add rational numbers quick check
Give me answers please
Which of the following describes the sum in terms of p and q?(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 |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 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.
Which number line shows the correct way to find the sum p+q if p is positive and q is negative?(1 point)
Use properties of operations to add (−3) and (−17).(1 point)
Responses
20
20
−14
negative 14
14
14
−20
Add (4) and (−15).(1 point)
Responses
19
19
−11
negative 11
11
11
−19
negative 19
Add (−18) and (5).(1 point)
Responses
−13
negative 13
23
23
13
13
−23
negative 23
1. The correct answer for the first question is "The sum p+(−q) is the number located a distance |q| from p in the positive direction."
2. The correct answer for the second question is the number line showing p on the right side and q on the left side.
3. The correct answer for the third question is "-19" or "negative 19".
4. The correct answer for the fourth question is "-13" or "negative 13".
To answer the questions about adding rational numbers, let's go through each question step by step:
1. Which of the following describes the sum in terms of p and q?
To determine the sum of p and (-q), we need to understand the concept of adding a negative number. When we add a negative number, it's the same as subtracting that number. So p + (-q) is equivalent to p - q. Now let's examine the given options to find the correct description.
Option 1: The sum p + (-q) is the number located a distance |q| from p in the positive direction.
Option 2: 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.
Option 3: The sum p + (-q) is the number located a distance |p| from q in the negative direction.
Option 4: 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.
Based on our understanding that p + (-q) is the same as p - q, we can eliminate options 1 and 3 because they do not represent subtraction. Now, comparing options 2 and 4, we can see that they are rephrased versions of each other using different words. Both options correctly state that the sum p + (-q) is a distance |q| from p, but differ in mentioning the directions. Since we know it is in the "positive direction," we can conclude that the correct description is option 2: 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.
2. Which number line shows the correct way to find the sum p+q if p is positive and q is negative?
To find the sum of p+q, we need to consider that p is positive and q is negative. When adding a positive and a negative number, we move to the left on the number line starting from the positive number and then move a distance equal to the absolute value of the negative number in the negative direction. Let's analyze the given options:
Option 1: 20
Option 2: -14
Option 3: 14
Option 4: -20
Since p is positive and q is negative, we start at a positive number and then move a distance equal to the absolute value of the negative number towards the negative direction. Comparing the options, we can see that option 2: -14, correctly represents this process and shows the correct way to find the sum p+q.
3. Use properties of operations to add (-3) and (-17).
To add (-3) and (-17), we simply add the two numbers together, keeping the negative sign:
(-3) + (-17) = -20
Therefore, the answer is -20.
4. Add (4) and (-15).
To add 4 and (-15), we add the two numbers together:
4 + (-15) = -11
Therefore, the answer is -11.
5. Add (-18) and (5).
To add (-18) and (5), we add the two numbers together:
(-18) + 5 = -13
Therefore, the answer is -13.
The correct answers for the given questions are:
1. The sum p+(−q) is the number located a distance |q| from p in the positive direction.
2. The correct number line to find the sum p+q if p is positive and q is negative is: <-q--p->
3. The sum of (-3) and (-17) is -20.
4. The sum of (4) and (-15) is -11.
5. The sum of (-18) and (5) is -13.