About this video
Sal multiplies 36 x 27 by finding 36 x 7 = 252 and 36 x 20 = 720, then adding them to get 972. He does it twice: first just following the digit steps, then again explaining what each digit and carried number really represents in place value.
You'll be able to
- multiply a 2-digit number by a 2-digit number by splitting the second number into tens and ones.
- explain why we write a 0 before multiplying by the tens digit.
- explain what a carried digit represents in place value.
Key words
- ones place
- The rightmost digit position, showing how many ones.
- tens place
- The position to the left of the ones, showing how many tens, so the 2 in 27 means 20.
- hundreds place
- The position to the left of the tens, showing how many hundreds.
- carry
- Move a ten (or hundred) into the next place when a product is 10 or more in one place.
Transcript
In this video, we're going to multiply 36 times 27. So we're multiplying a two-digit number times another two-digit number. And the way that we're going to tackle it is we're going to first multiply 36 times 7, figure out what that is. Then we're going to multiply 36 times 20, figure out what that is, and then add those two numbers together.
And what I want to do is first do this, just show you the process for how to multiply these two numbers. And then I'm going to do it again where we're going to think a little bit more about what the different numbers represent. So first let's start with the process.
So I'm going to multiply 36 times 7 or 7 times 36. So I can start in the ones place. 7 times 6 is 42. Write the 2 down here. And then the 4, which represents 40, I can put in the tens place. 7 times 3 is 21, plus 4 is 25. So I could write the 25 right over here.
There's no place to carry this 2, so I just wrote the 2 right over here in the hundreds place. Now let's move over. So let me clean this up so we don't get confused. So we just figured out what 7 times 36 is. It is 252. Now let's worry about what 36 times 20 is.
And so what we're going to do is we're going to throw a 0 right over here, because we're now going to multiply 36 times something in the tens place. This isn't just a 2. This is a 20. So let's just go with the digits right now and then we'll think about it in terms of place value the second time around.
2 times 6 is 12. Write the 2 right over here. Carry the 1. 2 times 3 is 6, plus 1 is 7. So we just figured out that 36 times 20 is 720. And just think about what would've happened if we didn't put the 0 here. Then we would have figured out that 36 times 2 is 72, but this 2 isn't just a 2.
This is a 20. So 36 times 20 is 720. And now we can add these two things because 36 times 27 is the same thing as 36 times 20 plus 36 times 7. So let's add these two numbers together. 2 plus 0 is 2. 5 plus 2 is 7. 2 plus 7 is 9. And we get 972. Now I'm going to do this exact same problem again.
But this time, I'm going to really talk about what these digits represent. Hopefully the first pass, you kind of saw the process for doing it. Now we're going to think about what these digits actually represent. So we're going to multiply 36 times 7. So 7 times 6 is 42.
We would write the 2 in the ones place, and then the 40 we can write in the tens place. This 4 represents 40. 7 times 30 is 210, plus 40 is 250. And we already had that 2 in the ones place, so we get 252. 36 times 7 is 252. Now let's clean this up. Now let's multiply-- 20 times 6 is going to give us 120.
So let's write the 20 in the tens place, and then carry the 100, or carry the 1, which represents 100. Now, 2 times-- or I should say 20 times 30 is going to give you 600, plus one more 100 is going to give you 700. So we just figured out that 36 times 20 is 720.
The 7 is in the hundreds place, 2 in the tens place. And then we can add again. And just like we did the last time, we got 972.
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