Video Transcript
Ethan used an area model to help
him multiply 248 by two. Find the answer to 248 multiplied
by two and show how to calculate the answer by adding partial products in
columns.
In this question, Ethan is trying
to multiply a three-digit number, the number 248, by a one-digit number, the number
two, and he’s using an area model to help him multiply. He’s broken the number 248 up into
its parts. In other words, he’s written it in
expanded form. The hundreds part of 248 is worth
200, the tens part is worth 40, and the ones part is worth eight. 200 plus 40 plus eight equals
248.
Next, Ethan can multiply each part
by two. The ones product is 16 because
eight multiplied by two is 16. The tens product is 80 because two
times 40 equals 80, and the hundreds product is 400. Two times 200 equals 400. We have to find the answer to 248
multiplied by two and show how to calculate the answer by adding partial products in
columns. So, we have to work out which of
these five calculations is correct. We know by looking at Ethan’s area
model that the ones product is 16, and each of our possible answers show 16 as its
ones product.
So, we need to keep working through
the calculations. Let’s keep going and Look at the
tens product. We know because of Ethan’s area
model that two times 40 is 80. We can rule out this possible
answer because the tens product is 40. It looks like they’ve confused the
hundreds and the tens digit, multiplied two 10s by two instead of four 10s by
two. Let’s look at our second possible
answer. Tens product is 80, so this could
be the correct answer.
This could also be the correct
answer. But we know that the product of 40
and two is not eight; it’s 80. Eight is the product of four times
two not 40 times two, so we can rule this one out. And it looks like there’s been some
confusion with the hundreds and the tens digits in this answer. Two 10s multiplied by two is 40,
but the product of four 10s or 40 times two is 80.
Let’s check the hundreds parts of
the calculation. We know from Ethan’s area model
that the product of two multiplied by 200 is 400. Both of our calculations have the
correct number of hundreds, but they both have different answers. So, let’s complete the final step
of the calculation by adding the partial products. Six plus zero plus zero is six. One 10 plus eight 10s gives us a
total of nine 10s.
We found the mistake: 16 plus 80
plus 400 is 496, not 486. This is the correct way to find the
answer to 248 multiplied by two by calculating partial products and then adding the
partial products in columns.
