Multi-digit multiplication
Multiple Digit Numbers Working our way up to multiplying multiple-digit numbers with each other
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- We now have the general tools
- to really tackle any multiplication problems.
- So in this video I'm just going to do a ton of examples.
- So let's start off with-- and I'll start in yellow.
- Let's start off with thirty-two times eighteen.
- Say eight times two is sixteen.
- Well, I'll do it in our head this time
- because you don't always have all this space to work with.
- So eight times two is sixteen.
- Put the one up there.
- Eight times three is twenty-four.
- Twenty-four plus one is twenty-five.
- So eight times thirty-two was two hundred fifty-six.
- Now we're going to have to multiply this one,
- which is really a ten, times thirty-two.
- I'll underline it with the orange.
- One times two-- oh, we have to be very careful here.
- One times two is two.
- So you might say hey, let me stick a two down there.
- Remember, this isn't a one.
- This is a ten, so we have to stick a zero there
- to remember that.
- So ten times two is twenty.
- Or you say one times two is two,
- but you're putting it in the tens place, so you still get twenty.
- So ten times two is twenty.
- It works out.
- Then one times three.
- And we have to be very careful.
- Let's get rid of what we had from before.
- One times three is three.
- There's nothing to add here, so you just get a three.
- And so you get ten times thirty-two is three hundred twenty.
- This one right here, that's a ten.
- Ten plus eight is eighteen.
- So now we just add up the two numbers.
- You add them up.
- Six plus zero is six.
- Five plus two is seven.
- Two plus three is five.
- Let's keep going.
- Let's do ninety-nine times eighty-eight.
- That's going to give us a big number!
- Eight times nine is seventy-two.
- Stick the seven up there.
- And then you have eight times nine again.
- Eight times nine is seventy-two, but now you have the seven up here.
- So seventy-two plus seven is seventy-nine.
- Fair enough.
- Now we're done with this.
- Let's just delete it
- just so that we don't get confused in our next step.
- In our next step, we're going to multiply this eight now times ninety-nine.
- But this eight is an eighty.
- So let's stick a zero down there.
- Eight times nine is seventy-two.
- Stick a seven up there.
- Then eight times nine is seventy-two.
- Plus seven is seventy-nine.
- Two plus zero is two.
- Let me switch colors.
- Nine plus two is eleven.
- Carry the one.
- One plus seven is eight.
- Eight plus nine is seventeen.
- Carry the one.
- One plus seven is eight.
- Eight thousand seven hundred twelve.
- Let's keep going.
- Can't do enough of these.
- All right, fifty-three times seventy-eight.
- I think you're getting the hang of it now.
- Let's multiply eight times fifty-three first.
- So eight times three is twenty-four.
- Stick the two up there.
- Eight times five is forty.
- Forty plus two is forty-two.
- Now we're going to have to deal with that seven.
- That seven right there, which is really a seventy.
- So we got to remember to put the zero there.
- Seven times three, and let's get rid of this.
- Don't want to get confused.
- Seven times three is twenty-one.
- Put the one there and put the two up here.
- Seven times five is thirty-five.
- Plus two is thirty-seven.
- Now we're ready to add.
- Four plus zero is four.
- Two plus one is three.
- Four plus seven is eleven.
- Carry the one.
- One plus three is four.
- Four thousand one hundred thirty-four.
- Let's up the stakes a little bit.
- So let's say I had seven hundred ninety-six times fifty-eight.
- Let's mix it up well.
- All right, so first we're just going to multiply eight times seven hundred ninety-six.
- And notice, I've thrown in an extra digit up here.
- So eight times six is forty-eight.
- Put the four up there.
- Eight times nine is seventy-two.
- Plus four is seventy-six.
- And then eight times seven is fifty-six.
- Fifty-six plus seven is sixty-three.
- I'm sure I'll make a careless mistake
- at some point in this video.
- And the goal for you is to identify if and when I do.
- All right, now we're ready,
- so we can get rid of these guys up here.
- Now we can multiply this five, which is in the tens place.
- It's really a fifty.
- Times this up here.
- Because it's a fifty we stick a zero down there.
- Five times six is thirty.
- Put the zero there, put the three up there.
- Five times nine is forty-five.
- Plus the three is forty-eight.
- Five times seven is thirty-five.
- Plus four is thirty-nine.
- Now we're ready to add.
- Eight plus zero is eight.
- Six plus zero is six.
- Three plus eight is eleven.
- One plus six is seven.
- Seven plus nine is sixteen.
- And then one plus three is four.
- So seven hundred ninety-six times fifty-eight is forty-six thousand one hundred sixty-eight.
- And that sounds about right,
- because seven hundred ninety-six-- it's almost eight hundred.
- You know, which is almost one thousand.
- So if we multiplied one thousand times fifty-eight we'd get fifty-eight thousand.
- But we're multiplying something a little bit smaller
- than one thousand times fifty-eight,
- so we're getting something a little bit smaller than fifty-eight thousand.
- So the number is in the correct ballpark.
- Now let's do one more here
- where I'm really going to step up the stakes.
- Let's do five hundred twenty-three times--
- I'm going to do a three-digit number now.
- Times seven hundred ninety-eight.
- That's a big three-digit number!
- But it's the same exact process.
- And once you kind of see the pattern
- you'll say, hey, this'll apply to any number of digits times any number of digits.
- It'll just start taking you a long time
- and your chances of making a careless mistake are going to go up,
- but it's the same idea.
- So we start with eight times five hundred twenty-three.
- Eight times three is twenty-four.
- Stick the two up there.
- Now eight times two is sixteen.
- Sixteen plus two is eighteen.
- Put the one up there.
- Eight times five is forty.
- Plus one is forty-one.
- So eight times five hundred twenty-three is four thousand one hundred eighty-four.
- We're not done.
- We have to multiply times the ninety and by the seven hundred.
- So let's do the ninety right there.
- So it's a ninety, so we'll stick a zero there.
- It's not a nine.
- And let's get rid of these guys right there.
- Nine times three is twenty-seven.
- Nine times two is eighteen.
- Eighteen plus two is twenty.
- And then we have nine times five is forty-five.
- Forty-five plus two is forty-seven.
- I don't want to write it that thick.
- Forty-seven.
- Let me make sure I did that one right,
- and let's just review it a little bit.
- Nine times three was twenty-seven.
- We wrote the seven down here and put the two up there.
- Nine times two is eighteen.
- We added two to that, so we wrote twenty.
- Wrote the zero down there and the two up there.
- The nine times five was forty-five.
- Plus two is forty-seven.
- You really have to make sure
- that you don't make careless mistakes with these.
- Then finally, we have to multiply the seven,
- which is really a seven hundred times five hundred twenty-three.
- When it was just an eight we just started multiplying here.
- When it was a ninety, when we were dealing with the tens place,
- we put a zero there.
- Now that we're dealing with something that's in the hundreds
- we're going to put two zeros there.
- And so you have seven-- and let's get rid of this stuff.
- Seven times three is twenty-one.
- Put the one there.
- Stick the two up there.
- Seven times two is fourteen.
- Fourteen plus our two is sixteen.
- Put the one up there.
- Seven times five is thirty-five.
- Plus one is thirty-six.
- And now we're ready to add.
- And hopefully we didn't make any careless mistakes.
- So four plus zero plus zero.
- That's easy.
- That's four.
- Eight plus seven plus zero.
- That's fifteen.
- Carry the one.
- One plus one plus one is three.
- Four plus seven plus six.
- That's what's?
- Four plus six is ten.
- It's seventeen.
- And then we have one plus four is five.
- Five plus six is eleven.
- Carry the one.
- One plus three is four.
- So five hundred twenty-three times seven hundred ninety-eight
- is four hundred seventeen thousand three hundred fifty-four.
- Now we can even check to make sure.
- And so this is the moment of truth.
- Let's see if we have-- let's see,
- five hundred twenty-three times seven hundred ninety-eight.
- There you go.
- Moment of truth.
- I don't have to re-record this video.
- It's four hundred seventeen thousand three hundred fifty-four.
- But we did it without the calculator,
- which is the important point.
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