1
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Let's now see if we can divide into larger numbers.

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And just as a starting point, in order to divide into larger numbers,

3
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you at least need to know your multiplication tables

4
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from the one-multiplication tables all the way to, at least, the ten-multiplication.

5
00:00:14,550 --> 00:00:17,080
So all the way up to ten times ten, which you know is one hundred.

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And then, starting at one times one and going up to two times three,

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all the way up to ten times ten.

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And, at least when I was in school,

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we learned through twelve times twelve.

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But ten times ten will probably do the trick.

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And that's really just the starting point.

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Because to do multiplication problems like this,

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for example, or division problems like this.

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Let's say I'm taking twenty-five and I want to divide it by five.

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So I could draw twenty-five objects,

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and then divide them into groups of five or divide them into five groups,

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and see how many elements are in each group.

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But the quick way to do is just to think about,

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well, five times what is twenty-five, right?

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Five times question mark is equal to twenty-five.

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And if you know your multiplication tables,

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especially your five-multiplication tables,

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you know that five times five is equal to twenty-five.

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So something like this, you'll immediately just be able to say,

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because of your knowledge of multiplication,

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that five goes into twenty-five five times.

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And you'd write the five right there.

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Not over the two,

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because you still want to be careful of the place notation.

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You want to write the five in the ones place.

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It goes into it five ones times, or exactly five times.

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And the same thing.

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If I said seven goes into forty-nine.

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That's how many times?

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Well you say, that's like saying seven times what--

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you could even, instead of a question mark, you could put a blank there--

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seven times what is equal to forty-nine?

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And if you know your multiplication tables,

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you know that seven times seven is equal to forty-nine.

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All the examples I've done so far is a number multiplied by itself.

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Let me do another example.

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Let me do nine goes into fifty-four how many times?

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Once again, you need to know your multiplication tables to do this.

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Nine times what is equal to fifty-four?

45
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And sometimes, even if you don't have it memorized,

46
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you could say nine times five is forty-five.

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And nine times six would be nine more than that, so that would be fifty-four.

48
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So nine goes into fifty-four six times.

49
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So just as a starting point,

50
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you need to have your multiplication tables from one times one

51
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all the way up the ten times ten memorized.

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In order to be able to do at least some of these more basic problems relatively quickly.

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Now, with that out of the way, let's try to do some problems

54
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that might not fit completely cleanly into your multiplication tables.

55
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So let's say I want to divide--

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I am looking to divide three into forty-three.

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And, once again, this is larger than three times ten or three times twelve.

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Actually, look.

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Well, let me do another problem.

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Let me do three into twenty-three.

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And, if you know your three-times tables,

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you realize that there's three times nothing is exactly twenty-three.

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I'll do it right now.

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Three times one is three.

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Three times two is six.

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Let me just write them all out.

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Three times three is nine, twelve, fifteen, eighteen, twenty-one, twenty-four, right?

68
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There's no twenty-three in the multiples of three.

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So how do you do this division problem?

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Well what you do is you think of what is the largest multiple of three that does go into twenty-three?

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And that's twenty-one.

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And three goes into twenty-one how many times?

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Well you know that three times seven is equal to twenty-one.

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So you say, well three will go into twenty-three seven times.

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But it doesn't go into it cleanly,

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because seven times three is twenty-one.

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So there's a remainder left over.

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So if you take twenty-three minus twenty-one, you have a remainder of two.

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So you could write that twenty-three divided by three is equal to seven,

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remainder-- maybe I'll just, well, write the whole word out --remainder two.

81
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So it doesn't have to go in completely cleanly.

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And, in the future, we'll learn about decimals and fractions.

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But for now, you just say, well it goes in cleanly seven times,

84
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but that only gets us to twenty-one.

85
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But then there's two left over.

86
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So you can even work with the division problems

87
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where it's not exactly a multiple of the number

88
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that you're dividing into the larger number.

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But let's do some practice with even larger numbers.

90
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And I think you'll see a pattern here.

91
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So let's do four going into--

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I'm going to pick a pretty large number here --three hundred forty-four.

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And, immediately when you see that,

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you might say, hey Sal, I know up to four times ten or four times twelve.

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Four times twelve is forty-eight.

96
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This is a much larger number.

97
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This is way out of bounds

98
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of what I know in my four-multiplication tables.

99
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And what I'm going to show you right now is a way of doing this,

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just knowing your four-multiplication tables.

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So what you do is you say

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four goes into this three how many times?

103
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And you're actually saying

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00:05:17,479 --> 00:05:20,430
four goes into this three how many hundred times?

105
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So this is-- because this is three hundred, right?

106
00:05:22,590 --> 00:05:24,880
This is three hundred forty-four.

107
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But four goes into three no hundred times, or four goes into--

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I guess the best way to think of it --four goes three zero times.

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So you can just move on.

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Four goes into thirty-four.

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So now we're going to focus on the thirty-four.

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So four goes into thirty-four how many times?

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And here we can use our four-multiplication tables.

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Four-- Let's see, four times eight is equal to thirty-two.

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Four times nine is equal to thirty-six.

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So four goes into thirty-four-- nine is too many times, right?

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Thirty-six is larger than thirty-four.

118
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So four goes into thirty-four eight times.

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There's going to be a little bit left over.

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Four goes into thirty-four eight times.

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So let's figure out what's left over.

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And really we're saying,

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four goes into three hundred forty how many ten times?

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So we're actually saying four goes into three hundred forty eighty times.

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Because notice we wrote this eight in the tens place.

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But just for our ability to do this problem quickly,

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you just say four goes into thirty-four eight times,

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but make sure you write the eight in the tens place right there.

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Eight times four.

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We already know what that is.

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Eight times four is thirty-two.

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And then we figure out the remainder.

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Thirty-four minus thirty-two.

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Well, four minus two is two.

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And then these threes cancel out.

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So you're just left with a two.

137
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But notice we're in the tens column, right?

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This whole column right here, that's the tens column.

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So really what we said is four goes into three hundred forty eighty times.

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Eighty times four is three hundred twenty, right?

141
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Because I wrote the three in the hundreds column.

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And then, there is--

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let me clean this up a little bit.

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I didn't want to make that line there look like a--

145
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when I was dividing the columns-- to look like a one.

146
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But then there's a remainder of two,

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but I wrote the two in the tens place.

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So it's actually a remainder of twenty.

149
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But let me bring down this four.

150
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Because I didn't want to just divide into three hundred forty.

151
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I divided into three hundred forty-four.

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So you bring down the four.

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Let me switch colors.

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And then-- So another way to think about it.

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We just said that four goes into three hundred forty-four eighty times, right?

156
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We wrote the eight in the tens place.

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And then eight times four is three hundred twenty.

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The remainder is now twenty-four.

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So how many times does four go into twenty-four?

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Well we know that.

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Four times six is equal to twenty-four.

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So four goes into twenty-four six times.

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And we put that in the ones place.

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Six times four is twenty-four.

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And then we subtract.

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Twenty-four minus twenty-four.

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That's-- We subtract at that stage, either case.

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And we get zero.

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So there's no remainder.

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So four goes into three hundred forty-four exactly eighty-six times.

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So if your took three hundred forty-four objects and divided them into groups of four,

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you would get eighty-six groups.

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Or if you divided them into groups of eighty-six,

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you would get four groups.

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Let's do a couple more problems.

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I think you're getting the hang of it.

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Let me do seven-- I'll do a simple one.

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Seven goes into ninety-one.

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So once again, well, this is beyond seven times twelve,

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which is eighty-four, which you know from our multiplication tables.

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So we use the same system we did in the last problem.

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Seven goes into nine how many times?

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Seven goes into nine one time.

184
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One times seven is seven.

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And you have nine minus seven is two.

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And then you bring down the one.

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Twenty-one.

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And remember, this might seem like magic,

189
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but what we really said was seven goes into ninety ten
times--

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ten because we wrote the one in the tens place--

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00:08:59,961 --> 00:09:02,466
ten times seven is seventy.

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Right?-- You could almost put a zero there if you like--

193
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And ninety-one minus seventy is twenty-one.

194
00:09:08,380 --> 00:09:12,640
So seven goes into ninety-one ten times remainder twenty-one.

195
00:09:12,640 --> 00:09:15,780
And then you say seven goes into twenty-one-- Well you know that.

196
00:09:15,780 --> 00:09:17,590
Seven times three is twenty-one.

197
00:09:17,590 --> 00:09:20,170
So seven goes into twenty-one three times.

198
00:09:20,170 --> 00:09:22,710
Three times seven is twenty-one.

199
00:09:22,710 --> 00:09:24,550
You subtract these from each other.

200
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Remainder zero.

201
00:09:26,375 --> 00:09:31,908
So ninety-one divided by seven is equal to thirteen.

202
00:09:31,908 --> 00:09:32,530
Let's do another one.

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00:09:32,530 --> 00:09:35,863
And I won't take that little break to explain the places and all of that.

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00:09:35,863 --> 00:09:36,800
I think you understand that.

205
00:09:36,800 --> 00:09:41,569
I want, at least, you to get the process down really really well in this video.

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00:09:41,580 --> 00:09:44,990
So let's do seven-- I keep using the number seven.

207
00:09:44,990 --> 00:09:46,510
Let me do a different number.

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00:09:46,510 --> 00:09:56,560
Let me do eight goes into six hundred eight how many times?

209
00:09:56,560 --> 00:09:59,440
So I go eight goes into six how many times?

210
00:09:59,440 --> 00:10:00,740
It goes into it zero times.

211
00:10:00,740 --> 00:10:01,980
So let me keep moving.

212
00:10:01,980 --> 00:10:05,360
Eight goes into sixty how many times?

213
00:10:05,360 --> 00:10:06,820
Let me write down the eight.

214
00:10:06,820 --> 00:10:09,110
Let me draw a line here so we don't get confused.

215
00:10:09,110 --> 00:10:11,340
Let me scroll down a little bit.

216
00:10:11,340 --> 00:10:13,760
I need some space above the number.

217
00:10:13,760 --> 00:10:15,580
So eight goes into sixty how many times?

218
00:10:15,580 --> 00:10:19,590
We know that eight times seven is equal to fifty-six.

219
00:10:19,590 --> 00:10:23,330
And that eight times eight is equal to sixty-four.

220
00:10:23,330 --> 00:10:25,640
So eight goes into-- sixty-four is too big.

221
00:10:25,640 --> 00:10:26,770
So it's not this one.

222
00:10:26,771 --> 00:10:29,876
So eight goes into sixty, seven times.

223
00:10:29,876 --> 00:10:31,740
There's going to be a little bit left over.

224
00:10:31,740 --> 00:10:34,600
So eight goes into sixty, seven times.

225
00:10:34,600 --> 00:10:35,728
Since we're doing the whole sixty,

226
00:10:35,728 --> 00:10:38,799
we put the seven above the ones place in the sixty,

227
00:10:38,799 --> 00:10:41,062
which is the tens place in the whole thing.

228
00:10:41,062 --> 00:10:44,970
Seven times eight, we know, is fifty-six.

229
00:10:44,970 --> 00:10:47,100
Sixty minus fifty-six.

230
00:10:47,100 --> 00:10:48,030
That's four.

231
00:10:48,030 --> 00:10:48,990
We could do that in our heads.

232
00:10:48,990 --> 00:10:50,270
Or if we wanted, we can borrow.

233
00:10:50,270 --> 00:10:51,510
That be a ten.

234
00:10:51,510 --> 00:10:53,380
That would be a five.

235
00:10:53,380 --> 00:10:54,890
Ten minus six is four.

236
00:10:54,890 --> 00:10:59,930
Then you bring down this eight.

237
00:10:59,930 --> 00:11:02,738
Eight goes into forty-eight how many times?

238
00:11:02,750 --> 00:11:06,260
Well what's eight times six?

239
00:11:06,260 --> 00:11:09,210
Well, eight times six is exactly forty-eight.

240
00:11:09,210 --> 00:11:13,170
So eight times-- eight goes into forty-eight six times.

241
00:11:13,170 --> 00:11:17,180
Six times eight is forty-eight.

242
00:11:17,180 --> 00:11:18,180
And you subtract.

243
00:11:18,180 --> 00:11:19,500
We subtracted up here as well.

244
00:11:19,500 --> 00:11:22,020
Forty-eight minus forty-eight is zero.

245
00:11:22,020 --> 00:11:25,260
So, once again, we get a remainder of zero.

246
00:11:25,260 --> 00:11:28,798
So hopefully, that gives you the hang of how to do these larger division problems.

247
00:11:28,798 --> 00:11:31,012
And all we really need to know to be able to do these,

248
00:11:31,012 --> 00:11:34,242
to tackle these, is our multiplication tables

249
00:11:34,242 --> 00:11:38,381
up to maybe ten times ten or twelve times twelve.