Verified Answer :

  • Begin at 0 on the number line and move 19 units to the right to reach the position 19.
  • Subtract 5 by moving 5 units to the left from your current position.
  • Observe that moving 5 units to the left from 19 results in the value 14.
  • The final result of the addition is \(\boxed{14}\).

Explanation

  1. Analyzing the Problem

To calculate the sum \(19 + (-5)\), we interpret this expression as a sequence of movements along a number line. We begin at the origin, move 19 units to the right, and then adjust our position by moving 5 units to the left, which represents adding a negative value.

  1. Moving to the Initial Position

Start at 0 on the number line. To represent the number 19, move 19 units to the right. This places us at the point 19 on the number line.

  1. Performing the Addition

From our current position at 19, adding \(-5\) corresponds to moving 5 units to the left along the number line. Starting from 19 and counting 5 units backward (18, 17, 16, 15, 14), we arrive at the final position.

  1. Identifying the Result

After moving 19 units to the right and then 5 units to the left, we are at the position 14 on the number line. Therefore, the sum is \(19 + (-5) = 14\). The final result is \(\boxed{14}\).

Examples

A practical example of using a number line to perform addition involving negative numbers is tracking a bank account balance. If your initial balance is \(\$19\) and you make a transaction that withdraws \(\$5\), you can visualize this on a number line where the starting point is \(\$19\) and the transaction is a shift of \(-5\) units to the left. The final position on the line, \(\$14\), represents your remaining account balance after the withdrawal. This method helps in visualizing debt or spending reductions in everyday personal finance.

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