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## Topic E: Extending fraction equivalence to fractions greater than 1

Current time:0:00Total duration:3:33

# Reading a line plot with fractions

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## Video transcript

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.