Which of the following describes the sum p + (−q) where p
and q
are positive numbers??(1 point)
Responses
The sum p+(−q) is the number located a distance |q| from p in the positive direction.
The sum p plus left parenthesis negative q right parenthesis is the number located a distance Start Absolute Value q End Absolute Value from p in the positive direction.
The sum p+(−q) is the number located a distance |q| from p in the negative direction.
The sum p plus left parenthesis negative q right parenthesis is the number located a distance Start Absolute Value q End Absolute Value from p in the negative direction.
The sum p+(−q) is the number located a distance |p| from q in the positive direction.
The sum negative p plus left parenthesis negative q right parenthesis is the number located a distance absolute value of p from q in the positive direction.
The sum p+(−q) is the number located a distance |p| from q in the negative direction.
The sum p + (-q) is the number located a distance |q| from p in the negative direction.
The correct response is: "The sum p+(−q) is the number located a distance |q| from p in the positive direction."
To understand why this is the correct answer, let's break it down step by step:
1. The term "p + (−q)" represents adding "p" and the additive inverse of "q" (which is −q).
2. The additive inverse of a positive number is its negative counterpart. So, the additive inverse of "q" is −q.
3. When we add "p" and −q, we are essentially moving a distance of −q in the negative direction from "p".
4. However, since both "p" and "q" are positive numbers, we ignore the negative sign and take the absolute value of −q, which is |q|.
5. Therefore, the sum "p + (−q)" is the number located a distance |q| from "p" in the positive direction.
Remember, to determine whether the answer is positive or negative, consider the signs of the numbers being added or subtracted. Since "p" and "q" are both positive, the distance (represented by |q|) will always be positive.