When multiplying two rational numbers, how is the sign of the product determined?
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 determined by the rule that states: the product is positive if the signs of the factors are the same, and the product is negative if the signs of the factors are different.
The correct answer is:
The product is positive if the signs of the factors are the same.
The product is negative if the signs of the factors are different.
To determine the sign of the product when multiplying two rational numbers, you need to consider two factors: the signs of the numbers you are multiplying.
1. If both factors have the same sign (either both positive or both negative), then the product will be positive. For example:
- Multiplying +3/4 and +2/3: (+3/4) * (+2/3) = +6/12 = +1/2.
2. If the signs of the factors are different (one is positive and the other is negative), then the product will be negative. For example:
- Multiplying -5/6 and +4/5: (-5/6) * (+4/5) = -20/30 = -2/3.
It is important to note that the sign of the product is not always the same as the larger factor. The sign depends solely on whether the factors have the same sign or different signs.
In summary, the sign of the product when multiplying two rational numbers is positive if the signs of the factors are the same, and negative if the signs of the factors are different.