Subtracting fractions with unlike denominators word problem

Silvia is growing tomato plants
and studying their heights.

Here is her data.

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

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

And they ask us, what
is the difference

between the heights
of the beefsteak,

so that's that one
right over there,

and the Roma tomato plants?

So they want us to find the
distance between these two

heights.

So this cherry tomato height
was really unnecessary

for the sake of this problem.

So we want to find the
difference in these two

heights.

So we want to subtract
the smaller of these

from the larger of these.

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

minus 2 and 7/8 is.

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

into mixed numbers.

Sorry, they're already
mixed numbers--

to convert both of these
into improper fractions.

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

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

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

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

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

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

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

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

It's 13/4, 13 over 4.

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

Well, that's 23/8.

So this is going to be
minus 23 over eight.

Now, we're subtracting
one fraction from another.

But we have different
denominators.

So we can't make
sense of this until we

have the same denominator.

And so what is the least
common multiple of these two

denominators, of both 4 and 8?

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

Well, 8 is divisible by 8.

And 8 is also divisible by 4.

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

then we are all set.

So let's try to do that.

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

as the denominator.

This one already has it.

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

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

by 2.

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

we have to multiply
the numerator

by that exact same value.

We've got to multiply it by 2.

So this becomes 26/8.

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

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

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

So it's 3/8.

So the difference between
the heights of the beefsteak

and Roma tomato plants-- 3/8.

And everything we've
been doing insofar

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