When multiplying two rational numbers, how is the sign of the product determined?
1. The product is positive if the signs of the factors are the same.
2. The product is negative if the signs of the factors are the same.
3. The sign of the product is always the same as the larger factor.
4. The sign of the product is always the same as the smaller factor.
1. The product is positive if the signs of the factors are the same.
1. 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. Here's how to do it:
1. If the signs of the factors are the same (both positive or both negative), then the product is positive. For example, if you multiply 3/4 by 2/3, both factors are positive, so the product is positive.
2. If the signs of the factors are different (one is positive and the other is negative), then the product is negative. For example, if you multiply 5/6 by -4/5, one factor is positive and the other is negative, so the product is negative.
3. The sign of the product is not determined by the larger factor. So, option 3 is incorrect. For example, if you multiply -1/2 by 8/9, the larger factor is positive but the product is negative.
4. Similarly, the sign of the product is not determined by the smaller factor either. So, option 4 is also incorrect. For example, if you multiply -1/2 by 2/3, the smaller factor is negative but the product is positive.
Therefore, the correct answer is option 2: "The product is negative if the signs of the factors are the same."