Multiplying Fractions Word Problem

U02_L2_T1_we4 Multiplying Fractions Word Problem

A recipe for banana oat muffins
calls for 3/4 of a cup

of old-fashioned oats.

You are making 1/2
of the recipe.

How much oats should you use?

So if the whole recipe requires
3/4 of a cup and

you're making half of
the recipe, you want

half of 3/4, right?

You want half of the number of
old-fashioned oats as the

whole recipe.

So you want 1/2 of 3/4.

So you just multiply 1/2 times
3/4, and this is equal to--

you multiply the numerators.

1 times 3 is 3.

2 times 4 is 8.

And we're done!

You need 3/8 of a cup of
old-fashioned oats.

And let's visualize that a
little bit, just so it makes a

little bit more sense.

Let me draw what 3/4 looks like,
or essentially how much

oats you would need in a normal
situation, or if you're

doing the whole recipe.

So let me draw.

Let's say this represents a
whole cup, and if we put it

into fourths-- let me divide
it a little bit better.

So if we put it into fourths,
3/4 would represent three of

these, so it would represent
one, two, three.

It would represent
that many oats.

Now, you want half
of this, right?

Because you're going to make
half of the recipe.

So we can just split
this in half.

Let me do this with
a new color.

So you would normally use this
orange amount of oats, but

we're going to do half the
recipe, so you'd want

half as many oats.

So you would want
this many oats.

Now, let's think about
what that is

relative to a whole cup.

Well, one way we can do it is
to turn each of these four

buckets, or these four pieces,
or these four sections of a

cup into eight sections
of a cup.

Let's see what happens
when we do that.

So we're essentially turning
each piece, each fourth, into

two pieces.

So let's divide each
of them into two.

So this is the first piece.

We're going to divide it into
two right there, so now it is

two pieces.

And then this is the second
piece right here.

We divide it into one piece
and then two pieces.

This is the third piece, so
we divide it into one, two

pieces, and this is the fourth
piece, or the fourth section,

and we divide it into
two sections.

Now, what is this as a fraction
of the whole?

Well, we have eight
pieces now, right?

One, two, three, four, five,
six, seven, eight, because we

turned each of the four, we
split them again into eight,

so we have 8 as the denominator,
and we took half

of the 3/4, right?

Remember, 3/4 was in orange.

Let me make this very
clear because this

drawing can get confusing.

This was 3/4 right there.

So that is 3/4.

This area in this purple color
is 1/2 of the 3/4.

But let's think about it
in terms of the eights.

How many of these sections
of eight is it?

Well, you have one section of
eight here, two sections of

eight there, three sections
of eight, so it is 3/8.

So hopefully that makes some
sense or gives you a more

tangible feel for what
it means when

you take 1/2 of 3/4.