The Product is Always Positive

Oct 13, 2025 by recoveryshake.com 15 views

When it comes to the multiplication of negative and positive integers, there are several statements that can be made. However, only one of these statements is true. In this article, we will explore each of these statements and determine which one is correct.

The Product is 0

The first statement claims that the product of a negative integer and a positive integer is 0. However, this is not always the case. When you multiply a negative integer by a positive integer, the result is not always 0. For example, if you multiply -3 by 4, the result is -12, not 0.

The Product is Always Positive

The second statement claims that the product of a negative integer and a positive integer is always positive. However, this is also not true. When you multiply a negative integer by a positive integer, the result is not always positive. As mentioned earlier, if you multiply -3 by 4, the result is -12, which is a negative number.

The Product is Always Negative

The third statement claims that the product of a negative integer and a positive integer is always negative. This statement is actually true. When you multiply a negative integer by a positive integer, the result is always a negative number. This is because the negative sign of the negative integer is multiplied by the positive integer, resulting in a negative number.

The Product Can Be Positive or Negative Depending on the Number

The fourth statement claims that the product of a negative integer and a positive integer can be positive or negative depending on the number. However, this is not true. As mentioned earlier, when you multiply a negative integer by a positive integer, the result is always a negative number.

Why is the Product Always Negative?

So, why is the product of a negative integer and a positive integer always negative? The reason for this is that the negative sign of the negative integer is multiplied by the positive integer, resulting in a negative number. This is a fundamental property of multiplication and is true for all integers.

Examples of Multiplying Negative and Positive Integers

To illustrate this concept, let's look at some examples of multiplying negative and positive integers.

-3 x 4 = -12
-5 x 2 = -10
-2 x 3 = -6
-1 x 6 = -6

As you can see, in each of these examples, the product of the negative integer and the positive integer is a negative number.

Conclusion

In conclusion, the statement that is true when a negative integer is multiplied by a positive integer is that the product is always negative. This is because the negative sign of the negative integer is multiplied by the positive integer, resulting in a negative number. This is a fundamental property of multiplication and is true for all integers.

Frequently Asked Questions

Q: Is the product of a negative integer and a positive integer always negative? A: Yes, the product of a negative integer and a positive integer is always negative.
Q: Why is the product of a negative integer and a positive integer always negative? A: The negative sign of the negative integer is multiplied by the positive integer, resulting in a negative number.
Q: Can the product of a negative integer and a positive integer be positive or negative? A: No, the product of a negative integer and a positive integer is always negative.

References

[1] Khan Academy. (n.d.). Multiplying Negative Numbers. Retrieved from <https://www.khanacademy.org/math/algebra/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c
Frequently Asked Questions: Multiplying Negative and Positive Integers ====================================================================

In this article, we will answer some of the most frequently asked questions about multiplying negative and positive integers.

Q: Is the product of a negative integer and a positive integer always negative?

A: Yes, the product of a negative integer and a positive integer is always negative. This is because the negative sign of the negative integer is multiplied by the positive integer, resulting in a negative number.

Q: Why is the product of a negative integer and a positive integer always negative?

A: The product of a negative integer and a positive integer is always negative because the negative sign of the negative integer is multiplied by the positive integer. This results in a negative number.

Q: Can the product of a negative integer and a positive integer be positive or negative?

A: No, the product of a negative integer and a positive integer is always negative. It cannot be positive or negative.

Q: What happens when you multiply a negative integer by a negative integer?

A: When you multiply a negative integer by a negative integer, the result is a positive number. This is because the two negative signs cancel each other out, resulting in a positive number.

Q: What happens when you multiply a positive integer by a positive integer?

A: When you multiply a positive integer by a positive integer, the result is a positive number. This is because the two positive signs multiply together, resulting in a positive number.

Q: Can you give me some examples of multiplying negative and positive integers?

A: Here are some examples of multiplying negative and positive integers:

-3 x 4 = -12
-5 x 2 = -10
-2 x 3 = -6
-1 x 6 = -6
3 x 4 = 12
5 x 2 = 10
2 x 3 = 6
1 x 6 = 6

Q: How do you know when to multiply a negative integer by a positive integer?

A: You know when to multiply a negative integer by a positive integer when you see a negative sign next to a positive number. For example, -3 x 4 is a negative integer multiplied by a positive integer.

Q: How do you know when to multiply a positive integer by a negative integer?

A: You know when to multiply a positive integer by a negative integer when you see a positive sign next to a negative number. For example, 3 x -4 is a positive integer multiplied by a negative integer.

Q: Can you give me some tips for multiplying negative and positive integers?

A: Here are some tips for multiplying negative and positive integers:

When multiplying a negative integer by a positive integer, the result is always negative.
When multiplying a positive integer by a negative integer, the result is always negative.
When multiplying two negative integers, the result is always positive.
When multiplying two positive integers, the result is always positive.
Make sure to follow the order of operations (PEMDAS) when multiplying negative and positive integers.

Q: What are some common mistakes to avoid when multiplying negative and positive integers?

A: Here are some common mistakes to avoid when multiplying negative and positive integers:

Not following the order of operations (PEMDAS)
Not paying attention to the signs of the numbers
Not multiplying the numbers correctly
Not checking the result to make sure it is correct

Conclusion

In conclusion, multiplying negative and positive integers can be a bit tricky, but with practice and patience, you can become a pro at it. Remember to follow the order of operations (PEMDAS), pay attention to the signs of the numbers, and multiply the numbers correctly. With these tips and tricks, you'll be able to multiply negative and positive integers like a pro in no time.

References

[1] Khan Academy. (n.d.). Multiplying Negative Numbers. Retrieved from <https://www.khanacademy.org/math/algebra/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c0/x2f4f7c