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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 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. 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.

1 answer

To find the sum \( p + q \) when \( p \) is a positive number and \( q \) is a negative number, you treat \( q \) as the absolute value in the opposite direction on the number line.

Given that \( p \) is positive, its point will be to the right of zero. Since \( q \) is negative, when we add \( q \) to \( p \), we essentially have to move left along the number line by the absolute value of \( q \) (which is a positive distance).

Among the given options, the third description matches this process correctly:

  • It shows \( p = 5 \) (located 5 intervals to the right of 0).
  • It indicates a leftward arrow starting at \( p \) and ending 4 intervals to the left of \( p \), which accurately represents \( q \) as a negative movement.

So, the correct answer 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.