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Question Video: Matching an Area Model to the Equivalent Multiplication Expression Mathematics • 4th Grade

Pick the multiplication expression that matches this area model. [A] 7 × 406 [B] 7 × 164 [C] 146 × 7 [C] 700 × 641 [D] 641 × 7

02:59

Video Transcript

Pick the multiplication expression that matches this area model. Seven times 406, seven times 164, 146 times seven, 700 times 641, or 641 times seven.

In the picture, we can see an area model, and we know that these are a way of helping us to visualize multiplications. They don’t tell us what the answer is, but they do give us an idea of how to get there. We’re asked to pick the multiplication expression that matches this model. And underneath, we’ve got five to choose from. So what’s this area model showing us? Firstly, we can see that this side of the rectangle is labeled seven. This tells us that one of the numbers we’re going to be multiplying by is going to be seven. Now, if we look at our possible answers, we can see that most of them do have seven as a factor. However, there’s one that doesn’t.

So perhaps, the first thing we can do is to cross off 700 multiplied by 641. This isn’t the right answer at all. But what are we multiplying seven by? This is where our area model becomes interesting because we can see that it’s been split up into three parts. The length of the first part is labeled 100. And because we know that the area of a rectangle is worth its length multiplied by its width, we know that the area of this first part is 100 multiplied by seven. The length of our second part is labeled 40. So we know that the area of this part is 40 times seven. And we can see that the area of our last part is six times seven.

So our area model seems to represent three multiplications, not one. But we know if we add these three partial products together, we can find the answer to an overall multiplication. 100 plus 40 plus six equals 146. And so, by adding together 100 times seven, 40 times seven, and six times seven, we can find the answer to 146 times seven. This area model is exactly the sort of thing we could sketch if we wanted to find the answer to 146 times seven. It shows us how we could partition the three-digit number to make it easier to multiply. The multiplication expression that matches this area model is 146 times seven.

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