- [Instructor] In a previous video,
we figured out a way to multiply a two-digit number
times one-digit number.
What we did is we broke up the two-digit numbers
in terms of its place value, so the three here in the tenths
place that's three tens, this is seven ones.
So we view 37 sixes as the same thing as 30 sixes,
three tens times six plus seven sixes, seven times six.
And then we added those together to get a total of 222.
What we'll try in this video is now see what happens if we
try to do two digits times two digits, so let's try
to tackle 37, 37 instead of six let's multiply that times 26
so we're trying to figure out 37 26's is one way
to think about it.
So pause this video and see if you can tackle that
and see if you can maybe use a similar method to what
we used before.
Well one way to think about it is you could view this
as 37 26's or you could view this as 37 sixes plus 37 20's.
So first we could do the 37 sixes which is exactly what
we did over here, we said hey that's the same thing and we
could do it in either order we could say hey let's first
think about 30 sixes, so we're going to multiply 30 times
six 30 sixes is 180, so that right over there is three tens
times six.
And then we could think about the seven ones times six.
And so that's going to be 42.
That's the seven ones times six or the seven sixes.
And then we could do the same thing with the 20's we could
say hey what are three tens, what are 30 20's going to be.
So let's write that over here or you could say what are
three tens times two tens.
Well that would be six times ten times ten, so let me write
this down this is three tens times two tens that's what
we're going to do now.
Times two tens and that's the same thing as which is
equal to 30 times 20 which is the same thing as three
times two times ten times ten.
Well that's going to be 600, so we could write that here
600 and just be very clear, we've already thought about
37 sixes, that's these two numbers up here we have to add
that we still have to add them.
But now we're thinking about 37 20's so first we thought
about 30 20's which is 600 and now we could think about
seven 20's so seven 20's is going to be seven times two
is 14 so seven times 20 is 140.
So I'll write that right over here.
140 to be clear this is seven ones times two tens.
Or seven 20's and now we can add it all together
to get what the total would be.
So in the total we have, that's why it's useful to have
everything stacked by their place value, we could look
at the ones place so we say okay we only have a total
of two ones here, so I'll put a two there.
Now let's see tens we have eight tens plus four tens
is 12 tens plus another four tens is 16 tens.
16 tens we can also break up as 106 tens, so we could write
the six tens here and then put that 100 up here.
So 100 plus another hundred is 200 plus 600's is 800's
plus one more hundred is 900's.
And so there you have it, this is equal to 962.
I really want you to understand what we just did,
it might look a little bit complicated but first we thought
about what is 37 sixes that's where we got these numbers
from and that's what we had done in a previous video.
And then we just thought about well what is 37 20's
going to be and that's where these numbers came from
and actually let me write that down.
This whole thing that I'm circling in orange, that is 37
sixes or I'll write it as 37 times six and then this is
37 20's so 37 times 20.
So if it's not obvious, pause the video or after this video
reflect on why this works, try it with other numbers
'cause if you really understand this then your
multiplication life and actually your mathematical lives
in your future will only become more and more intuitive.