We want to find the quotient using the
fraction strips provided below
where each fraction strip represents one whole. So here we have three divided by three-
fourths,
which is asking us how many three-fourths are there in three?
Before we determine the specific quotient though, let's determine a quotient that would be too
large,
and two small, based upon the given
quotient.
Well if we consider the quotient three
divided by one, this would be too small
compared to three divided by three-fourths, since one is greater than
three-fourths.
And we know if three divided by one is equal to three, so our quotient should be larger than three.
And now for a quotient that is too large
it's a little more challenging, but let's consider three divided by one-half.
There should be more one halves in three
than three-fourths in three,
since one-half is less than three-fourths. And again three divided by one-half would be
asking us how many one-halves are in
three.
Which hopefully we recognize would be six.
So six would be too large of a quotient,
and three would be too small of a quotient, which means our answer should be
somewhere between
three and six. And now to consider our specific quotient,
given we'll determine how many three-fourths there are in three.
To do this we'll cut or partition
each strip into fourths. Remember each
strip
represents one whole. So if we cut or partition
each strip into fourths, it would look
like this.
And now in this form, we can count the number of three-fourths
in three. So here we have one-fourth,
two-fourths, three-fourths. So here's
one three-fourth. Here we have one-fourth,
two-fourths, three-fourths. So here's
two three-fourths.
And then here we have
one.
And then here we have one,
two, three-fourths again, that's our third
three-fourths. And then finally,
notice how we have one, two,
three-fourths again. So notice how we have a total
of four three-fourths in three,
or we can say there are four copies of
three-fourths in three.
And therefore three divided by three-fourths
equals four.
So using fraction strips
can be a nice way to conceptualize
what's happening when we divide a whole
number
by a fraction.
I hope you found this
helpful.
