To analyze the expression \( p + (-q) \), we first recognize that subtracting a positive number \( q \) from \( p \) gives us \( p - q \).
Here's how we can interpret this mathematically:
- Since both \( p \) and \( q \) are positive numbers, the expression \( p - q \) will yield different results depending on the relative sizes of \( p \) and \( q \).
- If \( p > q \), \( p - q \) is positive.
- If \( p < q \), \( p - q \) is negative.
Given that we want to describe \( p + (-q) \) or \( p - q \) in terms of its location on the number line:
- \( p - q \) is the number that is \( |q| \) units to the left of \( p \) if \( p > q \) or \( |p| \) units to the right of \( q \) if \( p < q \).
However, since \( p \) and \( q \) are both positive, we can succinctly describe the nature of \( p + (-q) \):
The correct description is that “the sum \( p + (-q) \) is the number located a distance \( |q| \) from \( p \) in the negative direction.” This reflects that when you subtract \( q \), you move left on the number line starting from \( p \).
So the correct response is: The sum \( p + (-q) \) is the number located a distance \(|q|\) from \( p \) in the negative direction.