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Silvia is growing tomato plants
and studying their heights.

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Here is her data.

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So the beefsteak tomato type
had a height of 3 and 1/4 feet,

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Roma 2 and 7/8 feet,
cherry 3 and 1/2 feet.

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And they ask us, what
is the difference

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between the heights
of the beefsteak,

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so that's that one
right over there,

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and the Roma tomato plants?

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So they want us to find the
distance between these two

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heights.

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So this cherry tomato height
was really unnecessary

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for the sake of this problem.

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So we want to find the
difference in these two

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heights.

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So we want to subtract
the smaller of these

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from the larger of these.

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So we're really trying to
evaluate what 3 and 1/4

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minus 2 and 7/8 is.

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Now, the first thing that I like
to do is convert both of these

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into mixed numbers.

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Sorry, they're already
mixed numbers--

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to convert both of these
into improper fractions.

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So 3 and 1/4 is
the same thing as 3

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plus 1/4, which is the same
thing as 12/4 plus 1/4.

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That's the same
thing as 3 and 1/4.

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And from that, we're going
to subtract 2 and 7/8.

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2 and 7/8 is the same
thing as 2 plus 7/8.

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2 is the same thing
as 16/8 plus 7/8.

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So this is essentially what
we are trying to figure out.

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Now, what is 12/4 plus 1/4?

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It's 13/4, 13 over 4.

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And then, what's 16/8 plus 7/8?

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Well, that's 23/8.

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So this is going to be
minus 23 over eight.

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Now, we're subtracting
one fraction from another.

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But we have different
denominators.

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So we can't make
sense of this until we

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have the same denominator.

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And so what is the least
common multiple of these two

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denominators, of both 4 and 8?

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What is the smallest number that
is divisible by both 4 and 8?

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Well, 8 is divisible by 8.

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And 8 is also divisible by 4.

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So if we can rewrite 13/4 as
having 8 as a denominator,

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then we are all set.

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So let's try to do that.

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So we're going to write
both of these with 8

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as the denominator.

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This one already has it.

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So 13/4, I'm going to have
it with 8 as the denominator.

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So to get from 4 to 8, we have
to multiply the denominator

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by 2.

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So in order to not change
the value of the fraction,

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we have to multiply
the numerator

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by that exact same value.

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We've got to multiply it by 2.

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So this becomes 26/8.

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And from 26/8, we're
going to subtract 23/8.

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And so this is going to be
over 8-- 26 minus 23, which

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is equal to, and we deserve
our drum roll now, is 3.

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So it's 3/8.

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So the difference between
the heights of the beefsteak

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and Roma tomato plants-- 3/8.

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And everything we've
been doing insofar

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has been in feet,
so 3/8 of a foot.