We want to find the quotient using the
fraction strips provided below,
where each fraction strip represents one whole.
So we have three and two thirds divided
by five-sixths,
which means we're going to determine how many five-sixths there are
in three and two-thirds. Well to begin, notice how we have four strips,
which would be four. But we're starting with three and two-thirds, not four.
So to begin, we'll cut or denominate this first strip into three equal partitions,
let's say here, and here. And we'll
eliminate
this third so that we're starting with
three and two-thirds.
And now to determine the number of five-sixths,
in three and two-thirds, we'll cut or partition the strips
into one-sixths, which would look like this.
Again remember we discarded this piece so that we're starting with
three and two-thirds. In this form
we can go ahead and count or enumerate the number of five-sixths
in three and two-thirds. Every time we
have five pieces
it represents five-sixths. So here we have
one, two, three, four, five, sixths.
This would be one set or one copy of five-sixths
in three and two-thirds.
Here we have another
one, two, three, four, five, sixths. Here's our second set or second copy of five-sixths.
Here we have another one, two, three, four, five, sixths.
For our third set or third copy of five-sixths.
And here's our fourth copy or fourth set of five-sixths.
One, two, three, four, five, sixths.
And now for these remaining pieces we have to be careful.
Remember we're counting the number of five-sixths, where five-sixths consists of
five pieces. And we only have two pieces
remaining,
which means we have two-fifths of a
copy of
five-sixths remaining. So again these last two pieces
represent two-fifths
of five-sixths. We have two pieces,
of which five make up five-sixths.
Which means three and two-thirds divided
by five-sixths
equals four and two-fifths.
Let's take a
look at this again.
One common mistake is to think of these
two pieces
as two-sixths of a whole, or one-third.
But remember we're not counting the number of ones in three and two-thirds,
we're counting the number of five-sixths and three and two-thirds.
So these two pieces make up two of the  five pieces
that make up a five-sixth. Giving us a quotient of four and two-fifths.
I hope you found this helpful.
