Describe p + q as the number located a distance |q❘ from p in the positive or negative direction on the number line

Question

depending on whether q is a
positive or negative rational
number.
Make it look like a 7th grader wrote it

Find the sum of p and q if p and q
==
Reduce your answer to lowest terms.
Answer: -2

Answer 1

Alright, let's break it down in a way a 7th grader would understand!

So, imagine you have a number line, which is like a straight path where numbers are placed in order. When we talk about \( p + q \), we're trying to find a new spot on the number line starting from the number \( p \).

1. Understanding \( p \): Let's say \( p \) is a number on this line. It could be anything like 3, -1, 0, or even fractions.

2. Understanding \( q \): Now, \( q \) is another number, which can be either positive (like 2) or negative (like -3).

3. Moving from \( p \):

   • If \( q \) is positive, we move to the right from \( p \).
   • If \( q \) is negative, we move to the left from \( p \).

So, \( p + q \) is just the new location you end up at after moving \( |q| \) (which is the distance of \( q \) without considering if it's negative) from \( p \) in the correct direction (right for positive, left for negative).

Example:

If \( p = 3 \) and \( q = 2 \), then \( 3 + 2 = 5 \). You start at 3 and move 2 steps to the right to get to 5.

If \( p = 3 \) and \( q = -2 \), then \( 3 + (-2) = 1 \). You start at 3 and move 2 steps to the left to get to 1.

Problem Part:

Now, you mentioned finding the sum of \( p \) and \( q \) and that the answer is -2. We don’t know what \( p \) and \( q \) are exactly, but we can check if they work out.

Let’s say \( p = -1 \) and \( q = -1 \):

• \( -1 + (-1) = -2 \)

So that works! The answer is -2, which is already in its lowest terms.

Overall, finding \( p + q \) is like starting at \( p \) and moving the distance of \( q \) in the right direction—simple as that!

Answer 2

simplify it but still have information

Answer 3

Sure! Let’s simplify it while keeping the important info.

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When we add \( p + q \), we’re finding a new number on the number line.

1. Starting Point \( p \): Imagine \( p \) is on the number line.

2. Move \( q \):

   • If \( q \) is positive, you move to the right (add).
   • If \( q \) is negative, you move to the left (subtract).

So, \( p + q \) means you start at \( p \) and then move the distance of \( |q| \) in the right direction for positive \( q \) or left for negative \( q \).

Example:

• If \( p = 3 \) and \( q = 2\), then \( 3 + 2 = 5\).
• If \( p = 3 \) and \( q = -2\), then \( 3 + (-2) = 1\).

Given:

You said the sum is -2.

For instance, if \( p = -1 \) and \( q = -1 \):

• Then \( -1 + (-1) = -2\).

So, that’s how \( p + q \) works! It’s just moving in the right or left direction based on whether \( q \) is positive or negative.

Answer 4

it appears to not fit entirley in a text box so size it down

Answer 5

Sure! Here's a more concise version that fits better in a text box:

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When we add \( p + q \), we find a new number on the number line.

1. Start at \( p \): This is your starting point.

2. Move \( q \):

   • If \( q \) is positive, move right.
   • If \( q \) is negative, move left.

So, \( p + q \) means starting at \( p \) and moving \( |q| \) units in the right or left direction.

Example:

• If \( p = 3 \) and \( q = 2\), then \( 3 + 2 = 5\).
• If \( p = 3 \) and \( q = -2\), then \( 3 + (-2) = 1\).

Given Sum:

If \( p + q = -2\), for example, with \( p = -1 \) and \( q = -1\):

• Then \( -1 + (-1) = -2\).

It’s all about moving from \( p \) based on \( q \)!