Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityMedium
A civil engineer is surveying a new building site. The elevation at the highest point is +32.5 meters relative to sea level, and the lowest point is -8.75 meters relative to sea level. What is the total vertical distance between these two points?
- A40.25 meters
- B23.75 meters
- C41.25 meters
- D23.25 meters
Show answer & explanationAnswer & explanation
Correct answer: C. 41.25 meters
To find the total vertical distance between two points with positive and negative elevations, add the absolute values of their elevations. This accounts for the distance above and below the reference point.
Why the other options are wrong
- A. This is an arithmetic error in addition of 32.5 + 8.75.
- B. This is the result of subtracting the absolute values (32.5 - 8.75), which is incorrect for total distance.
- D. This is an arithmetic error in subtraction of 32.5 - 8.75.
Distance on a Number Line
The distance between two numbers on a number line, regardless of their sign, is found by taking the absolute value of their difference, or by adding their absolute values if they are on opposite sides of zero.
- Distance is always a non-negative value.
- Can be calculated using absolute values.
- For points on opposite sides of zero, add their absolute values.
Memory trick: From here to there, ignore the sign, just count the space.