Video: Using Absolute Value to Calculate Distance between Two Quantities in a Word Problem

Mt. Mansalu is the eighth highest mountain in the world, with its peak 8,156 meters above sea level. The shores of the Dead Sea, Earth’s lowest land elevation, are 430.5 meters below sea level. What is the difference between these two elevations?

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Video Transcript

Mount Mansalu is the eighth highest mountain in the world, with its peak 8,156 meters above sea level. The shores of the Dead Sea, Earth’s lowest land elevation, are 430.5 meters below sea level. What is the difference between these two elevations?

We are told that the mountain has a peak of 8,156 meters above sea level. This can be represented by the number positive 8,156. We’re also told that the shores of the Dead Sea are 430.5 meters below sea level. This can be represented by the number negative 430.5.

To calculate the difference between the two elevations, we could use one of two methods. Firstly, as difference means subtract, we could subtract negative 430.5 from 8,156. Subtracting a negative number is the same as adding the absolute value of that number. We have 8,156 plus 430.5. This gives us a total of 8,586.5. The difference between the two elevations is 8,586.5 meters.

Our alternative method would be to add the absolute value of both numbers. The absolute value or modulus of a number is denoted by two vertical parallel lines, as shown. We have the absolute value of 8,156 plus the absolute value of negative 430.5. The absolute value of any number is the distance between the number and zero. As the absolute value of any negative number is positive, we’re left with 8,156 plus 430.5 once again. This gives us the same answer of 8,586.5 meters.

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