1
00:00:00,165 --> 00:00:01,946
It never hurts to get a lot of practice.

2
00:00:01,961 --> 00:00:02,845
So, in this video I'm just going to do

3
00:00:02,845 --> 00:00:07,540
a bunch more of essentially what we call long division problems.

4
00:00:07,540 --> 00:00:17,040
And so if you have four divided into two thousand two hundred ninety-two.

5
00:00:17,050 --> 00:00:20,280
And I don't know exactly why they call it long division,

6
00:00:20,280 --> 00:00:23,580
and we saw this in the last video a little bit.

7
00:00:23,580 --> 00:00:25,548
I didn't call it long division then,

8
00:00:25,548 --> 00:00:28,486
but I think the reason why is it takes you a long time

9
00:00:28,486 --> 00:00:31,890
or it takes a long piece of your paper.

10
00:00:31,890 --> 00:00:35,102
As you go along, you kind of have this thing,

11
00:00:35,102 --> 00:00:37,270
this long tail that develops on the problem.

12
00:00:37,280 --> 00:00:39,663
So all of those are, at least, reasons in my head

13
00:00:39,663 --> 00:00:41,060
why it's called long division.

14
00:00:41,060 --> 00:00:44,588
But we saw in the last video there's a way to tackle any division problem

15
00:00:44,588 --> 00:00:46,746
while just knowing your multiplication tables

16
00:00:46,746 --> 00:00:49,810
up to maybe ten times ten or twelve times twelve.

17
00:00:49,820 --> 00:00:52,034
But just as a bit of review, this is the same thing

18
00:00:52,034 --> 00:00:57,854
as two thousand two hundred ninety-two divided by four.

19
00:00:57,854 --> 00:00:59,368
And it's actually the same thing--

20
00:00:59,368 --> 00:01:01,385
you probably haven't seen this notation before--

21
00:01:01,385 --> 00:01:06,644
as two thousand two hundred ninety-two divided by four.

22
00:01:06,644 --> 00:01:09,006
These-- This, this, and this--

23
00:01:09,006 --> 00:01:12,780
are all equivalent statements on some level.

24
00:01:12,790 --> 00:01:14,930
And you could say, hey Sal, that looks like a fraction.

25
00:01:14,930 --> 00:01:17,040
In case you have seen fractions already.

26
00:01:17,040 --> 00:01:18,550
And that is exactly what it is.

27
00:01:18,560 --> 00:01:20,060
It is a fraction.

28
00:01:20,060 --> 00:01:21,865
But anyway, I'll just focus on this format

29
00:01:21,865 --> 00:01:26,870
and in future videos we'll think about other ways to represent division.

30
00:01:26,870 --> 00:01:28,460
So let's do this problem.

31
00:01:28,460 --> 00:01:31,210
So four goes into two how many times?

32
00:01:31,210 --> 00:01:34,580
It goes into two no times, so let's move on to--

33
00:01:34,590 --> 00:01:35,320
let me switch colors--

34
00:01:35,320 --> 00:01:37,250
Let's move on to the twenty-two.

35
00:01:37,260 --> 00:01:40,100
Four goes into twenty-two how many times?

36
00:01:40,100 --> 00:01:40,380
Let's see.

37
00:01:40,390 --> 00:01:45,140
Four times five is equal to twenty.

38
00:01:45,140 --> 00:01:49,590
Four times six is equal to twenty-four.

39
00:01:49,590 --> 00:01:51,430
So six is too much.

40
00:01:51,430 --> 00:01:55,405
So four goes into twenty-two five times.

41
00:01:55,405 --> 00:01:58,050
Five times four is twenty.

42
00:01:58,059 --> 00:01:59,908
There's going to be a little bit of a leftover,

43
00:01:59,908 --> 00:02:02,166
And then we subtract.

44
00:02:02,166 --> 00:02:03,843
Twenty-two minus twenty?

45
00:02:03,843 --> 00:02:05,692
Well that's just two.

46
00:02:05,692 --> 00:02:08,710
And then you bring down this nine.

47
00:02:08,720 --> 00:02:11,148
And you saw in the last video exactly what this means, right?

48
00:02:11,148 --> 00:02:13,706
When you wrote this five up here, notice you wrote hundreds place.

49
00:02:13,706 --> 00:02:15,595
So this is really a five hundred.

50
00:02:15,595 --> 00:02:17,856
But in this video I'm just going to focus more on the process,

51
00:02:17,856 --> 00:02:19,860
and you can think more about what it actually means

52
00:02:19,870 --> 00:02:21,650
in terms of where I'm writing the numbers.

53
00:02:21,650 --> 00:02:24,358
But I think the process is going to be crystal clear,

54
00:02:24,358 --> 00:02:25,780
hopefully, by the end of this video.

55
00:02:25,780 --> 00:02:27,030
So we brought down the nine.

56
00:02:27,030 --> 00:02:29,960
Four goes into twenty-nine how many times?

57
00:02:29,970 --> 00:02:31,370
It goes into it at least six times.

58
00:02:31,380 --> 00:02:32,740
What's four times seven?

59
00:02:32,750 --> 00:02:34,840
Four times seven is twenty-eight.

60
00:02:34,840 --> 00:02:36,610
So it goes into it at least seven times.

61
00:02:36,610 --> 00:02:38,760
What's four times eight?

62
00:02:38,770 --> 00:02:41,770
Four times eight is thirty-two, so it can't go into it eight times.

63
00:02:41,770 --> 00:02:43,210
So it's going to go into it seven.

64
00:02:43,210 --> 00:02:46,390
Four goes into twenty-nine seven times.

65
00:02:46,400 --> 00:02:49,700
Seven times four is twenty-eight.

66
00:02:49,710 --> 00:02:51,684
Twenty-nine minus twenty-eight,

67
00:02:51,684 --> 00:02:56,370
to get our remainder for this step in the problem, is one.

68
00:02:56,370 --> 00:02:59,520
And now we're going to bring down this two.

69
00:02:59,530 --> 00:03:03,760
We're going to bring it down and you get a twelve.

70
00:03:03,770 --> 00:03:04,750
Four goes into twelve?

71
00:03:04,750 --> 00:03:05,170
That's easy.

72
00:03:05,180 --> 00:03:06,680
Four times three is twelve.

73
00:03:06,680 --> 00:03:09,080
Four goes into twelve three times.

74
00:03:09,080 --> 00:03:11,390
Three times four is twelve.

75
00:03:11,400 --> 00:03:13,360
Twelve minus twelve is zero.

76
00:03:13,360 --> 00:03:14,730
We have no remainder.

77
00:03:14,740 --> 00:03:20,390
So four goes into two thousand two hundred ninety-two exactly five hundred seventy-three times.

78
00:03:20,400 --> 00:03:26,500
So this two thousand two hundred ninety-two divided by four we can say is equal to five hundred seventy-three.

79
00:03:26,500 --> 00:03:32,240
Or we could say that this thing right here is equal to five hundred and seventy-three.

80
00:03:32,250 --> 00:03:34,680
Let's do a couple of more.

81
00:03:34,680 --> 00:03:39,080
Let's do a few more problems.

82
00:03:39,090 --> 00:03:40,960
So I'll do that red color.

83
00:03:40,960 --> 00:03:50,800
Let's say we had seven going into six thousand four hundred seventy-five.

84
00:03:50,810 --> 00:03:52,200
Maybe it's called long division

85
00:03:52,200 --> 00:03:54,350
because you write it nice and long up here and you have this line.

86
00:03:54,360 --> 00:03:55,610
I don't know.

87
00:03:55,610 --> 00:03:58,160
There's multiple reasons why it could be called long division.

88
00:03:58,160 --> 00:04:00,760
So you say seven goes into six zero times.

89
00:04:00,770 --> 00:04:03,660
So we need to keep moving forward.

90
00:04:03,660 --> 00:04:06,050
So then we go to sixty-four.

91
00:04:06,060 --> 00:04:09,160
Seven goes into sixty-four how many times?

92
00:04:09,160 --> 00:04:11,040
Let's see.

93
00:04:11,050 --> 00:04:15,300
Seven times seven is?

94
00:04:15,300 --> 00:04:16,800
Well, that's way too small.

95
00:04:16,800 --> 00:04:18,060
Let me think about it a little bit.

96
00:04:18,060 --> 00:04:20,610
Well seven times nine is sixty-three.

97
00:04:20,620 --> 00:04:21,390
That's pretty close.

98
00:04:21,390 --> 00:04:23,350
And then seven times ten is going to be too big.

99
00:04:23,360 --> 00:04:25,126
Seven times ten is seventy.

100
00:04:25,126 --> 00:04:25,982
So that's too big.

101
00:04:25,982 --> 00:04:29,681
So seven goes into sixty-four nine times.

102
00:04:29,711 --> 00:04:32,680
Nine times seven is sixty-three.

103
00:04:32,690 --> 00:04:38,040
Sixty-four minus sixty-three, to get our remainder at this stage, is one.

104
00:04:38,050 --> 00:04:41,230
Bring down the seven.

105
00:04:41,240 --> 00:04:43,110
Seven goes into seventeen how many times?

106
00:04:43,120 --> 00:04:45,240
Well, seven times two is fourteen.

107
00:04:45,240 --> 00:04:47,000
And then seven times three is twenty-one.

108
00:04:47,000 --> 00:04:48,590
So three is too big.

109
00:04:48,600 --> 00:04:51,490
So seven goes into seventeen two times.

110
00:04:51,500 --> 00:04:54,350
Two times seven is fourteen.

111
00:04:54,350 --> 00:04:57,610
Seventeen minus fourteen is three.

112
00:04:57,620 --> 00:05:03,527
And now we bring down the five.

113
00:05:03,527 --> 00:05:05,336
And seven goes into thirty-five--

114
00:05:05,350 --> 00:05:07,810
That's in our seven multiplication tables-- five times.

115
00:05:07,810 --> 00:05:14,093
Five times seven is thirty-five.

116
00:05:14,093 --> 00:05:15,465
And there you go.

117
00:05:15,465 --> 00:05:17,990
So the remainder is zero.

118
00:05:17,990 --> 00:05:20,120
So all the examples I did so far had no remainders.

119
00:05:20,120 --> 00:05:22,230
Let's do one that maybe might have a remainder.

120
00:05:22,240 --> 00:05:23,694
And to ensure it has a remainder,

121
00:05:23,694 --> 00:05:24,860
I'll just make up the problem.

122
00:05:24,870 --> 00:05:27,300
It's much easier to make problems that have remainders

123
00:05:27,310 --> 00:05:29,510
than the ones that don't have remainders.

124
00:05:29,510 --> 00:05:37,016
So let's say I want to divide three into--

125
00:05:37,016 --> 00:05:40,343
I'm going to divide it into

126
00:05:40,343 --> 00:05:47,365
let's say, one seven three five zero nine two.

127
00:05:47,365 --> 00:05:49,480
This will be a nice, beastly problem.

128
00:05:49,490 --> 00:05:50,940
So if we can do this we can handle everything.

129
00:05:50,940 --> 00:05:54,210
So it's one million seven hundred thirty-five thousand ninety-two.

130
00:05:54,220 --> 00:05:56,514
That's what we're dividing three into.

131
00:05:56,529 --> 00:05:58,721
So, three goes into--

132
00:05:58,721 --> 00:06:00,390
And actually, I'm not sure if this will have a remainder.

133
00:06:00,390 --> 00:06:03,136
In the future video I'll show you

134
00:06:03,136 --> 00:06:06,260
how to figure out whether something is divisible by three.

135
00:06:06,260 --> 00:06:07,150
Actually, we can do it right now.

136
00:06:07,160 --> 00:06:08,780
We can just add up all these digits.

137
00:06:08,790 --> 00:06:10,920
One plus seven is eight.

138
00:06:10,930 --> 00:06:13,180
Eight plus three is eleven.

139
00:06:13,180 --> 00:06:15,680
Eleven plus five is sixteen.

140
00:06:15,680 --> 00:06:20,240
Sixteen plus nine is twenty-five.

141
00:06:20,250 --> 00:06:22,190
Twenty-five plus two is twenty-seven.

142
00:06:22,190 --> 00:06:24,660
So actually, this number is divisible by three.

143
00:06:24,670 --> 00:06:27,420
So if you add up all of the digits, you get twenty-seven.

144
00:06:27,420 --> 00:06:28,878
And then you can add up those digits--

145
00:06:28,878 --> 00:06:30,545
Two plus seven is nine.

146
00:06:30,545 --> 00:06:32,120
So that is divisible by three.

147
00:06:32,120 --> 00:06:34,050
That's a trick that only works for three.

148
00:06:34,060 --> 00:06:35,880
So this number actually is divisible by three.

149
00:06:35,890 --> 00:06:37,698
So let me change it a little bit,

150
00:06:37,698 --> 00:06:41,260
so it's not divisible by three.

151
00:06:41,260 --> 00:06:44,867
Let me make this into a one.

152
00:06:44,867 --> 00:06:46,940
Now this number will not be divisible by three.

153
00:06:46,940 --> 00:06:50,425
I definitely want a number where I'll end up with a remainder.

154
00:06:50,425 --> 00:06:53,090
Just so you see what it looks like.

155
00:06:53,100 --> 00:06:54,570
So let's do this one.

156
00:06:54,570 --> 00:06:57,010
Three goes into one zero times.

157
00:06:57,020 --> 00:06:57,889
So we can just move forward.

158
00:06:57,889 --> 00:06:59,368
You could write a zero here,

159
00:06:59,368 --> 00:07:00,878
and multiply that out.

160
00:07:00,878 --> 00:07:03,207
But that just makes it a little bit messy in my head.

161
00:07:03,207 --> 00:07:04,368
So we just move one to the right.

162
00:07:04,383 --> 00:07:06,880
Three goes into seventeen how many times?

163
00:07:06,880 --> 00:07:11,050
Well, three times five is equal to fifteen.

164
00:07:11,060 --> 00:07:13,930
And three times six is equal to eighteen and that's too big.

165
00:07:13,930 --> 00:07:18,010
So three goes into seventeen right here five times.

166
00:07:18,010 --> 00:07:20,570
Five times three is fifteen.

167
00:07:20,570 --> 00:07:22,000
And we subtract.

168
00:07:22,010 --> 00:07:27,010
Seventeen minus fifteen is two.

169
00:07:27,010 --> 00:07:31,410
And now we bring down this three.

170
00:07:31,420 --> 00:07:33,480
Three goes into twenty-three how many times?

171
00:07:33,480 --> 00:07:36,740
Well, three times seven is equal to twenty-one.

172
00:07:36,750 --> 00:07:38,350
And three times eight is too big.

173
00:07:38,350 --> 00:07:40,010
That's equal to twenty-four.

174
00:07:40,010 --> 00:07:44,070
So three goes into twenty-three seven times.

175
00:07:44,080 --> 00:07:46,850
Seven times three is twenty-one.

176
00:07:46,860 --> 00:07:47,910
Then we subtract.

177
00:07:47,910 --> 00:07:51,740
Twenty-three minus twenty-one is two.

178
00:07:51,750 --> 00:07:53,420
Now we bring down the next number.

179
00:07:53,420 --> 00:07:54,570
We bring down the five.

180
00:07:54,570 --> 00:07:57,350
I think you can appreciate why it's called long division now.

181
00:07:57,360 --> 00:08:00,050
We bring down this five.

182
00:08:00,060 --> 00:08:02,040
Three goes into twenty-five how many times?

183
00:08:02,040 --> 00:08:04,506
Well three times eight gets you pretty close

184
00:08:04,506 --> 00:08:06,153
and three times nine is too big.

185
00:08:06,153 --> 00:08:08,230
So it goes into it eight times.

186
00:08:08,240 --> 00:08:10,170
Eight times three is twenty-four.

187
00:08:10,170 --> 00:08:12,210
I'm going to run out of space.

188
00:08:12,220 --> 00:08:14,170
You subtract, you get one.

189
00:08:14,180 --> 00:08:16,810
Twenty-five minus twenty-four is one.

190
00:08:16,810 --> 00:08:20,146
Now we can bring down this zero.

191
00:08:20,146 --> 00:08:23,059
You bring down this zero, just like that.

192
00:08:23,059 --> 00:08:25,254
And you get three goes into ten how many times?

193
00:08:25,254 --> 00:08:25,840
That's easy.

194
00:08:25,850 --> 00:08:26,940
It goes into it three times.

195
00:08:26,940 --> 00:08:28,000
Three times three is nine.

196
00:08:28,010 --> 00:08:30,070
That's about as close to ten as we can get.

197
00:08:30,080 --> 00:08:32,870
Three times three is nine.

198
00:08:32,870 --> 00:08:33,612
Ten minus nine--

199
00:08:33,612 --> 00:08:36,150
I'm going to have to scroll up and down here a little bit--

200
00:08:36,150 --> 00:08:37,712
Ten minus nine is one,

201
00:08:37,712 --> 00:08:39,681
and then we can bring down the next number.

202
00:08:39,681 --> 00:08:41,420
I'm running out of colors.

203
00:08:41,420 --> 00:08:44,750
I can bring down that nine.

204
00:08:44,750 --> 00:08:46,590
Three goes into nineteen how many times?

205
00:08:46,600 --> 00:08:48,880
Well, six is about as close as we can get.

206
00:08:48,880 --> 00:08:49,861
That gets us to eighteen.

207
00:08:49,861 --> 00:08:51,867
So three times six.

208
00:08:51,867 --> 00:08:53,659
Three goes into nineteen six times.

209
00:08:53,659 --> 00:08:56,390
Six times three-- let me scroll down.

210
00:08:56,400 --> 00:08:59,520
Six times three is eighteen.

211
00:08:59,530 --> 00:09:01,560
Nineteen minus eighteen-- we subtract it up here too.

212
00:09:01,570 --> 00:09:04,360
Nineteen minus eighteen is one and then we're almost done.

213
00:09:04,370 --> 00:09:06,120
I can revert back to the pink.

214
00:09:06,120 --> 00:09:09,900
We bring down this one right there.

215
00:09:09,910 --> 00:09:11,830
Three goes into eleven how many times?

216
00:09:11,840 --> 00:09:15,670
Well, that's three times because three times four is too big.

217
00:09:15,670 --> 00:09:17,170
Three times four is twelve, so that's too big.

218
00:09:17,170 --> 00:09:18,890
So it goes into it three times.

219
00:09:18,890 --> 00:09:22,260
So three goes into eleven three times.

220
00:09:22,260 --> 00:09:26,180
Three times three is nine.

221
00:09:26,190 --> 00:09:30,590
And then we subtract and we get a two.

222
00:09:30,600 --> 00:09:32,669
And there's nothing left to bring down.

223
00:09:32,669 --> 00:09:34,675
Right? When we look up here there's nothing left to bring down.

224
00:09:34,675 --> 00:09:35,750
So we're done!

225
00:09:35,750 --> 00:09:37,896
So we're left with the remainder of two,

226
00:09:37,896 --> 00:09:40,410
after doing this entire problem.

227
00:09:40,410 --> 00:09:45,313
So the answer, three goes into one million seven hundred thirty-five thousand ninety-one--

228
00:09:45,313 --> 00:09:52,940
it goes into it five hundred seventy-eight thousand three hundred sixty-three remainder two.

229
00:09:52,950 --> 00:09:57,190
And that remainder two was what we got all the way down there.

230
00:09:57,190 --> 00:09:58,417
So hopefully you now appreciate

231
00:09:58,417 --> 00:10:01,140
that you can tackle pretty much any division problem.

232
00:10:01,140 --> 00:10:02,940
And you also, through this exercise,

233
00:10:02,955 --> 00:10:06,110
can appreciate why it's called long division.