To understand the expression \( p + (-q) \), we can rewrite it as \( p - q \). Here, since \( p \) and \( q \) are both positive numbers, the quantity \( p - q \) will depend on the relative sizes of \( p \) and \( q \).
- If \( p > q \), then \( p - q \) is positive.
- If \( p < q \), then \( p - q \) is negative.
- If \( p = q \), then \( p - q = 0 \).
For positive \( p \) and \( q \), \( p + (-q) \) or \( p - q \) describes the distance from \( q \) in the positive or negative direction depending on the values of \( p \) and \( q \).
The correct response among those you provided is:
The sum \( p + (-q) \) is the number located a distance |q| from p in the negative direction.
This is because \( p + (-q) \) essentially means you are subtracting \( q \) from \( p \), which implies moving back (negative direction) from \( p \) by the value of \( q\).
2 answers