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 |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 p from q in the positive direction.
The sum negative p plus left parenthesis negative q right parenthesis is the number located a distance 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.
The sum p+(−q) is the number located a distance |q| from p in the positive direction.
The correct response is: The sum p+(−q) is the number located a distance |p| from q in the negative direction.
Which number line shows the correct way to find the sum p+q if p is positive and q is negative?(1 point)
Responses
A number line is shown with arrows at both ends, and hashmarks at unit intervals. The second mark from the left is labeled 0. Point p is located 5 intervals to the right of 0. A leftward curved arrow, labeled absolute value of q, starts at p and ends 4 intervals to the left of p.
Image with alt text: A number line is shown with arrows at both ends, and hashmarks at unit intervals. The second mark from the left is labeled 0. Point p is located 5 intervals to the right of 0. A leftward curved arrow, labeled absolute value of q, starts at p and ends 4 intervals to the left of p.
A number line is shown with arrows at both ends, and hashmarks at unit intervals. The second point from the left is labeled p. Zero is marked at 6 intervals to the right of point p. A rightward curved arrow, labeled absolute value of q, starts at p and ends 4 intervals to the right of p.
Image with alt text: A number line is shown with arrows at both ends, and hashmarks at unit intervals. The second point from the left is labeled p. Zero is marked at 6 intervals to the right of point p. A rightward curved arrow, labeled absolute value of q, starts at p and ends 4 intervals to the right of p.
A number line ranging from 0 in unit increments shows an arrow, labeled absolute value of q, starting at point p and ending 4 units to the right.
Image with alt text: A number line ranging from 0 in unit increments shows an arrow, labeled absolute value of q, starting at point p and ending 4 units to the right.
A number line is shown with arrows at both ends, and hashmarks at unit intervals. Point p is marked on the seventh interval from the left. Zero is marked 2 intervals to the right of p. A leftward curved arrow, labeled absolute value of q, points from p to the second interval from the left.
Image with alt text: A number line is shown with arrows at both ends, and hashmarks at unit intervals. Point p is marked on the seventh interval from the left. Zero is marked 2 intervals to the right of p. A leftward curved arrow, labeled absolute value of q, points from p to the second interval from the left.
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The correct response is: A number line is shown with arrows at both ends, and hashmarks at unit intervals. The second mark from the left is labeled 0. Point p is located 5 intervals to the right of 0. A leftward curved arrow, labeled absolute value of q, starts at p and ends 4 intervals to the left of p.
Which number line correctly represents −7+8?
(1 point)
Responses
Option 3
Option 3
Option 2
Option 2
Option 4
Option 4
Option 1
Option 1
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The correct response is: Option 3
Use properties of operations to add (−3) and (−17).(1 point)
Responses
−14
negative 14
14
14
20
20
−20
negative 20
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The correct response is: -20 or negative 20.
Add (4) and (−15).(1 point)
Responses
11
11
−11
negative 11
19
19
−19
negative 19
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The correct response is: -11 or negative 11.
To determine which option describes the sum in terms of p and q, let's break down each option and analyze them:
Option 1: The sum of p + (-q) is the number located a distance |p| from q in the negative direction.
Explanation: This option states that when you add p to -q, the resulting number is a distance of |p| from q in the negative direction.
Option 2: The sum -p + (-q) is the number located a distance p from q in the positive direction.
Explanation: This option states that when you add -p to -q, the resulting number is a distance of p from q in the positive direction.
Option 3: The sum p + (-q) is the number located a distance |q| from p in the negative direction.
Explanation: This option states that when you add p to -q, the resulting number is a distance of |q| from p in the negative direction.
Option 4: The sum p + (-q) is the number located a distance |q| from p in the positive direction.
Explanation: This option states that when you add p to -q, the resulting number is a distance of |q| from p in the positive direction.
To determine the correct option, we need to consider the signs (+/-) in front of p and q in each option.
The correct option is the one where both p and q are being subtracted (due to the negative sign (-)), represented as p + (-q).
From the given options, we can see that only Options 1 and 3 have p being added to -q. Now, let's compare the remaining differences:
Option 1 states that the resulting number is a distance of |p| from q in the negative direction.
Option 3 states that the resulting number is a distance of |q| from p in the negative direction.
Since the options ask for the sum of p + (-q), the correct answer is Option 1: "The sum p + (-q) is the number located a distance |p| from q in the negative direction."