Ordering rational numbers compared to an average | Grade 8 (TX) | Khan Academy

We're told four friends completed a 5 km run. Their average time to complete the run was 24 minutes. To compare their times, they created a table that shows the difference between each person's time and the average time, with negative numbers representing times less than the average. So that's the data right over here.

Who had the fastest time? Pause this video and see if you can figure that out before we do that together.

Alright, so the person with the fastest time is going to be whoever had the lowest number or the lowest time. Now, this is all compared to the average. So, one way to think about it is whoever is going to be the most below average in terms of time is actually the fastest. Or, one way to think about it is whoever is going to be the most negative.

Now we could eyeball this right over here and say, well, anyone who is above average in terms of time is going to be below average in terms of speed. They're not going to have the fastest time. So these people are both above average in terms of time, so they're below average in terms of speed.

And then if we were to compare these two right over here, we would say, well, look, Vlad is further below average time than Bianca is. Vlad's at -2 while Bianca is at -1.5 or negative one and a half. So just looking at it, I would say that Vlad has the fastest time.

Now, there are other ways you could have done this. Oftentimes, if you're comparing numbers, it's easier to convert them all into decimals. So you might have said something like Pedro is 0.5 minutes above average in terms of time. Joselin, if you were to convert this into a decimal, is 2.75 minutes above average. Vlad is 2 minutes below average in terms of time, and Bianca is a minute and a half below average.

Then you could sort all of these. So, the slowest time is this one. Maybe I'll do it in terms of slowest. Slowest, let me do it in a different color. Well, I'll just order it this way.

The slowest is 2.75; that is Joselyn. She has the most above average time. Then next, the next slowest is 0.5; that is Pedro. And then the next slowest is going to be Bianca at -1.5, so 1.5 minutes below average. And then, last but not least, we have Vlad who is 2 minutes below average.

So, once again, when you order it this way, we see that Vlad has the fastest time and, if you want to know who is the slowest, it is Joselyn.