The question in the image asks:

"Which conjecture, if any, could you make about the product of an odd integer and an even integer?"

The options are:

• a. The product will be an even integer.
• b. The product will be an odd integer.
• c. The product will be negative.
• d. It is not possible to make a conjecture.

Correct Answer:

The correct conjecture is a. The product will be an even integer.

Explanation:

1. Odd integer: An odd number can be expressed as $2k + 1$, where $k$ is an integer.
2. Even integer: An even number can be expressed as $2m$, where $m$ is an integer.
3. Product of odd and even: $(2k + 1) \cdot 2m = 4km + 2m$, which is always divisible by 2, making it an even number.

Would you like further clarification or additional examples?

Related Questions:

1. What is the result of multiplying two even integers?
2. What is the result of multiplying two odd integers?
3. Is the sum of an odd and an even integer odd or even?
4. How can you prove the distributive property with odd and even numbers?
5. What is the general form of odd and even integers?

Tip:

When working with odd and even integers, always focus on their divisibility by 2 to classify results.