Identify 15 over 8, or 15/8, as a
proper or improper fraction.
So proper fraction just means that the numerator is equal or
less than, or less than or equal to the denominator.
So proper fraction, numerator, the number on top, is less
than or equal to the denominator.
In an improper fraction, the numerator is greater than the
denominator.
And we see in our example right here our numerator is
greater than our denominator, so we are dealing with an
improper fraction.
Now, a more interesting question is what does 15/8
even represent?
So let's think about that a little bit.
We saw in the last couple of videos that the denominator
tells you essentially how many slices of pie there are, I
guess is one way to think about it.
So let me draw something with eight--
let me divide something.
Maybe we could view this as a square pizza or a square pie
of some kind.
So let's say that's the entire pie.
I'm dividing it into two.
That would divide it into four, and then to divide it
into eight, I'd be just like that.
So this would be one whole pie.
Now, what does one of these boxes represent?
What does that box right there represent?
Well, we've seen this is one of the eight
total pieces of pie.
So this represents 1/8.
Now, if I were to shade in blue this box and that box
right there, and I were to say what fraction of my pie is
shaded in blue?
Well, you'd say I have two boxes shaded in blue: one,
two, out of a total of eight boxes.
This, these two right here, are 2/8 of the entire pie.
Or another way to think about it, this is equal to two of
these pieces, right?
So you could say this is also equal to 2 times 1/8, because
each of these boxes is 1/8.
We saw that right there.
It is one of the total eight pieces, so two of the eight,
that's really just two of these one-eighth boxes.
Now, if everything I've just said makes sense, let's think
a about what 15/8 mean.
So if you imagine these boxes like that,
let's try to do 15/8.
So if you were to draw, that's 1/8 right there.
I'm going to do it in the same size as these boxes.
Let me copy and paste this.
So let me copy and then let me paste.
So then that would be 2/8.
Let me do 3/8 and then 4.
We're going to go all the way up to 15.
I hope it doesn't bore you.
That is 5, 6, 7, 8, and now we've made a whole pie, but
we're only at 8.
We have to get to 15.
So let's keep going.
So then we're going to start another pie.
So it's 1, 2, 3.
So far, how many do we have?
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 and 15.
So what have I just drawn here with all these pink squares?
Each of these is 1/8.
Each of these boxes is 1/8 of a pie, I guess is how you
could think about it.
This is 1/8.
And I've just drawn 15 times 1/8, so all of these combined
are 15 times 1/8, or we could say that this is also equal
to, if we just use the logic we did before, 15/8.
Now, how many pies do I have here?
Well, these first 8 of the 15, this right here, that is 8 out
of 8, or 8 one-eighths, and that's equal to one whole pie.
So this right here is equal to one.
That right there is equal to one.
And what do we have over here?
We have one whole pie, 8 out of 8 pieces of a potential
pie, or 8 out of 8 one-eighths of a pie, I guess you could
call it, and then over here we have 7/8 of a pie, right?
You could imagine a whole pie would involve another grid
right there, would involve one more over here, but this is 7
out of the 8.
So this right here-- let me do this in another color-- this
piece right here represents 7, 7 times 1/8, or 7/8.
So if you were to say what 15/8 kind of represents, it
represents one whole pie, and then 7/8 of another pie.
You can even write that down as a mixed number.
And it's a mixed number because it has a whole number
and a fraction.
So this is equal to one whole pie right there and 7/8 of
another pie.
And that's all it represents when you think
about what 15/8 means.
Now, I had to draw it out like this, but a quick way you can
do to solve this is to divide 8 into 15.
So if you were to take-- let me do this
with the new colors.
So if you were to take that 8 right there, you
divide 8 into 15.
You see that it's equal to-- well, 8 goes into 15 one time,
because 2 times 8 is 16, so that's too big.
So 1 times 8 is 8.
You subtract 15 minus 8 is 7.
So to get 1 and 7/8, this 1 right here-- so you get one
whole 8 in there.
If you have 15/8, you get a whole 8 in there and then you
have 7 left over, but these are 7/8, so that's where that
7/8 come from.
You have to write the remainder over 8.
Hopefully, you found out helpful.