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The problem asks how the product in a multiplication problem changes when one of the factors is doubled. To answer this, let's look at what happens mathematically when we double one of the factors in a multiplication problem:

### Conclusion:
When one of the factors in a multiplication problem is doubled, the product is also doubled. This is because multiplication is commutative and associative, so if we have two factors \( a \times b \) and we double \( a \) (making it \( 2a \)), the new product becomes \( 2a \times b \), which is the same as \( 2 \times (a \times b) \).

### Examples:
1. **Example 1:**
   \[
   \text{Original: } 3 \times 4 = 12
   \]
   If we double the first factor:
   \[
   \text{New: } (2 \times 3) \times 4 = 6 \times 4 = 24
   \]
   The product has doubled from 12 to 24.

2. **Example 2:**
   \[
   \text{Original: } 5 \times 7 = 35
   \]
   If we double the second factor:
   \[
   5 \times (2 \times 7) = 5 \times 14 = 70
   \]
   The product has doubled from 35 to 70.

This shows that the product of the multiplication problem doubles when one of the factors is doubled.

Do you want more details or have any questions?

### Related Questions:
1. What happens if we triple one of the factors in a multiplication problem?
2. How would the product change if both factors are doubled?
3. Can you explain why the product changes in terms of the distributive property?
4. What if we halve one of the factors? How does the product change?
5. How does this principle apply to more complex expressions, such as polynomials?

### Tip:
Remember that multiplication is a scaling operation. Doubling one of the factors means scaling the original product by 2.

How does the product change when one of the factors in a multiplication problem is doubled? Give two examples to support your conclusion.

Understand how the product changes when one factor in a multiplication problem is doubled, with two examples to support this conclusion. Key concepts include the commutative and associative properties of multiplication. Ideal for students in Grades 4-6.

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