Multiplying fractions word problem: muffins

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.