Add Rational Numbers Quick Check

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Question
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 |p| from q in the negative direction.
The sum p plus left parenthesis negative q right parenthesis is the number located a distance Start Absolute Value p End Absolute Value from q in the negative direction.

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 |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 |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.
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Answer 1

To analyze the expression \( p + (-q) \), we can rewrite it as \( p - q \). Since both \( p \) and \( q \) are positive numbers, the result will depend on the relative sizes of \( p \) and \( q \).

1. If \( p > q \), then \( p - q \) will be positive.
2. If \( p < q \), then \( p - q \) will be negative.
3. If \( p = q \), then \( p - q = 0\).

Now, focusing on the interpretation given the options:

• The phrase "located a distance |p| from q in the negative direction" would imply moving left on the number line from \( q \) by the value \( p \), but this does not accurately describe \( p + (-q) \).

• The phrase "located a distance |q| from p in the positive direction" is also inaccurate, as it implies moving right from \( p \) by \( q \), which does not hold for the subtraction.

• The phrase "located a distance |p| from q in the positive direction" is incorrect as it implies that you would be adding \( p \) to \( q \).

• The phrase "located a distance |q| from p in the negative direction" seems more correct because if \( p \) is less than \( q\), \( p + (-q) \) would indeed point towards negative values depending on how far apart they are.

So, the correct answer would likely be:

The sum \( p + (-q) \) is the number located a distance |q| from p in the negative direction.

Answer 2

is that correct

Answer 3

Let's clarify the expression \( p + (-q) \) again.

When we express \( p + (-q) \), it can be simplified to \( p - q \). The behavior of this operation depends on the relative sizes of the two positive numbers \( p \) and \( q \):

1. If \( p > q \):

   • Then \( p - q \) is positive and represents a point that is \( p - q \) units to the right of \( 0 \).

2. If \( p < q \):

   • Then \( p - q \) is negative, and it represents a point that is \( |p - q| \) units to the left of \( 0 \).

3. If \( p = q \):

   • The result would be \( 0 \).

In the context of the answers provided, the correct interpretation of \( p + (-q) \) (or \( p - q \)) is best captured by:

• "The sum \( p + (-q) \) is the number located a distance |q| from p in the negative direction."

This is because:

• When \( q \) is subtracted from \( p \), if \( q > p \), you would end up with a negative result that is as far as \( q \) is from \( p \).
• If you visualize this on a number line, moving \( |q| \) units left from \( p \) would yield \( p - q \).

Thus, yes, that statement is indeed correct, and confirms how the sum \( p + (-q) \) behaves depending on the values of \( p \) and \( q \).