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.
