Question

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. 9+(−7) (1 point) Responses 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 0 and –9. Sebastian should have used 0 and –9. Sebastian should have used –9 and 7.

Answer 1

To understand Sebastian's movement, let's break down what he did:

1. He started at an initial floor (let’s assume it’s floor 0 for simplicity).
2. He went up 7 floors, which can be represented as +7.
3. Then, he went down 9 floors, which can be represented as -9.

Hence, his overall movement can be represented as:

\[ 0 + 7 - 9 \]

This simplifies to:

\[ 0 + (7 - 9) = 0 - 2 = -2 \]

This indicates he ended up 2 floors below the starting point.

Now, evaluating the expression he used: 9 + (−7)

This expression describes going up 7 floors and then starting at 9, which doesn't properly align with the sequence of his movements. The preferable way to express his movements using the sum would be:

\[ -9 + 7 \]

This means he started at 0, went up 7, and then went down 9, leading to the correct calculation of his final position.

Looking at the options provided, the best choice is:

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

This correctly illustrates his process of moving up 7 floors and then down 9 floors, starting from the initial point.