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The problem presented asks for two numbers that multiply to give 48 (the top number) and add to give 14 (the bottom number).

We need to find two numbers that satisfy these conditions:

1. **Product = 48**
2. **Sum = 14**

Let's break it down:

- Factors of 48: (1, 48), (2, 24), (3, 16), (4, 12), (6, 8)
- From these factor pairs, we check which ones add up to 14:
  - \( 6 + 8 = 14 \)

Thus, the two numbers are **6** and **8**.

### Answer:
The two numbers are **6** and **8**.

Would you like further details on how these types of problems are solved? Here are five related questions to expand on this topic:

1. What happens if no two factors satisfy both conditions of addition and multiplication?
2. Can you solve this type of problem when the product or sum involves negative numbers?
3. How would you solve this problem if the numbers were decimals or fractions?
4. What mathematical techniques can help solve quadratic equations that involve similar conditions?
5. How can this problem be extended to systems of equations in algebra?

**Tip:** When solving problems with sums and products, listing the factor pairs systematically makes it easier to check each pair against the given sum.

What adds to be the bottom number but also multiplies to be the top? (48 and 14)

Learn how to solve a sum and product problem where two numbers multiply to 48 and add to 14. This algebraic problem involves key concepts like factoring and systematic problem-solving, suitable for students in Grades 6-8.

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