To find the sum \( p + q \) using a number line, follow these steps with \( p = -19 \) and \( q = 12.1 \):
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Draw a Number Line: Start by drawing a horizontal line. Mark some evenly spaced points on it, representing integers. Make sure to include negative numbers to accommodate \( p = -19 \) and enough positive numbers to include \( q = 12.1 \).
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Locate \( p \): Find the point that represents \( p = -19 \) on the number line. Mark this point clearly.
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Moving Right for \( q \): Since \( q = 12.1 \) is a positive number, you need to move to the right from -19. The total move will be \( +12.1 \).
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Calculate the Move: Start from -19 and move right. First, move 19 units to reach 0. Then from 0, move an additional 12.1 units to the right.
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Mark the Sum: After moving from -19 to 0 (19 units) and then an additional 12.1 units, the end point is \( 0 + 12.1 = 12.1 \). Mark this point clearly on the number line as well.
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Final Result: The point you have reached, 12.1, represents the sum \( p + q \). Therefore, \( p + q = -19 + 12.1 = -6.9 \).
Now you can clearly see the process of adding negative and positive numbers using the number line. The final answer is: \[ p + q = -6.9 \]