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## Multiply 2-digit numbers with partial products

Current time:0:00Total duration:4:07

# Multiplying 2-digit numbers

CCSS.Math:

## Video 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.