To find the sum of the two numbers when their product is given and one of the numbers is known, we can use the following steps:

1. Identify the given information:

   • Product of the two numbers: $311.25$
   • One of the numbers: $12.5$

2. Let the unknown number be $x$.

3. Set up the equation: $12.5 \times x = 311.25$

4. Solve for $x$: $x = \frac{311.25}{12.5}$

5. Perform the division: $x = \frac{311.25}{12.5} = 24.9$

6. Find the sum of the two numbers: $\text{Sum} = 12.5 + 24.9$

7. Calculate the sum: $\text{Sum} = 37.4$

Thus, the sum of the two numbers is $37.4$.

Do you want more details or have any questions?

Here are some related questions you might find interesting:

1. What is the process for solving quadratic equations?
2. How do you find the greatest common divisor (GCD) of two numbers?
3. Can you explain the concept of prime factorization?
4. How do you calculate the least common multiple (LCM) of two numbers?
5. What is the difference between rational and irrational numbers?
6. How do you simplify fractions?
7. What are the properties of real numbers?
8. How do you solve linear equations with one variable?

Tip: Always double-check your calculations to ensure accuracy, especially when dealing with decimals and fractions.