Ordering rational numbers compared to an average
About this video
Four friends' 5 km run times are given as differences from the average of 24 minutes, with negative numbers meaning faster than average. Sal reasons that the most negative difference is the fastest time, converts the differences to decimals, and orders them from slowest (Jocelyn, +2.75) to fastest (Vlad, -2).
You'll be able to
- interpret positive and negative numbers as above or below an average.
- convert mixed numbers and fractions to decimals to compare them.
- order rational numbers, including negatives, in a real-world context.
Key words
- average
- A typical value for a group; here the friends' average time was 24 minutes.
- negative number
- A number less than zero; here it means a time below (faster than) the average.
- difference from the average
- How far one value is above (+) or below (-) the average.
Transcript
- [Instructor] We're told four friends completed a five kilometer 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 negative two, while Bianca is at negative 1.5 or negative one and a half. So just looking at it, I would say that Vlad has the fastest time. Now there's 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. Jocelyn, if you were to convert this into a decimal, is 2.75 minutes above average. Vlad is two minutes below average in terms of time. And Bianca is a minute and a half below average.
And then you could sort all of these. So, the slowest time is this one. Maybe I'll do it in terms of slowest, slowest. Maybe I'll do that in a different color. Well, I'll just order it this way. The slowest is 2.75. That is Jocelyn. She is the most above average time.
The next slowest is 0.5. That is Pedro. And then the next slowest is going to be Bianca at negative 1.5. So 1.5 minutes below average. And then last but not least we have Vlad, who is two minutes below average. So once again, when you order it this way, we see that Vlad is the fastest, has the fastest time.
And if you wanna know who is the slowest, it is Jocelyn.
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