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Sebastian was in a hotel lobby and took the elevator up 8 floors to his room. Then he took the elevator down 5 floors to the parking garage. He described his movement with the expression below.

5+(−8)



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(1 point)
Responses

Sebastian should have used –5 and 8.
Sebastian should have used –5 and 8.

Sebastian should have started at zero before adding –8.
Sebastian should have started at zero before adding –8.

Sebastian should have used 0 and –8.
Sebastian should have used 0 and –8.

Sebastian should have switched the two addends and written −8+5
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1 answer

To understand the correct representation of Sebastian's movements, we can break down his actions:

  1. Starting at Ground Level: We'll consider the ground level as 0.
  2. Going Up 8 Floors: From 0, if he goes up 8 floors, we can represent this as +8.
  3. Then Going Down 5 Floors: After reaching the 8th floor, he goes down 5 floors. This can be represented as -5.

Now, if we put this together:

  • Starting from 0: +8 (going up 8 floors)
  • After going up, he is at +8: -5 (going down 5 floors)

We can express this whole situation as: \( (0 + 8) + (-5) = 3 \).

Looking at the options provided:

  1. Sebastian should have used –5 and 8. (Not accurate, as the sequence matters.)
  2. Sebastian should have started at zero before adding –8. (Not the best representation, as it doesn't capture both movements.)
  3. Sebastian should have used 0 and –8. (Missing the upward movement.)
  4. Sebastian should have switched the two addends and written −8 + 5. (This changes the sequence of the operations incorrectly.)

The best answer based on his movements is that he should have represented it as: \( +8 - 5 \) or rearranged as \( 8 + (-5) \).

None of the options accurately represent his movement based on the explanation, but if one of the responses were to indicate something similar to what he did (like +8 then -5), it would be the best choice. Since the choices are limited, the closest fit could be considered: Sebastian should have started at zero before adding –8 (because it indicates starting from a base level, focusing on elevation). However, note that this still is not accurate.

If you are asked to choose one, select the option that reflects the need to consider the movement starting from a baseline, even if it’s not perfect.