Multiplying 3-digit by 1-digit (regrouping)
About this video
The video multiplies 7 x 253 with the standard method. 7 x 3 = 21 (write 1, carry 2), 7 x 5 = 35 plus the carried 2 is 37 (write 7, carry 3), and 7 x 2 = 14 plus 3 is 17, giving 1,771.
You'll be able to
- line up a three-digit and a one-digit number to multiply.
- carry (regroup) when a product is 10 or more.
- add the carried number after multiplying the next digit.
Key words
- carry
- Move the tens part of a product to the next place to the left, like carrying the 2 from 21.
- standard method
- The usual written way to multiply, working right to left and carrying.
- regroup
- Trade 10 of one place for 1 of the next, like 21 ones becoming 2 tens and 1 one.
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.
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