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 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 answer is: "The product is positive if the signs of the factors are the same."
To determine the sign of the product when multiplying two rational numbers, you need to consider the signs of the factors. If both factors have the same sign, either both positive or both negative, then the product will be positive.
For example:
- If you multiply two positive rational numbers, like (3/4) * (2/5), both factors are positive and the product will be positive: (3/4) * (2/5) = 6/20 = 3/10.
- If you multiply two negative rational numbers, like (-2/3) * (-4/7), both factors are negative and the product will also be positive: (-2/3) * (-4/7) = 8/21.
However, if the signs of the factors are different, one positive and one negative, then the product will be negative.
For example:
- If you multiply a positive rational number and a negative rational number, like (5/6) * (-3/8), the factors have different signs and the product will be negative: (5/6) * (-3/8) = -15/48 = -5/16.