Multiplying unit fractions: expression to area model
About this video
The video picks the area model that shows 1/6 x 1/4. It first sketches a square split into sixths one way and fourths the other, where the overlap is 1/24 of the whole. It then checks the choices and picks C, which shows the same product turned around as 1/4 x 1/6.
You'll be able to
- sketch an area model for the product of two unit fractions.
- match an expression like 1/6 x 1/4 to the right diagram, even if it is turned around.
- find the product 1/6 x 1/4 = 1/24 from an area model.
Key words
- area model
- A square or rectangle split into equal parts to show multiplication.
- product
- The answer when you multiply numbers.
- overlap
- The part where two shaded regions cross; it shows the product.
Transcript
- [Instructor] We are asked to select the diagram that represents 1/6 times 1/4. So why don't you pause this video? Have a go at it before we do this together. Okay, before I even look at these choices, I could think about what this might look like. So if I had a square unit, I'm just gonna hand draw it so it's a little bit shaky here.
So I could imagine having 1/6 on the left side and then 1/4 on top. So how would I do that? So I would divide it into six equal sections horizontally. So I could do it like this. So it could look something like this where each of these is 1/6 and then I'm going to multiply and maybe I would put that maybe in that color and then in the other direction I would divide it into fourths.
So let's see, that's about half. And then I will put those in half to get fourths. So 1/6 times 1/4. And so the fourth, let me do this in a light color so it doesn't write over. It would be that- Well, lemme do it in the color that you can actually see. It might be all of that right over there.
And then their overlap would be right over here. So this would be 1/6 times 1/4 and that's actually 1/24 of this entire square. So let's see. Do I see anything that looks like that? Let's see. This first one looks like 1/4 times 1/4. That's not right. This one looks like 1/6 'cause this is 1/6 right here, but it's 1/6 times 1/2 'cause in this direction we're only split into two.
This one over here doesn't look like what we did. But if we turn it around and if we do it the other way, where if we divide it into fourths on horizontally and then into sixths vertically, it looks a lot like choice C. So if I divided into sixths here, so if I had 1/4 times 1/6, 1/4 would be that entire row.
1/6 would be this entire column. When you take their product, you would get that shaded area, which is exactly what they did in choice C. So this is 1/4 times 1/6, and you get that shaded area. So I like choice C.
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