Answer:
Jaime is correct, -1 x n is always equal to n ÷ (-1) for all values of n.
- To see why this is true, we can use the properties of multiplication and division of real numbers. In particular, we can use the fact that multiplying by -1 is the same as changing the sign of a number and dividing by -1 is the same as multiplying by -1.
- So, starting with -1 x n, we can rewrite this expression as (-1) x n or -(1 x n), which means we are taking the opposite of the product of -1 and n. Since the opposite of a number is just that number with its sign changed, we can simplify this expression to -n.
- Next, let's consider n ÷ (-1). This means we are dividing n by -1, which is the same as multiplying n by the reciprocal of -1, which is -1/1 or simply -1. So, n ÷ (-1) is equal to n x (-1), which is just -n.
Thus, we can see that -1 x n and n ÷ (-1) both simplify to -n. Therefore, Jaime is correct, the value of -1 x n is always equal to the value of n ÷ (-1) for all values of n.