Line plots with fractions

What we're going to do in this video is review what we know about line plots but apply them in a situation where some of our data involves fractions. So, they tell us the lengths of some caterpillars are shown below and so we can see that here in the line plot. Just to refresh our minds how to read a line plot, this tells us that we have two caterpillars that are four centimeters long. These three show that we have three caterpillars that are seven centimeters long. Each dot represents a caterpillar whose length we are measuring, and it allows us to see how those lengths are distributed.

So, for example, we have a lot of caterpillars at this length. What is that length? Well, we can see that it is exactly halfway between four and five, so that is four and one-half centimeters long. We divide the section between four and five into two equal sections, and we're going one of those two equal sections towards five. So, this is four and a half centimeters.

So, I can ask you some questions. How many total caterpillars were measured? Pause this video and think about that. Well, each dot represents a caterpillar measurement, so we have one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen. So, we have a total of 17 caterpillars.

Now, another question we could ask ourselves is how many of the caterpillars are 5 and 1/4 centimeters long? Pause the video and think about that. Well, 5 and 1/4 is going to be more than 5, and what we would want to do to get to 5 and 1/4 is divide the interval or the length between five and six into four equal sections. They already did that: one, two, three, four. So, and then we want to go one of those four equal sections. So, five and one-fourth is right over here, and we can see that there's one caterpillar that is 5 and 1/4 centimeters long.

We can ask ourselves other questions. How many caterpillars—let me write it over here—how many have a length more than six and one-half centimeters? Pause the video and try to answer that. So, where is six and a half centimeters? Well, we can divide the section between six and seven into two equal sections, and if you go one of those two equal sections, that is six and a half. So, that is six and a half right over there.

How many have a length more than or greater than six and a half centimeters? Well, we can see it right over here: one, two, three, four, five, six. Six of them do, and we could even try to answer questions like how many more have a length of nine and a half centimeters than five and one-fourth centimeters. Try to answer that question.

Well, nine and a half centimeters, that's halfway between nine and ten, right over there. We can see two of them have a length of nine and a half centimeters, and we already know that one of them has a length of five and one-fourth. So, how many more have nine and a half centimeters versus five and one-fourth? Well, that would be two minus one or one more. We have one more caterpillar with a length of nine and a half centimeters than we do with five and one-fourth.

I’ll leave you there. We have plenty of examples on Khan Academy for you to practice this.