Question

Which statements are true about the rules of multiplication for signed numbers? Check all that apply. The product of two negative integers is positive. The product of two integers with different signs is positive. If two numbers are the same sign, then the product is positive. The product of a positive and a negative is negative. If the signs of two integers are different, then the product is positive.

Answer 1

The product of two negative integers is positive=True

If two numbers are the same sign, then the product is positive=False

The product of a positive and a negative is negative=True

If the signs of two integers are different, the the product is positive=False

Explanation:

The reason A and C are true is because of the rules of integers.

Two numbers with the same sign = positive product

Two numbers with different signs = negative product

This is how I learned it at my school, anyway. Hope this answers your question.

Answer 2

A, C, D

Explanation:

As important rules of thumb that you should remember:

- the product of 2 negatives ALWAYS makes a positive

- the product of 2 positives ALWAYS makes a positive

- the product of 1 positive and 1 negative ALWAYS makes a negative

Now, look at the answer choices:

- "The product of two negative integers is positive" this is true

- "The product of two integers with different signs is positive" this is essentially saying that the product of a positive integer with a negative integer is positive, which is false

- "If two numbers are the same sign, then the product is positive" this is true, as can be seen by the first two bullet points at the beginning

- "The product of a positive and a negative is negative" this is true

- "If the signs of two integers are different, then the product is positive" this is false because of the third statement above

The answers are A, C, and D.