How to Find the Distance Between Two Numbers | Measuring Distance, Absolute Value

How do we find the distance between two numbers? We go over this important concept in today's video math lesson!

By observing a number line, we can easily see that the distance from 5 to 2 is 3. However, we don't want to always have to look at a number line to find distance, so we want a mathematical operation that we can use instead!

At first, subtraction seems promising because 5 - 2 is also equal to 3. However, there is a problem with using subtraction for distance. It shouldn't matter what order we put the numbers in to calculate distance, because the distance between 5 and 2 is the same as the distance between 2 and 5, but with subtraction we see that 2 - 5 is equal to -3, so changing the order does change the result.

To fix this, we use absolute value! But what is absolute value? The absolute value of 5 - 2, written |5 - 2|, is equal to 3, and so is the absolute value of 2 - 5, written |2 - 5|! The absolute value of a negative quantity is a positive quantity, and so absolute value fixes our problem! We are not interested in negative numbers when we discuss distance, because we are only concerned with the distance between the numbers, which is a positive measure.

So, we can find the distance between two numbers by subtracting them in any order, then taking the absolute value of that! Hooray for absolute value!

The distance between -2 and 5: |-2 - 5| = |-7| = 7
The distance between -3 and 3: |-3 - 3| = |-6| = 6
The distance between 4 and 7: |7 - 4| = |3| = 3

The important property at work here is that for two numbers a and b, |a - b| = |b - a|.

I hope you find this video helpful, and be sure to ask any questions down in the comments!

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