Multiplying Whole Numbers and Applications 2

U01_L3_T1_we2 Multiplying Whole Numbers and Applications 2

Compute 23 times 44.

And maybe the hardest part of
this problem, or maybe the

first hard part, is to recognize
that that dot even

means multiplication.

This could have also been
written as 23 times 44, or

they could have written it as 23
in parentheses times 44, so

you just put the
two parentheses

next to each other.

That also implies
multiplication.

So now that we know we're
multiplying, let's actually do

the problem.

So we're going to multiply 23--
I'll write it bigger.

We're going to multiply
23 by 44.

I'll write the traditional
multiplication sign there,

just so that we know
we're multiplying.

When you write it vertically
like this, you very seldom put

a dot there.

So let's do some
multiplication.

Let's start off multiplying
this 4 in the

ones place times 23.

So you have 3 times 4 is 12.

We can write 2 in the ones
place, but then we want to

carry the 1, or we want
to regroup that

1 in the tens place.

So it's 12, so you put
the 1 over here.

And now you have 4 times
2 is 8 plus 1 is 9.

So you can think about
it as 4, this 4 right

here, times 23 is 92.

That's what we just
solved for.

Now, we want to figure out
what this 4 times 23 is.

Now what we do here is, when you
just do it mechanically,

when you just learn the process,
you stick a 0 here.

But the whole reason why you're
putting a 0 here is

because you're now dealing with
a 4 in the tens place.

If you had another-- I don't
know, a 3 or a 4 or whatever

digit, and you're dealing with
the hundreds place, you'd put

more zeroes here, because we're
going to find out 4

times 23 is 92.

We just figured that out.

If we just multiplied this
4 times 23 again, we

would get 92 again.

But this 4 is actually a 40, so
it actually should be 920,

and that's why we're
putting that 0.

Now you're going to see
it in a second.

So we have-- so let me put this
in a different color.

So this 4 now we're
multiplying.

4 times 3 is 12.

Let's put the 2 right here.

It should be in the tens place
because this is really a 40

times the 3.

Just think about it,
or you could just

think of the process.

It's the next space
that's free.

4 times 3 is 12.

Carry the 1.

This blue 1 is from last time.

You ignore it now.

You don't want to make
that mess it up.

That's when we multiplied
this 4.

So now we have 4 times
2 is 8 plus 1 is 9.

So what we figured out so far is
4 times 23 is 92, and this

green 4 times 23 is 920, and
that's because this green 4

actually represents 40.

It's in the tens place.

So when you multiply 44 times
23, it's going to be 4 times

23, which is 92, plus 40
times 23, which is 920.

I just want to make
sure we understand

what we're doing here.

And so we can take
their sum now.

Let's add them up.

2 plus 0 is 2.

9 plus 2 is 11.

Carry the 1.

1 plus 9 is 10.

Put a comma here, just
so it's easy to

read, every third digit.

So 23 times 44 is 1,012.