Multiplying Three-Digit Numbers by
One-Digit Numbers: Adding Partial Products
In this video, we’re going to learn
how to multiply three-digit numbers by one-digit numbers by calculating partial
products and using expanded column multiplication.
In this example, we have to
multiply a three-digit number, the number 135, by a one-digit number, the number
three. We know that three-digit numbers
have a hundreds, tens, and ones digit. So, to help us multiply 135 by
three, we could partition the number or break it apart into its hundreds, tens, and
ones, and then we can multiply each part by three. If 100 plus 30 plus five is 135,
then to find 135 times three, we would need to multiply each part by three.
We could use an area model to help
us multiply each of our three parts. We need to multiply three by 100
and three by 30 and three by five. Let’s start by multiplying the ones
in 135 by three. Three times five ones is 15. Next, we need to multiply the tens
part of our number by three. What is three times 30? We know that three times three is
nine. So, three times 30 is 10 times
greater than nine, which is 90. And finally, we can multiply the
hundreds part of the number 135 by three. Three multiplied by 100 is 300. Now, what we need to do is add our
partial products together: 300 plus 90 plus 15. The total of our ones is five, the
total of our tens is 10, and we’ve got a total of four 100s. Three times 135 equals 405.
Let’s recap what we’ve learned
about multiplying three-digit numbers by one-digit numbers using partial
products. The first thing we did was to
partition or break apart our three-digit number into its hundreds part, tens part,
and ones part. Next, we drew an area model, which
shows our three-digit number written in expanded form. Then we used the distributive
property to multiply each of the parts. Then all we had to do was add our
three partial products. Three times 135 is 405. Let’s practice what we’ve learned
and answer some questions where we need to multiply a three-digit number by a
one-digit number using partial products.
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
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
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
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.
Use partial products to calculate
124 times four.
In this question, the calculation
has been set out for us. We’re multiplying our three-digit
number, 124, by four. And we can see from the red arrow
that we have to multiply the ones part of 124 first. What is four multiplied by
four? 16. Next, we have to calculate two 10s
or 20 multiplied by four. 20 times four is 80. So, we’ve got our ones product and
now our tens product. Finally, we need to find the
hundreds product. The one in 124 is worth 100, so we
need to multiply 100 by four, which is 400.
Now, all we have to do is add
together our three partial products. We’ve got a total of six ones, nine
10s, and four 100s. 124 multiplied by four is 496. We used partial products to
calculate the answer.
Find the product. 213 multiplied by two.
In this question, we have to
multiply our three-digit number, 213, by a one-digit number, the number two. First, we need to find the ones
product. And we know the ones digit in 213
is three, so we have to multiply two by three, which is six. Next, we need to find the tens
product. 213 has one 10, so we need to
multiply two by 10. So, our product is 20. And finally, we need to find the
hundreds product. The hundreds digit in 213 is two,
worth 200. So, we’re multiplying two by
200. Two times 200 is 400.
Now, what we need to do is add our
three partial products. We’ve got six in the ones column, a
total of two in the tens column, and a total of four in the hundreds column. The product of 213 multiplied by
two is 426.
What have we learned in this
video? We have learned how to multiply
three-digit numbers by one-digit numbers by calculating partial products and using
expanded column multiplication.