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)



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(1 point)
Responses

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

Sebastian should have used –9 and 7.

Answer 1

To analyze Sebastian's movements, we can describe them mathematically.

He first goes up 7 floors, which can be represented as +7. After that, he goes down 9 floors, which can be represented as -9.

So, his overall movement can be expressed as:

• Starting at the ground floor (0), he goes up 7 floors: 0 + 7 = 7.
• Then he goes down 9 floors from where he is (which is now 7 floors up): 7 - 9 = -2 (indicating he is now two floors below ground level).

The original expression, 9 + (−7), does not correctly represent his movements because it does not consider that he started at the ground floor.

The most appropriate response would be that Sebastian should have started at zero before adding -7, but his overall expression for vertical movement starting from ground level would ideally be expressed as:

0 + 7 (going up) + (-9) (going down) which simplifies to 7 - 9.

Since he started at 0 (ground level), the correct interpretation for his movements in mathematical terms would be starting at zero before incorporating both movements. Thus, the closest and best response is:

Sebastian should have started at zero before adding -7.

Answer 2

wrong

Answer 3

I apologize for the confusion. Let's clarify the scenario:

1. Sebastian is at the ground level (let’s denote this as 0).
2. He goes up 7 floors, which can be represented as +7.
3. Then he goes down 9 floors. Since he started at 7 floors up, going down 9 floors can be represented as -9 from there.

Putting this together with a starting point of 0:

• From 0, he goes up 7: \(0 + 7 = 7\).
• Then he goes down 9: \(7 - 9 = -2\).

If we break this down to just focus on the net effect: Moving up 7, then going down 9 can also be represented as:

• The initial up movement +7,
• The subsequent down movement -9.

Mathematically, this can properly be represented as \( -9 + 7 \) (which is equivalent to \( 7 + (-9) \)) or \( 7 + (-9) \).

Among the given response options:

• "Sebastian should have switched the two addends and written \(-7 + 9\)" is incorrect because it changes the direction of the movements.
• "Sebastian should have used -9 and 7" would accurately convey that he is going down first and then up, which is incorrect given he is moving up first.

Given the movements of up and down, the most appropriate action was not listed in the options, but since it closely aligns with how he could express his movements, a better way to express his total movement is indeed:

Sebastian should have used -9 and +7.

If you're still seeing a discrepancy, please let me know specifically what aspect is incorrect, and I'll gladly help clear it up!