When multiplying two rational numbers, how is the sign of the product determined?(1 point)
Responses
The product is positive if the signs of the factors are the same.
The product is positive if the signs of the factors are the same.
The product is negative if the signs of the factors are the same.
The product is negative if the signs of the factors are the same.
The sign of the product is always the same as the larger factor.
The sign of the product is always the same as the larger factor.
The sign of the product is always the same as the smaller factor.
The sign of the product is always the same as the smaller factor.
The product is positive if the signs of the factors are the same.
The product is positive if the signs of the factors are the same.
The correct response is:
The product is positive if the signs of the factors are the same.
To understand why, we can examine the rules of multiplying signed numbers. The product of two positive numbers is always positive, so if both factors are positive, the product will be positive as well. Similarly, the product of two negative numbers is also positive.
On the other hand, if the signs of the factors are different, meaning one is positive and the other is negative, the product will be negative. This is because multiplying a positive number by a negative number gives a negative result.
To summarize, when multiplying two rational numbers, if the signs of the factors are the same, the product will be positive. If the signs of the factors are different, the product will be negative.