Fraction multiplication: area model to expression
About this video
A unit square has one of its 5 columns shaded purple and 3 of its 4 rows shaded blue. The video reads this area model as 3/4 x 1/5 (or 1/5 x 3/4) and finds the product by counting: the overlap is 3 of 20 equal rectangles, so 3/20.
You'll be able to
- read the two fractions being multiplied from an area model.
- find the product of a unit fraction and a non-unit fraction, like 3/4 x 1/5 = 3/20, by counting equal parts.
Key words
- area model
- A shape split into equal rows and columns and shaded to show multiplying fractions.
- overlap
- The part where two shadings cross; it shows the product.
- unit square
- A square with area 1 square unit, used as the whole.
Transcript
- [Instructor] We're told that the area of the entire figure below is one square unit. So that's the square right over here. And then we see the square is shaded in very interesting ways. It looks like we have this purple column shaded in, and then we have these three blue rows shaded in.
And then this little pattern here looks like the overlap of those two. And what I will tell you is that this is an area model that's representing the multiplication of two fractions. And what I want you to figure out, pause this video and see if you can figure out what two fractions we are multiplying.
And then you could even think about what is the product of those two fractions based on the area model. Okay, now let's think about this together. So first, let's just think about what this purple column that is shaded in, what this represents right over here, relative to the whole.
Well, we could see that there's one, two, three, four, five of these equal columns. They're each 1/5 of the whole. So that's 1/5, that's 1/5, that's 1/5. And then that's 1/5, and then that's 1/5. I'm talking about the entire columns here, not just each of those rectangles.
And so our first one represents 1/5. Now, let's think about the rows here. So each of these rows, we can see that we have four equal rows. So that's one. We have two, we have three, and then we have four equal rows. So each of these are 1/4. But if we think about the entire blue region that's shaded in, it's three of those rows.
So it is 3/4. And the overlap between the two, this right over here, lemme do that in another color, the overlap, this right over here, this is essentially where you're multiplying this 3/4 times this 1/5. And so what we could say is this overlap is 3/4 times 1/5.
We could also write it as 1/5 times 3/4. And if we wanna think about what that is, we just have to say look, the whole is now split into 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 equal rectangles. And you could have also said, "Hey, there's just four rows of five here."
Four times five is 20. So each of these are 1/20 and we have one, two, three of those 1/20s filled in. So this is going to be equal to 3/20.
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