Video: Using a Visual Model to Apply the Distributive Property of Multiplication

Use the model to help you multiply. Write the multiplication expression that is missing. (8 × 5) = (_) + (3 × 5) = 25 + 15 = 40.

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Video Transcript

Use the model to help you multiply. Write the multiplication expression that is missing. Eight times five equals what plus three times five, equals 25 plus 15, equals 40.

The model that we’ve got on the right here is called the area model of multiplication. It’s a way of showing multiplications using rectangles and squares. We know that the area or the space inside a rectangle or a square is found by multiplying the length by the width. And so if we’re multiplying two numbers together, we can draw a rectangle with the length of one of the numbers and the width of the other of the numbers. And we know that the area then will be the answer to the multiplication. It’s a good way of modeling multiplications.

So here we can see that one large rectangle has been drawn. Its height is eight squares. We’ll call this its length just so that we’re talking about length and width. And we can see that the width of the rectangle is five squares. And so the area inside the whole rectangle — that’s the orange part and the green part together — is worth eight times five, which we can see on the left-hand side.

Well, even if we didn’t already know that eight fives are 40, we can actually see it in the calculation. But let’s imagine that we didn’t know this fact. Let’s imagine that we were going to find eight times five very difficult to work out. What could we do to make it easier?

Well, we could partition eight into two numbers that we do know how to multiply by five. We can see that this is what’s happened to our rectangle. It’s been partitioned into two smaller rectangles. The height of the rectangle, eight, or we call it the length, has been partitioned into three and five. Three plus five equals eight.

Now that we know the length of the side of the first shape, the orange shape, we can write the multiplication inside it. The length is five and the width is five. It’s a square. So to find the area, we need to multiply five by five.

And this is the interesting thing about multiplication. If we don’t know what eight times five is, we can partition it into five and three and then work out five times five and three times five and add the two together. And they’ll make the same as if we just multiplied eight times five.

Let’s continue through the calculation to finish it off. Five times five — that’s the area of the orange square — equals 25. Then the area of the green rectangle, three times five, is equal to 15. Then if we add the two parts together, we can find the area of the whole rectangle. 25 plus 15 equals 40, which is the same as eight times five. The multiplication expression that’s missing equals five times five.

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