Multiplying unit fractions: area model to expression
About this video
A square of area 1 square unit is split into 5 equal parts one way and 3 equal parts the other way, and one small piece is striped. The video writes the striped area as the multiplication expression 1/5 x 1/3 = 1/15, because the striped piece is one of 15 equal pieces.
You'll be able to
- read the side lengths of a piece in an area model as unit fractions.
- write a multiplication equation like 1/5 x 1/3 = 1/15 for a shaded piece of a unit square.
Key words
- square unit
- The area of a square with sides of length 1.
- multiplication expression
- A way of writing a product, like 1/5 x 1/3.
- unit fraction
- A fraction with 1 on top, like 1/5 or 1/3.
Transcript
- [Instructor] We are told the area of the entire figure below is one square unit so that's this entire thing. Write a multiplication expression to represent the area of the striped piece, so this area right over here. So pause this video, have a go at this before we do this together.
Okay, so first of all, what is a multiplication expression? Well, we're really gonna write something times something else is going to be equal to something else on top of that, a third something. So let's think about how to do this. Well, we could think about what we're multiplying on each of these sides of this square.
So, on the left side here, we have divided this square into 1, 2, 3, 4, 5 equal section. So one way to think about it is each of these are a fifth, for example, that's a fifth. That's a fifth, that's a fifth, I guess I'll keep doing it. That's a fifth and then that is another fifth.
Five-fifths is equal to whole. Now, if I look at the width up here, I have 1, 2, 3, equal section. So I could view that as a third. This as a third, and then this is a third. And so this area, the one that's striped, that area is going to be one-fifth times one-third, one-fifth times one-third.
And then what's that going to be equal to? Well, this whole thing is one square unit, and this is one of the 15 that we see. We can count them. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15. This is one of the 15 equal areas we have here. So this is gonna be one-15th of the entire square.
So there we have it. There's our multiplication expression. One-fifth times one-third is equal to 1-15th. One-fifth times one-third is equal to 1-15th.
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