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- 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.