitute the values: \n$$\frac{7 \times 12 + 5}{12} = \frac{84 + 5}{12} = \frac{89}{12}$$\n5. The improper fraction $\frac{89}{12}$ is the simplified form of the mixed number $7 \frac{5}{12}$.\n6. This fraction cannot be simplified further because 89 is a prime number and does not share any common factors with 12.\n7. Therefore, the final answer is $\frac{89}{12}$.