Line plots with fractions
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The amount of rain that falls in various cities in France varies. The line plot below shows the average monthly rainfall in 13 different cities. Measurements are rounded to the nearest 1/4 of a centimeter. How much more rain falls in the rainiest city than the second rainiest city? So let's make sure we understand what they're calling a line plot right over here. Each of these dots represents one of the cities whose average monthly rainfall was measured. And so, for example, putting this dot here shows that this is the only city that had 6 centimeters of average monthly rainfall. Here, this shows that there were two cities that had an average monthly rainfall of-- looks like 8 and 3/4 centimeters. There are two cities that had an average monthly rainfall of 12 and 3/4 centimeters. So at any given amount of rainfall, it's essentially showing you how many cities had that amount of rainfall on average per month. Now that we understand this diagram, let's answer the question. How much more rain falls in the rainiest city? So the rainiest city here, well, there's only one city that's up here at 13 and 1/2 centimeters of rainfall. So this right over here, let me mark this off. This is 13 and 1/2 centimeters. How much more rain falls in the rainiest city than in the second rainiest city? Well, this is the second rainiest city, is this city right over here. This is 13 and 1/4 centimeter. So the difference between the two is just one notch here. It's just one notch, going from 13 and 1/4 to 13 and 1/2, so one notch right over here. We see that there's four notches per centimeter. One notch over here is 1/4 of a centimeter. So just looking at it, you could say that the difference is 1/4 of a centimeter. Now, if it wasn't so clear, because here we're just looking one notch right over here, you could take the larger of the two and subtract from that the smaller of the two. So you could take 13 and 1/2, and from that, subtract 13 and 1/4. And there's multiple ways of doing this. You could subtract the 13 from the 13, and then subtract the 1/4 from the 1/2, and then you would get 1/4. Another way is you could convert these both into improper fractions. So 13 and 1/2 is the same thing as 2 times 13 is 26 plus 1 is 27. So that's 27/2. And then we could say minus-- let's see, 4 times 13 is 52, plus 1 is 53, so minus 53/4. And then in order to do the subtraction, you have to have the same denominator. And so 4 is a multiple of 2, so we just have to multiply the numerator and denominator here by 2. So we have 54/4 minus 53/4, which is equal to-- well, 54 minus 53 is 1, over 4-- 1/4 of a centimeter. For this problem, this would clearly be a little bit too much that you would have to do. But this is useful to know just in case it wasn't as obvious that these weren't just next to each other.