Sebastian was in a hotel lobby and took the elevator up 7 floors to his room. Then he took the elevator down 9 floors to the parking garage. He described his movement with the expression below.

Question

9+(−7)


NOTE: There is a check answer button in the bottom right corner. Click this to check your answer before moving on to the next question. It will not tell you the correct answer, but it will tell you if the answer you selected is correct. You can use this feature once per question.

(1 point)
Responses

Sebastian should have started at zero before adding –7.
Sebastian should have started at zero before adding –7.

Sebastian should have used 0 and –9.
Sebastian should have used 0 and –9.

Sebastian should have switched the two addends and written −7+9
.
Sebastian should have switched the two addends and written negative 7 plus 9.

Sebastian should have used –9 and 7.
Sebastian should have used –9 and 7.

Answer 1

To analyze the expression Sebastian used, we need to break down his movement mathematically.

1. Starting Point: Let's assume Sebastian starts at the ground floor (0).
2. Going Up 7 Floors: He takes the elevator up 7 floors, which can be represented as +7.
3. Going Down 9 Floors: Then he takes the elevator down 9 floors, which can be represented as -9.

Now, if we follow the order of his movements mathematically:

• He first goes up 7 floors, so we can represent that as: 0 + 7 = 7 (now he is on the 7th floor).
• Then he goes down 9 floors from there, which would be: 7 - 9 = -2 (indicating he goes down 2 floors below the ground, i.e., parking garage).

The correct way to represent his overall movement would be: -7 (the floors up) + 9 (the floors down). However, if you look at his expression of 9 + (-7), we can see that it's essentially the same as saying he is moving down 9 floors and then up 7 floors.

Among the choices provided, the best option is: Sebastian should have switched the two addends and written -7 + 9.

This correctly reflects the order in which he moved.

Answer 2

wrong

Answer 3

I apologize for the confusion. Let's reevaluate the situation step-by-step to clarify Sebastian's movement.

1. Starting Point: Let's assume Sebastian starts at 0 (the ground floor).
2. Moving Up: He goes up 7 floors, represented as +7. After moving up, he is at floor 7 (0 + 7 = 7).
3. Moving Down: He then goes down 9 floors, which can be represented as -9. So from floor 7, moving down 9 floors would be 7 - 9 = -2 (indicating he goes to a point 2 floors below the ground, possibly to the parking garage).

To express the total movement in a mathematically correct way:

• His upward movement can be represented as +7, and his downward movement as -9.
• The correct expression to describe this movement would be: \( +7 + (-9) \) which simplifies to \( 7 - 9 = -2 \).

Now, let's interpret Sebastian's original expression, \( 9 + (-7) \):

• By using this expression, it seems like he is saying he moves down 9 and goes up 7, instead of accurately capturing his movement sequence (up then down).

Correct Conclusion: He's effectively represented the situation incorrectly in terms of the order of operations, where he should have expressed the downward movement as negative.

The statement "Sebastian should have used –9 and 7." is the appropriate choice.

This reflects his downward movement (which is negative) first before the upward movement (+7), leading to his final location. Thank you for your patience!