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 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 |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 |q| from p in the negative direction.
The sum p+(−q) is the number located a distance |q| from p in the negative direction.
Add Rational Numbers Quick Check
2 of 52 of 5 Items
Question
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 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 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. 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.
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.
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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.
Use properties of operations to add (−3) and (−17).(1 point)
Responses
14
14
20
20
−20
negative 20
−14
(-3) + (-17) = -20
The correct response is:
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 negative direction."
To understand why this is the correct answer, let's break down the terms in the sum:
- "p" represents a number or a distance in the positive direction.
- "(−q)" represents the negation of the number or distance q, which means moving in the opposite direction of q (negative direction).
So, when you add p and (−q), you are essentially adding a positive quantity and a negative quantity. In this case, p represents a distance in the positive direction, and (−q) represents a distance in the negative direction.
Since −q represents a negative distance or number, when you add it to p, you are effectively subtracting the magnitude of q from p. In terms of distances, it means moving a distance |q| (absolute value of q) from p in the negative direction. Therefore, the sum p+(−q) is the number located a distance |q| from p in the negative direction.