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CCSS Math: 5.NF.B.6

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.