WHEN MULTIPLYING TWO RATIONAL NUMBERS HOW IS THE SIGN OF THE PRODUCT DETERMINED
A. THE PRODUCT IS PSITIVE IF THE SIGN OF THE FACTORS ARE THE SAME
B. THE PRODUCT IS NEGATIVE IF THE SIGN OF THE FACTORS ARE THE SAME
C. THE SIGN OF THE PRODUCT IS ALWAYS THE SAME AS THE LARGER FACTOR
D. THE SIGN OF THE PRODUCT IS ALWAYS THE SAME AS THE SMALLER FACTOR
A. THE PRODUCT IS POSITIVE IF THE SIGN OF THE FACTORS ARE THE SAME
The sign of the product of two rational numbers is determined as follows:
A. The product is positive if the signs of the factors are the same.
For example:
- If both factors are positive (e.g., 3/5 * 2/7), the product is positive.
- If both factors are negative (e.g., -3/5 * -2/7), the product is positive.
B. The product is negative if the signs of the factors are different.
For example:
- If one factor is positive and the other is negative (e.g., 3/5 * -2/7), the product is negative.
- If one factor is negative and the other is positive (e.g., -3/5 * 2/7), the product is negative.
Therefore, for option A, the product is positive if the sign of the factors are the same.
When multiplying two rational numbers, the sign of the product is determined by the signs of the factors according to the following rules:
A. The product is positive if the signs of the factors are the same. In other words, if both factors are either positive or negative, the product will be positive. For example, multiplying (+2) and (+3) will result in a positive product (+6), as both factors are positive.
B. The product is negative if the signs of the factors are different. In other words, if one factor is positive and the other is negative, the product will be negative. For example, multiplying (+2) and (-3) will result in a negative product (-6), as one factor is positive and the other is negative.
C. The sign of the product is always the same as the larger factor. If one factor is greater in absolute value than the other, the product will retain the sign of the larger factor. For example, multiplying (+2) and (-3) will still result in a negative product (-6), even though the sign of the smaller factor is positive.
D. The sign of the product is always the same as the smaller factor. If one factor is smaller in absolute value than the other, the product will take the sign of the smaller factor. For example, multiplying (-2) and (+3) will result in a negative product (-6), even though the sign of the larger factor is positive.
Therefore, the correct answer to the question "When multiplying two rational numbers, how is the sign of the product determined?" is A. The product is positive if the sign of the factors are the same.