When is the opposite of the opposite of a number the same as the original number?(1 point)
Responses
when the original number is negative
when the original number is negative
never
never
when the original number is positive
when the original number is positive
always
never
The correct response is: never
The opposite of a number can be found by changing its sign. For example, the opposite of -5 is 5, and the opposite of 3 is -3.
To find the opposite of the opposite of a number, we need to find the opposite of the opposite. This means we need to change the sign of the opposite number.
Let's consider the cases:
- When the original number is negative (-): In this case, the opposite of the original number is positive (+), and the opposite of a positive number is negative. So, the opposite of the opposite of a negative number (+(-n)) is -(-n) = n, which is the same as the original number. Therefore, the statement is true when the original number is negative.
- When the original number is positive (+): In this case, the opposite of the original number is negative (-), and the opposite of a negative number is positive. So, the opposite of the opposite of a positive number (-(+n)) is +(-n) = -n, which is not the same as the original number. Therefore, the statement is false when the original number is positive.
Thus, the correct answer is: when the original number is negative.