Dividing Fractions

U02_L2_T3_we2 Dividing Fractions

Divide and write the answer
as a mixed number.

And we have 3/5 divided
by 1/2.

Now, whenever you're dividing
any fractions, you just have

to remember that dividing by a
fraction is the same thing as

multiplying by its reciprocal.

So this thing right here is the
same thing as 3/5 times--

so this is our 3/5 right here,
and instead of a division

sign, you want a multiplication
sign, and

instead of a 1/2, you want to
take the reciprocal of 1/2,

which would be 2/1--
so times 2/1.

So dividing by 1/2 is the
exact same thing as

multiplying by 2/1.

And we just do this as a
straightforward multiplication

problem now.

3 times 2 is 6, so our
new numerator is 6.

5 times 1 is 5.

So 3/5 divided by 1/2 as an
improper fraction is 6/5.

Now, they want us to write
it as at mixed number.

So we divide the 5 into
the 6, figure out how

many times it goes.

That'll be the whole number
part of the mixed number.

And then whatever's left over
will be the remaining

numerator over 5.

So what we'll do is
take 5 into 6.

5 goes into 6 one time.

1 times 5 is 5.

Subtract.

You have a remainder of 1.

So 6/5 is equal to one whole,
or 5/5, and 1/5.

This 1 comes from whatever
is left over.

And now we're done!

3/5 divided by 1/2
is 1 and 1/5.

Now, the one thing that's not
obvious is why did this work?

Why is dividing by 1/2 the
same thing as multiplying

essentially by 2.

2/1 is the same thing as 2.

And to do that, I'll do a little
side-- fairly simple--

example, but hopefully, it
gets the point across.

Let me take four objects.

So we have four objects:
one, two, three, four.

So I have four objects, and if
I were to divide into groups

of two, so I want to divide
it into groups of two.

So that is one group of two and
then that is another group

of two, how many groups
do I have?

Well, 4 divided by 2, I have two
groups of two, so that is

equal to 2.

Now, what if I took those
same four objects:

one, two, three, four.

So I'm taking those
same four objects.

Instead of dividing them into
groups of two, I want to

divide them into groups of 1/2,
which means each group

will have half of
an object in it.

So let's say that would be
one group right there.

That is a second group.

That is a third group.

I think you see each group has
half of a circle in it.

That is the fourth.

That's the fifth.

That's the sixth.

That's the seventh, and then
that's the eighth.

You have eight groups of 1/2,
so this is equal to 8.

And notice, now each of the
objects became two groups.

So you could say how many
groups do you have?

Well, you have four objects
and each of

them became two groups.

I'm looking for a
different color.

Each of them became
two groups, and so

you also have eight.

So dividing by 1/2 is the same
thing as multiplying by 2.

And you could think about it
with other numbers, but

hopefully, that gives you a
little bit of an intuition.