Fraction multiplication: expression to area model
About this video
The video selects the diagram that shows 2/3 x 1/4. It thinks of this as two thirds of one fourth: shade one of four equal sections, then split the whole into thirds and shade two. The overlap is 2 of 12 squares (2/12, also 1/6), and the matching diagram is B.
You'll be able to
- read 2/3 x 1/4 as 'two thirds of one fourth'.
- build an area model for a fraction times a unit fraction and find the overlap.
- choose the diagram that matches a multiplication expression.
Key words
- area model
- A rectangle split into equal parts and shaded to show multiplication.
- overlap
- Where the two shadings cross; it shows the product.
- twelfths
- Parts you get when a whole is split into 12 equal pieces.
Transcript
- [Instructor] So we're told to select the diagram that represents two thirds times one fourth, and they give us some choices. Why don't you pause the video, have a go at this before we do this together? Okay, now let's do this together. So one way to think about this is this is two thirds of one fourth.
So let me draw a whole here and I'll make it the same, roughly the same-looking rectangle that we see in these choices. And let me start with one fourth. So to have one fourth, I could divide this whole into four equal sections. I'm hand drawing it, so it's not going to be perfect, but these need to be equal sections.
That's pretty good, actually. Pretty good. So I think we all get that these are each fourths. And so if we wanted to focus on one of those fourths, we could look at maybe this one, and actually, maybe I'll use similar colors to what they're using. So that is one fourth right over there, and then I think about what is two thirds of one fourth?
Well, I could divide this whole into thirds and then take two of them, so let me do that. So let me take this whole and divide it into thirds, and then I can highlight two of those thirds. So this is a third, and then that is a third of the whole. So maybe let me do this in a, well, I'll do the same color.
So this right over here is one third, and then we have our second third right over there, and if I wanted to know what two thirds times one fourth is, or what two thirds of that fourth is, I would look at where they're overlapping. So I could see here that two thirds of that one fourth are these two right over here, these two squares, I should say.
And we could calculate what those actually are. We could see that when we have split the whole in this way, each of those squares, we have one, two, three, four, this way, and three this way, so we have 12 squares and we've just doubly highlighted, or there's an overlap in two twelfths of those, so we could say this is two twelfths.
You might also recognize that as being one sixth, but that's not what they're asking us. They just want us to select the diagram that represents this multiplication, and so this first one right over here looks like they have a fourth, but they're multiplying it times one third, so I don't like that one.
Here, they have a fourth and they're multiplying it by two thirds. I like this choice. Here, they have a half that they're multiplying by three fourths. I don't like that one either, so B is definitely our choice.
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