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Compute 23 times 44.

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

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first hard part, is to recognize that that dot even

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means multiplication.

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

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

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you just put the two parentheses

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next to each other.

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That also implies multiplication.

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

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the problem.

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

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We're going to multiply 23 by 44.

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I'll write the traditional multiplication sign there,

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just so that we know we're multiplying.

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

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a dot there.

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So let's do some multiplication.

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Let's start off multiplying this 4 in the

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ones place times 23.

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So you have 3 times 4 is 12.

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

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carry the 1, or we want to regroup that

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1 in the tens place.

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

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

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

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here, times 23 is 92.

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That's what we just solved for.

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

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

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

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

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

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

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

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

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times 23 is 92.

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We just figured that out.

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If we just multiplied this 4 times 23 again, we

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would get 92 again.

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

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

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

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

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So this 4 now we're multiplying.

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4 times 3 is 12.

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Let's put the 2 right here.

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

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times the 3.

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Just think about it, or you could just

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think of the process.

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It's the next space that's free.

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4 times 3 is 12.

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Carry the 1.

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This blue 1 is from last time.

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You ignore it now.

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

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That's when we multiplied this 4.

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

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

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

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actually represents 40.

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It's in the tens place.

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

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

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I just want to make sure we understand

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what we're doing here.

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And so we can take their sum now.

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Let's add them up.

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2 plus 0 is 2.

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9 plus 2 is 11.

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Carry the 1.

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1 plus 9 is 10.

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

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read, every third digit.

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So 23 times 44 is 1,012.

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