A building has 23 floors of offices above ground and 5 floors below ground. Nathan parks on the 2nd floor below ground and has an office on the 18th floor. The ground floor is floor zero. Which absolute value expression represents how many floors he must go up to get from his car to his office?
A.
|−5|+|23|
B.
|−2|+|18|
C.
|−5|+|18|
D.
|−2|+|23|
The distance between the floor of his car and the floor of his office is the absolute value of the difference between their floor numbers: |−2−18|=|-20|=20. Therefore, he must go up 20 floors. The only expression that gives us 20 when we follow the order of operations is option D: |−2|+|23|. Therefore, the answer is D.
To find the absolute value expression that represents how many floors Nathan must go up to get from his car to his office, we need to calculate the absolute difference between the floor where he parked his car and the floor where his office is located.
Nathan parks on the 2nd floor below ground, so the value representing the floor where he parked his car is -2.
His office is on the 18th floor, which is above ground, so the value representing the floor where his office is located is 18.
Using the absolute value notation, the absolute difference between these two values is given by |−2−18|. Simplifying this expression, we get |-2 - 18| = |-20|. The absolute value of -20 is 20.
Therefore, the correct absolute value expression that represents how many floors Nathan must go up to get from his car to his office is:
|-2| + |18|
Therefore, the correct answer is B.
The absolute value of a number represents its distance from zero on the number line.
Since Nathan parks on the 2nd floor below ground, the absolute value of that floor is |-2|.
Since his office is on the 18th floor, the absolute value of that floor is |18|.
Therefore, the absolute value expression that represents how many floors he must go up to get from his car to his office is:
|-2| + |18|
Therefore, the correct option is B.