Which number line shows the correct way to find the sum p + q if p is positive and q is negative?

1 answer

To find the sum \( p + q \) where \( p \) is positive and \( q \) is negative, you would typically start at \( p \) on the number line and then move to the left by the absolute value of \( q \).

Here’s a step-by-step breakdown of how this would work on a number line:

  1. Locate \( p \): Start at the point that represents the positive number \( p \).
  2. Identify \( q \): Since \( q \) is negative, you need to determine its value (let's say \( q = -|q| \), where \( |q| \) is the absolute value of \( q \)).
  3. Move Left: From the point that represents \( p \), move to the left by \( |q| \). The farther you move left corresponds to adding a negative number.

The result of this movement will be the sum \( p + q \).

If you visualize or depict this scenario on a number line:

  • You'd have a point at \( p \) (e.g., 5),
  • Then an arrow going left by \( |q| \), for example if \( q = -3\), you'd move 3 units to the left from 5 to land at 2.

This visual representation effectively communicates how to find the sum of a positive and a negative number on a number line.