Question

Which numerical expression equals - 1?

A)- 1(1-1)
B)- (- 1)(-1)
C) (-1) + 1-1 (-1)
D) -(-1)-(- 1)(-1)

Answer 1

Option B, which is - (- 1)(-1), is the numerical expression that equals -1. This is because the double negative becomes positive, and then positive 1 multiplied by negative 1 equals -1. Based on these calculations, the numerical expression that equals -1 is option B) - (- 1)(-1).

Step-by-step explanation:

To find out which numerical expression equals -1, we need to evaluate each option provided.

1. A) - 1(1-1) simplifies to -1(0) because 1-1 equals 0. Multiplying -1 by 0 gives us 0, not -1. So, option A does not equal -1.
2. B) - (- 1)(-1) simplifies to +1(-1) because the double negative cancels out making it positive. Then, multiplying +1 by -1 gives us -1. Therefore, option B equals -1.
3. For C) (-1) + 1 -1 (-1), we combine like terms to find that (-1)+1 equals 0, and -1(-1) equals +1 when we apply the multiplication rules for negative numbers. Adding 0 to +1 gives us +1, not -1, so option C does not equal -1.
4. Looking at D) -(-1)-(- 1)(-1), we resolve the subtractions by converting them into addition of the opposite number: +1 - 1, as -(-1) becomes +1 and -(-1)(-1) converts to -(-1) which is +1, then becomes -1. Adding +1 to -1 gives 0, which is still not -1. Consequently, option D does not equal -1.

Based on these calculations, the numerical expression that equals -1 is option B) - (- 1)(-1).