1
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2
00:00:00,740 --> 00:00:03,400
Let's now see if we can divide into larger numbers.

3
00:00:03,399 --> 00:00:06,660
And just as a starting point, in order to divide into larger

4
00:00:06,660 --> 00:00:09,919
numbers, you at least need to know your multiplication tables

5
00:00:09,919 --> 00:00:12,949
from the 1-multiplication tables all the way to, at

6
00:00:12,949 --> 00:00:14,539
least, the 10-multiplication.

7
00:00:14,539 --> 00:00:17,079
So all the way up to 10 times 10, which you know is 100.

8
00:00:17,079 --> 00:00:20,269
And then, starting at 1 times 1 and going up to 2 times 3, all

9
00:00:20,269 --> 00:00:22,320
the way up to 10 times 10.

10
00:00:22,320 --> 00:00:24,350
And, at least when I was in school, we learned

11
00:00:24,350 --> 00:00:25,339
through 12 times 12.

12
00:00:25,339 --> 00:00:28,100
But 10 times 10 will probably do the trick.

13
00:00:28,100 --> 00:00:29,770
And that's really just the starting point.

14
00:00:29,769 --> 00:00:32,549
Because to do multiplication problems like this, for

15
00:00:32,549 --> 00:00:34,149
example, or division problems like this.

16
00:00:34,149 --> 00:00:39,640
Let's say I'm taking 25 and I want to divide it by 5.

17
00:00:39,640 --> 00:00:42,980
So I could draw 25 objects and then divide them into groups of

18
00:00:42,979 --> 00:00:46,049
5 or divide them into 5 groups and see how many elements

19
00:00:46,049 --> 00:00:47,589
are in each group.

20
00:00:47,590 --> 00:00:49,900
But the quick way to do is just to think about, well

21
00:00:49,899 --> 00:00:52,929
5 times what is 25, right?

22
00:00:52,929 --> 00:00:58,100
5 times question mark is equal to 25.

23
00:00:58,100 --> 00:00:59,859
And if you know your multiplication tables,

24
00:00:59,859 --> 00:01:02,070
especially your 5-multiplication tables,

25
00:01:02,070 --> 00:01:06,280
you know that 5 times 5 is equal to 25.

26
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So something like this, you'll immediately just be able to

27
00:01:08,480 --> 00:01:12,230
say, because of your knowledge of multiplication, that 5

28
00:01:12,230 --> 00:01:14,840
goes into 25 five times.

29
00:01:14,840 --> 00:01:16,320
And you'd write the 5 right there.

30
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Not over the 2, because you still want to be careful

31
00:01:18,579 --> 00:01:20,039
of the place notation.

32
00:01:20,040 --> 00:01:21,650
You want to write the 5 in the ones place.

33
00:01:21,650 --> 00:01:25,480
It goes into it 5 ones times, or exactly five times.

34
00:01:25,480 --> 00:01:26,189
And the same thing.

35
00:01:26,189 --> 00:01:31,769
If I said 7 goes into 49.

36
00:01:31,769 --> 00:01:33,250
That's how many times?

37
00:01:33,250 --> 00:01:36,909
Well you say, that's like saying 7 times what-- you could

38
00:01:36,909 --> 00:01:38,849
even, instead of a question mark, you could put a blank

39
00:01:38,849 --> 00:01:43,129
there --7 times what is equal to 49?

40
00:01:43,129 --> 00:01:45,759
And if you know your multiplication tables, you know

41
00:01:45,760 --> 00:01:50,090
that 7 times 7 is equal to 49.

42
00:01:50,090 --> 00:01:52,159
All the examples I've done so far is a number

43
00:01:52,159 --> 00:01:53,149
multiplied by itself.

44
00:01:53,150 --> 00:01:55,030
Let me do another example.

45
00:01:55,030 --> 00:02:01,840
Let me do 9 goes into 54 how many times?

46
00:02:01,840 --> 00:02:03,840
Once again, you need to know your multiplication

47
00:02:03,840 --> 00:02:05,100
tables to do this.

48
00:02:05,099 --> 00:02:09,289
9 times what is equal to 54?

49
00:02:09,289 --> 00:02:10,965
And sometimes, even if you don't have it memorized, you

50
00:02:10,966 --> 00:02:14,719
could say 9 times 5 is 45.

51
00:02:14,719 --> 00:02:19,469
And 9 times 6 would be 9 more than that, so that would be 54.

52
00:02:19,469 --> 00:02:22,379
So 9 goes into 54 six times.

53
00:02:22,379 --> 00:02:24,389
So just as a starting point, you need to have your

54
00:02:24,389 --> 00:02:27,929
multiplication tables from 1 times 1 all the way up the

55
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10 times 10 memorized.

56
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In order to be able to do at least some of these more basic

57
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problems relatively quickly.

58
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Now, with that out of the way, let's try to do some problems

59
00:02:39,060 --> 00:02:41,599
that's might not fit completely cleanly into your

60
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multiplication tables.

61
00:02:43,990 --> 00:02:47,189
So let's say I want to divide-- I am looking

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00:02:47,189 --> 00:02:54,800
to divide 3 into 43.

63
00:02:54,800 --> 00:02:58,439
And, once again, this is larger than 3 times 10 or 3 times 12.

64
00:02:58,439 --> 00:02:58,930
Actually, look.

65
00:02:58,930 --> 00:03:00,950
Well, let me do another problem.

66
00:03:00,949 --> 00:03:04,259
Let me do 3 into 23.

67
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And, if you know your 3-times tables, you realize that

68
00:03:07,150 --> 00:03:10,060
there's 3 times nothing is exactly 23.

69
00:03:10,060 --> 00:03:10,909
I'll do it right now.

70
00:03:10,909 --> 00:03:13,280
3 times 1 is 3.

71
00:03:13,280 --> 00:03:15,689
3 times 2 is 6.

72
00:03:15,689 --> 00:03:16,870
Let me just write them all out.

73
00:03:16,870 --> 00:03:24,689
3 times 3 is 9, 12, 15, 18, 21, 24, right?

74
00:03:24,689 --> 00:03:27,699
There's no 23 in the multiples of 3.

75
00:03:27,699 --> 00:03:29,699
So how do you do this division problem?

76
00:03:29,699 --> 00:03:32,879
Well what you do is you think of what is the largest multiple

77
00:03:32,879 --> 00:03:34,439
of 3 that does go into 23?

78
00:03:34,439 --> 00:03:36,639
And that's 21.

79
00:03:36,639 --> 00:03:39,169
And 3 goes into 21 how many times?

80
00:03:39,169 --> 00:03:44,149
Well you know that 3 times 7 is equal to 21.

81
00:03:44,150 --> 00:03:48,520
So you say, well 3 will go into 23 seven times.

82
00:03:48,520 --> 00:03:50,570
But it doesn't go into it cleanly because

83
00:03:50,569 --> 00:03:53,849
7 times 3 is 21.

84
00:03:53,849 --> 00:03:55,750
So there's a remainder left over.

85
00:03:55,750 --> 00:04:00,169
So if you take 23 minus 21, you have a remainder of 2.

86
00:04:00,169 --> 00:04:08,009
So you could write that 23 divided by 3 is equal to 7

87
00:04:08,009 --> 00:04:10,780
remainder-- maybe I'll just, well, write the whole

88
00:04:10,780 --> 00:04:15,009
word out --remainder 2.

89
00:04:15,009 --> 00:04:17,050
So it doesn't have to go in completely cleanly.

90
00:04:17,050 --> 00:04:19,790
And, in the future, we'll learn about decimals and fractions.

91
00:04:19,790 --> 00:04:22,470
But for now, you just say, well it goes in cleanly 7 times,

92
00:04:22,470 --> 00:04:24,290
but that only gets us to 21.

93
00:04:24,290 --> 00:04:26,110
But then there's 2 left over.

94
00:04:26,110 --> 00:04:28,830
So you can even work with the division problems where it's

95
00:04:28,829 --> 00:04:31,939
not exactly a multiple of the number that you're dividing

96
00:04:31,939 --> 00:04:33,310
into the larger number.

97
00:04:33,310 --> 00:04:37,720
But let's do some practice with even larger numbers.

98
00:04:37,720 --> 00:04:40,520
And I think you'll see a pattern here.

99
00:04:40,519 --> 00:04:47,719
So let's do 4 going into-- I'm going to pick a pretty

100
00:04:47,720 --> 00:04:51,800
large number here --344.

101
00:04:51,800 --> 00:04:55,340
And, immediately when you see that you might say, hey Sal, I

102
00:04:55,339 --> 00:04:57,849
know up to 4 times 10 or 4 times 12.

103
00:04:57,850 --> 00:04:59,850
4 times 12 is 48.

104
00:04:59,850 --> 00:05:01,340
This is a much larger number.

105
00:05:01,339 --> 00:05:03,689
This is way out of bounds of what I know in my

106
00:05:03,689 --> 00:05:05,420
4-multiplication tables.

107
00:05:05,420 --> 00:05:07,610
And what I'm going to show you right now is a way of doing

108
00:05:07,610 --> 00:05:10,910
this just knowing your 4-multiplication tables.

109
00:05:10,910 --> 00:05:12,920
So what you do is you say 4 goes into this

110
00:05:12,920 --> 00:05:16,800
3 how many times?

111
00:05:16,800 --> 00:05:18,910
And you're actually saying 4 goes into this 3 how

112
00:05:18,910 --> 00:05:20,430
many hundred times?

113
00:05:20,430 --> 00:05:22,590
So this is-- Because this is 300, right?

114
00:05:22,589 --> 00:05:24,879
This is 344.

115
00:05:24,879 --> 00:05:30,180
But 4 goes into 3 no hundred times, or 4 goes into-- I guess

116
00:05:30,180 --> 00:05:32,810
the best way to think of it --4 goes 3 0 times.

117
00:05:32,810 --> 00:05:34,470
So you can just move on.

118
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4 goes into 34.

119
00:05:36,259 --> 00:05:41,459
So now we're going to focus on the 34.

120
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So 4 goes into 34 how many times?

121
00:05:43,899 --> 00:05:46,899
And here we can use our 4-multiplication tables.

122
00:05:46,899 --> 00:05:51,949
4-- Let's see, 4 times 8 is equal to 32.

123
00:05:51,949 --> 00:05:56,209
4 times 9 is equal to 36.

124
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So 4 goes into 34-- 30-- 9 is too many times, right?

125
00:05:59,629 --> 00:06:01,500
36 is larger than 34.

126
00:06:01,500 --> 00:06:03,740
So 4 goes into 34 eight times.

127
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There's going to be a little bit left over.

128
00:06:06,000 --> 00:06:09,050
4 goes in the 34 eights times.

129
00:06:09,050 --> 00:06:10,860
So let's figure out what's left over.

130
00:06:10,860 --> 00:06:15,000
And really we're saying 4 goes into 340 how many ten times?

131
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We're actually saying 4 goes into 340 eighty times.

132
00:06:17,800 --> 00:06:20,040
Because notice we wrote this 8 in the tens place.

133
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But just for our ability to do this problem quickly, you just

134
00:06:23,019 --> 00:06:26,399
say 4 goes into 34 eight times, but make sure you write the 8

135
00:06:26,399 --> 00:06:28,769
in the tens place right there.

136
00:06:28,769 --> 00:06:30,099
8 times 4.

137
00:06:30,100 --> 00:06:30,970
We already know what that is.

138
00:06:30,970 --> 00:06:34,140
8 times 4 is 32.

139
00:06:34,139 --> 00:06:36,289
And then we figure out the remainder.

140
00:06:36,290 --> 00:06:38,160
34 minus 32.

141
00:06:38,160 --> 00:06:40,400
Well, 4 minus 2 is 2.

142
00:06:40,399 --> 00:06:42,029
And then these 3's cancel out.

143
00:06:42,029 --> 00:06:43,299
So you're just left with a 2.

144
00:06:43,300 --> 00:06:46,120
But notice we're in the tens column, right?

145
00:06:46,120 --> 00:06:48,709
This whole column right here, that's the tens column.

146
00:06:48,709 --> 00:06:55,120
So really what we said is 4 goes into 340 eighty times.

147
00:06:55,120 --> 00:06:58,350
80 times 4 is 320, right?

148
00:06:58,350 --> 00:07:00,850
Because I wrote the 3 in the hundreds column.

149
00:07:00,850 --> 00:07:04,000
And then there is-- and I don't want to make this look like a--

150
00:07:04,000 --> 00:07:06,319
I don't want to make this look like a-- Let me clean

151
00:07:06,319 --> 00:07:07,110
this up a little bit.

152
00:07:07,110 --> 00:07:09,009
I didn't want to make that line there look like a-- when I was

153
00:07:09,009 --> 00:07:10,509
dividing the columns --to look like a 1.

154
00:07:10,509 --> 00:07:12,379
But then there's a remainder of 2, but I wrote the

155
00:07:12,379 --> 00:07:14,269
2 in the tens place.

156
00:07:14,269 --> 00:07:15,740
So it's actually a remainder of 20.

157
00:07:15,740 --> 00:07:16,990
But let me bring down this 4.

158
00:07:16,990 --> 00:07:18,660
Because I didn't want to just divide into 340.

159
00:07:18,660 --> 00:07:20,290
I divided into 344.

160
00:07:20,290 --> 00:07:22,290
So you bring down the 4.

161
00:07:22,290 --> 00:07:24,439
Let me switch colors.

162
00:07:24,439 --> 00:07:26,670
And then-- So another way to think about it.

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00:07:26,670 --> 00:07:31,250
We just said that 4 goes into 344 eighty times, right?

164
00:07:31,250 --> 00:07:33,050
We wrote the 8 in the tens place.

165
00:07:33,050 --> 00:07:35,550
And then 8 times 4 is 320.

166
00:07:35,550 --> 00:07:38,170
The remainder is now 24.

167
00:07:38,170 --> 00:07:40,800
So how many times does 4 go into 24?

168
00:07:40,800 --> 00:07:41,620
Well we know that.

169
00:07:41,620 --> 00:07:46,000
4 times 6 is equal to 24.

170
00:07:46,000 --> 00:07:49,089
So 4 goes into 24 six times.

171
00:07:49,089 --> 00:07:50,549
And we put that in the ones place.

172
00:07:50,550 --> 00:07:53,480
6 times 4 is 24.

173
00:07:53,480 --> 00:07:54,560
And then we subtract.

174
00:07:54,560 --> 00:07:56,269
24 minus 24.

175
00:07:56,269 --> 00:07:58,490
That's-- We subtract at that stage, either case.

176
00:07:58,490 --> 00:07:59,530
And we get 0.

177
00:07:59,529 --> 00:08:01,049
So there's no remainder.

178
00:08:01,050 --> 00:08:05,850
So 4 goes into 344 exactly eighty-six times.

179
00:08:05,850 --> 00:08:09,180
So if your took 344 objects and divided them into groups of

180
00:08:09,180 --> 00:08:10,900
4, you would get 86 groups.

181
00:08:10,899 --> 00:08:12,949
Or if you divided them into groups of 86, you

182
00:08:12,949 --> 00:08:13,879
would get 4 groups.

183
00:08:13,879 --> 00:08:15,639
Let's do a couple more problems.

184
00:08:15,639 --> 00:08:18,439
I think you're getting the hang of it.

185
00:08:18,439 --> 00:08:21,180
Let me do 7-- I'll do a simple one.

186
00:08:21,180 --> 00:08:24,790
7 goes into 91.

187
00:08:24,790 --> 00:08:28,710
So once again, well, this is beyond 7 times 12, which

188
00:08:28,709 --> 00:08:31,339
is 84, which you know from our multiplication tables.

189
00:08:31,339 --> 00:08:34,649
So we use the same system we did in the last problem.

190
00:08:34,649 --> 00:08:37,750
7 goes into 9 how many times?

191
00:08:37,750 --> 00:08:41,220
7 goes into 9 one time.

192
00:08:41,220 --> 00:08:44,639
1 times 7 is 7.

193
00:08:44,639 --> 00:08:48,330
And you have 9 minus 7 is 2.

194
00:08:48,330 --> 00:08:51,190
And then you bring down the 1.

195
00:08:51,190 --> 00:08:51,770
21.

196
00:08:51,769 --> 00:08:53,590
And remember, this might seem like magic, but what we really

197
00:08:53,590 --> 00:08:58,530
said was 7 goes into 90 ten times-- 10 because we wrote the

198
00:08:58,529 --> 00:09:02,839
1 in the tens place --10 times 7 is 70, right?

199
00:09:02,840 --> 00:09:05,000
You can almost put a 0 there if you like.

200
00:09:05,000 --> 00:09:08,409
And 90 with the remainder-- And 91 minus 70 is 21.

201
00:09:08,409 --> 00:09:12,639
So 7 goes into 91 ten times remainder 21.

202
00:09:12,639 --> 00:09:15,779
And then you say 7 goes into 21-- Well you know that.

203
00:09:15,779 --> 00:09:17,589
7 times 3 is 21.

204
00:09:17,590 --> 00:09:20,170
So 7 goes into 21 three times.

205
00:09:20,169 --> 00:09:22,709
3 times 7 is 21.

206
00:09:22,710 --> 00:09:24,550
You subtract these from each other.

207
00:09:24,549 --> 00:09:26,339
Remainder 0.

208
00:09:26,340 --> 00:09:32,000
So 91 divided by 7 is equal to 13.

209
00:09:32,000 --> 00:09:32,639
Let's do another one.

210
00:09:32,639 --> 00:09:34,939
And I won't take that little break to explain the

211
00:09:34,940 --> 00:09:35,860
places and all of that.

212
00:09:35,860 --> 00:09:36,800
I think you understand that.

213
00:09:36,799 --> 00:09:39,799
I want, at least, you to get the process down really

214
00:09:39,799 --> 00:09:41,579
really well in this video.

215
00:09:41,580 --> 00:09:44,990
So let's do 7-- I keep using the number 7.

216
00:09:44,990 --> 00:09:46,509
Let me do a different number.

217
00:09:46,509 --> 00:09:56,559
Let me do 8 goes into 608 how many times?

218
00:09:56,559 --> 00:09:59,439
So I go 8 goes into 6 how many times?

219
00:09:59,440 --> 00:10:00,740
It goes into it 0 time.

220
00:10:00,740 --> 00:10:01,980
So let me keep moving.

221
00:10:01,980 --> 00:10:05,360
8 goes into 60 how many times?

222
00:10:05,360 --> 00:10:06,820
Let me write down the 8.

223
00:10:06,820 --> 00:10:09,110
Let me draw a line here so we don't get confused.

224
00:10:09,110 --> 00:10:11,340
Let me scroll down a little bit.

225
00:10:11,340 --> 00:10:13,759
I need some space above the number.

226
00:10:13,759 --> 00:10:15,580
So 8 goes into 60 how many times?

227
00:10:15,580 --> 00:10:19,590
We know that 8 times 7 is equal to 56.

228
00:10:19,590 --> 00:10:23,330
And that 8 times 8 is equal to 64.

229
00:10:23,330 --> 00:10:25,639
So 8 goes into-- 64 is too big.

230
00:10:25,639 --> 00:10:26,769
So it's not this one.

231
00:10:26,769 --> 00:10:30,000
So 8 goes into 60 seven times.

232
00:10:30,000 --> 00:10:31,539
And there's going to be a little bit left over.

233
00:10:31,539 --> 00:10:34,599
So 8 goes into 60 seven times.

234
00:10:34,600 --> 00:10:37,790
Since we're doing the whole 60, we put the 7 above the ones

235
00:10:37,789 --> 00:10:41,029
place in the 60, which is the tens place in the whole thing.

236
00:10:41,029 --> 00:10:44,970
7 times 8, we know, is 56.

237
00:10:44,970 --> 00:10:47,100
60 minus 56.

238
00:10:47,100 --> 00:10:48,029
That's 4.

239
00:10:48,029 --> 00:10:48,990
We could do that in our heads.

240
00:10:48,990 --> 00:10:50,269
Or if we wanted, we can borrow.

241
00:10:50,269 --> 00:10:51,509
That be a 10.

242
00:10:51,509 --> 00:10:53,379
That would be a 5.

243
00:10:53,379 --> 00:10:54,889
10 minus 6 is 4.

244
00:10:54,889 --> 00:10:57,129
Then you bring down this 8.

245
00:10:57,129 --> 00:10:59,980


246
00:10:59,980 --> 00:11:02,750
8 goes into 48 how many times?

247
00:11:02,750 --> 00:11:06,259
Well what's 8 times 6?

248
00:11:06,259 --> 00:11:09,210
Well, 8 times 6 is exactly 48.

249
00:11:09,210 --> 00:11:13,170
So 8 times-- 8 goes into 48 six times.

250
00:11:13,169 --> 00:11:17,179
6 times 8 is 48.

251
00:11:17,179 --> 00:11:18,179
And you subtract.

252
00:11:18,179 --> 00:11:19,500
We subtracted up here as well.

253
00:11:19,500 --> 00:11:22,019
48 minus 48 is 0.

254
00:11:22,019 --> 00:11:25,259
So, once again, we get a remainder of 0.

255
00:11:25,259 --> 00:11:27,659
So hopefully, that gives you the hang of how to do these

256
00:11:27,659 --> 00:11:28,789
larger division problems.

257
00:11:28,789 --> 00:11:31,149
And all we really need to know to be able to do these, to

258
00:11:31,149 --> 00:11:34,779
tackle these, is our multiplication tables up to

259
00:11:34,779 --> 00:11:38,149
maybe 10 times 10 or 12 times 12.

260
00:11:38,149 --> 00:11:38,278