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## Arithmetic

### Course: Arithmetic > Unit 7

Lesson 3: Multiply with partial products# Multiplying 3-digit by 1-digit (regrouping)

CCSS.Math:

Learn to multiply a 3-digit number by a 1-digit number using regrouping. In this video, we will multiply 7x253. Created by Sal Khan.

## Want to join the conversation?

- okay so a lot of people say that the new way of this generation's math is very easy but it is actually very complicated. The old way is a lot easier so you schools that are doing great1(23 votes)
- I agree. It is very hard! I hope Sal Khan fixes it to be easier.(6 votes)

- Has anyone ever wondered 4 digit by 4 digit(15 votes)
- did anyone else notice that he said one thousand seven hundred AND seventy one? The proper grammar is one thousand seven hundred seventy one.(8 votes)
- yeah i noticed that as well i'm kinda surprised he made that mistake since hes the one teaching us grammar(4 votes)

- how do you solve it with 10 digits?//(7 votes)
- What do you mean by 10 digits? Multiple 10 digits with 10 digits?(5 votes)

- What is the biggest number's name like maybe 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 is the biggest?(5 votes)
- What is 305 x 6?(4 votes)
- first

Multiply 300 by 6 which is 1800. Now you know your answer is at least 1800.

Next multiply 6 by the remaining number 05 which same as 5. 3x5 is 30. Add your two answers and you'll get 1830 :)(4 votes)

- why are all these comments so long ag(5 votes)
- why do you put the biger number out and the low number in ?(3 votes)
- Just like Addition and Subtraction Regrouping/Carrying sums you're writing the numbers under the correct Place Value.

When Multiplying the Ones place wright the Ones under the Ones Place then move the 10 over to the Tens Place, Multiplying the Tens Place wright the Tens under the Tens Place and move the Hundreds over to the Hundreds Place :)

Remember in these Multiplication Regrouping/Carrying Sums to Multiply the number in the Place Value first before adding onto it the number you moved over.(1 vote)

- Why do you have to multiply each digit by the ones place?(3 votes)
- how do you solve it with 10 digits?(3 votes)

## Video transcript

Let's multiply 7 times
253 and see what we get. So just like in the last
example, what I like to do is I like to rewrite the
largest number first. So that's 253. And then write the
smaller number below it and align the
place value, the 7. It only has a ones place, so
I'll put the 7 right over here below the ones place in 253. And then put the multiplication
symbol right over here. So you could read
this as 253 times 7, which we know is the same
thing as 7 times 253. And now we are ready to compute. And there are many
ways of doing this, but this one you could
call the standard way. So what I do is I
start with my 7. And I multiply it times
each of the numbers up here, and I carry appropriately. So first I start with 7 times 3. Well, 7 times 3 we know is 21. Let me write that down. 7 times 3 is equal to 21. You could do this
part in your head, but I just want to
make it clear where I'm getting these numbers from. What I would do in
the standard method is I would write the
1 into 21 down here, but then carry the
2 to the tens place. Now I want to figure
out what 7 times 5 is. We know from our multiplication
tables that 7 times 5 is equal to 35. Now, we can't just somehow
put the 35 down here. We still have to deal with
this 2 that we carried. So we compute 7 times 5 is 35,
but then we also add that 2. So it's 35 plus 2 is 37. Now, we write the 7 right
over here in the tens place and carry the 3. Now we need to compute
what 7 times 2 is. We know that 7 times 2 is 14
from our multiplication tables. We can't just put
a 14 down here. We have this 3 to add. So 7 times 2 is
14, plus 3 is 17. So now we can write
the 17 down here, because 2 is the last number
that we had to deal with. And so we have our answer. 7 times 253 is 1,771.