Introduction to Absolute Value 03:21 minutes

Video Transcript

Transcript Introduction to Absolute Value

Phillip and Lara are saying hello from the Netherlands, where the topography is very flat. Most of the land is barely above sea level!

Since they're having so much fun on their vacation, Phillip and Lara are already thinking about where to go for their next trip. Lara loves to climb mountains, but Phillip loves to scuba dive.

Phillip and Lara might not agree on what to do, but they do agree on where to go. They both want to get as far away from sea level as possible. Wherever that place is, that's where they'll go.

Lara suggests Mount Everest, the point with the highest altitude on Earth, with an elevation of 29,000 feet above sea level. Phillip proposes a trip to visit the Mariana Trench, the deepest place on Earth, around negative 36,000 feet, or 36,000 feet below sea level. Let’s analyze the facts and help Phillip and Lara decide where to go on their next trip.

What is Absolute Value?

We know negative numbers are less than positive numbers. So, negative 36,000 feet, the depth of the Mariana Trench, is less than the elevation of Mount Everest, which reaches a height of 29,000 feet. So does that mean Mount Everest is the place to go?

Not necessarily. To solve this problem, we need to know the absolute value of the height and depth of each location. The absolute value of a number is the number's distance from zero, regardless of whether the number is positive or negative.

Absolute Value Example

  • A depth of negative 36,000 feet is 36,000 feet from sea level. So the absolute value of negative 36,000 is 36,000.
  • A height of 29,000 feet is 29,000 feet from sea level. So the absolute value of 29,000 is 29,000. Absolute values are always positive numbers. Always!
  • The absolute value of negative 36,000 is greater than the absolute value of 29,000 because 36,000 is greater than 29,000.

So he lowest point of the Mariana Trench is farther from sea level than is Mount Everest's peak. We have a winner!

Before Phillip and Lara pack up their scuba gear and suntan lotion, let’s summarize the facts:

  • The absolute value of a positive number is simply equal to the number.
  • The absolute value of a negative number is equal to the opposite of that number, which is always positive, and the absolute value of zero is zero.

More Examples

Let's look at a few more situations:

  • What's the negative of the absolute value of a positive number? It's a negative number.
  • What's the negative of the absolute value of a negative number? A negative number also.
  • What if there's an expression inside the absolute value bars? You must simplify the expression first then determine the absolute value. If the expression is a big one, remember to use PEMDAS.

In the Mariana Trench, Phillip is having the time of his life scuba diving in very deep water, but what about Lara?

How about that? She found a mountain to climb, after all. Uh oh. I don't think that's a mountain.

2 comments
  1. Djk bdk on walmart horse

    Informative, but unrealistic. Both of those situations are far more lethal than the video suggests.

    Posted by Plano Kellmeyer, 12 months ago
  2. Anime girl cute wallpaper

    great video helps a lot.

    Posted by Jasmine C., about 1 year ago