1
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2
00:00:00,720 --> 00:00:03,729
I think we're just about ready to learn how to subtract pretty

3
00:00:03,730 --> 00:00:06,129
much any number from any other number.

4
00:00:06,129 --> 00:00:08,750
So let's just review a little bit of what we know already.

5
00:00:08,750 --> 00:00:14,559
So if I were to ask you what 16 minus 4 is, I could draw

6
00:00:14,560 --> 00:00:17,789
16 apples and then take away 4 of the apples.

7
00:00:17,789 --> 00:00:20,339
Or I could actually draw a number line, and actually let

8
00:00:20,339 --> 00:00:23,739
me do it here just to start off the video to get warmed up.

9
00:00:23,739 --> 00:00:25,139
I could draw the number line and maybe that's

10
00:00:25,140 --> 00:00:28,210
16, maybe that's 17.

11
00:00:28,210 --> 00:00:35,160
It's 15, 14, 13, 12, let me go down all the way to 11.

12
00:00:35,159 --> 00:00:37,589
I could keep going but I've run out of space.

13
00:00:37,590 --> 00:00:41,720
Now, if I don't know in my head what 16 minus 4 is, and it's a

14
00:00:41,719 --> 00:00:44,960
pretty good one to eventually know in your head, you could

15
00:00:44,960 --> 00:00:46,920
start in your number line or you could imagine the number

16
00:00:46,920 --> 00:00:49,730
line in your brain and you could go down by 4's.

17
00:00:49,729 --> 00:00:58,349
16 minus 1 is 15 minus 2 is 14 minus 3 is 13 minus 4 is 12.

18
00:00:58,350 --> 00:00:59,560
And you would have the answer.

19
00:00:59,560 --> 00:01:02,120
16 minus 4 is 12.

20
00:01:02,119 --> 00:01:07,859
Now an even easier way to do this problem is just to focus

21
00:01:07,859 --> 00:01:10,489
on the places of the digits.

22
00:01:10,489 --> 00:01:12,819
Now let me be clear what I mean when I say that.

23
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Let me re-write it.

24
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16 minus 4, and I've gone over this a little bit

25
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in the addition videos.

26
00:01:19,519 --> 00:01:22,339
This is the ones place.

27
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The 6 is in the ones place.

28
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The 4 is in the ones place.

29
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The 1, right here, this right here, or there was something

30
00:01:31,480 --> 00:01:35,880
down here, this column, that is the tens place.

31
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Now what do we mean by that?

32
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Well 16 is the same thing as 10 plus 6.

33
00:01:44,620 --> 00:01:48,100
So when we write it, this 1 literally means one 10.

34
00:01:48,099 --> 00:01:51,169
If you think of it in money it means one $10 bill.

35
00:01:51,170 --> 00:01:55,430
If I had a 2 there, if I had 26, that means two $10 bills.

36
00:01:55,430 --> 00:01:58,040
Two $10 bills would mean $20.

37
00:01:58,040 --> 00:02:01,730
So that's two $10 bills and then six $1 bills.

38
00:02:01,730 --> 00:02:04,350
You can view this as a $1 bill place, that's

39
00:02:04,349 --> 00:02:05,949
the $10 bill place.

40
00:02:05,950 --> 00:02:15,259
If I had 357, you could view this as three $100 bills, five

41
00:02:15,259 --> 00:02:19,879
$10 bills, and seven $1 bills, and that's why this is called

42
00:02:19,879 --> 00:02:24,509
the hundredths, that's the hundredths place, this is the

43
00:02:24,509 --> 00:02:28,289
tens place, and this is the ones place.

44
00:02:28,289 --> 00:02:32,030
And we'll dig a little bit deeper into this as we explore

45
00:02:32,030 --> 00:02:35,069
borrowing and regrouping more in this video and in others.

46
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But I wanted to label these places because what I want to

47
00:02:37,599 --> 00:02:41,030
show you is you don't even have to think about 16 minus 4.

48
00:02:41,030 --> 00:02:43,599
You can actually just look at just the ones place and think

49
00:02:43,599 --> 00:02:47,944
about 6 minus 4, and say 6 minus 4 -- well you could draw

50
00:02:47,944 --> 00:02:50,599
a number line or you could even use your fingers if you have

51
00:02:50,599 --> 00:02:52,340
to, but you probably have that memorized.

52
00:02:52,340 --> 00:02:56,009
You could probably visualize it in your head, 6 minus 4 is 2.

53
00:02:56,009 --> 00:02:59,259


54
00:02:59,259 --> 00:03:02,780
And then 1, then we go to the tens place, 1 minus nothing --

55
00:03:02,780 --> 00:03:03,840
there's nothing over here.

56
00:03:03,840 --> 00:03:07,789
So 1 minus nothing is 1, and you get 12.

57
00:03:07,789 --> 00:03:10,299
Same answer, we were able to simplify a little bit.

58
00:03:10,300 --> 00:03:13,010
Let's try another problem like that.

59
00:03:13,009 --> 00:03:22,719
If I were to ask you what 78 minus 37 is.

60
00:03:22,719 --> 00:03:26,439
So we start off in the ones place and we say 8 minus 7 --

61
00:03:26,439 --> 00:03:30,340
that's 8 ones minus seven ones, or just 8 minus 7.

62
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8 minus 7 is equal to 1.

63
00:03:33,675 --> 00:03:37,000


64
00:03:37,000 --> 00:03:38,550
Then we go to the tens place.

65
00:03:38,550 --> 00:03:43,370
7 minus 3 -- now remember, this is seven 10s, or seven $10

66
00:03:43,370 --> 00:03:46,490
bills, minus three $10 bills.

67
00:03:46,490 --> 00:03:50,210
If I had seven $10 bills and I give away three of those $10

68
00:03:50,210 --> 00:03:54,570
dollar bills, then I'll have four $10 bills, or 7

69
00:03:54,569 --> 00:03:56,799
minus 3 is equal to 4.

70
00:03:56,800 --> 00:03:58,880
And just like that we were able to figure out that

71
00:03:58,879 --> 00:04:02,490
78 minus 37 is 41.

72
00:04:02,490 --> 00:04:04,120
This would have been really hard to do, it would take me

73
00:04:04,120 --> 00:04:07,939
forever to draw 78 apples and to cross out 37 of them.

74
00:04:07,939 --> 00:04:10,150
Or to draw a number line all the way up to 78

75
00:04:10,150 --> 00:04:12,450
then go back 37 spaces.

76
00:04:12,449 --> 00:04:14,269
That would have given you the answer, but it would have

77
00:04:14,270 --> 00:04:16,389
taken you forever to solve it that way.

78
00:04:16,389 --> 00:04:19,310
Just by focusing on just each column, you're able

79
00:04:19,310 --> 00:04:21,079
to get the right answer.

80
00:04:21,079 --> 00:04:24,589
Well, you might say, hey Sal, but what happens if I can't --

81
00:04:24,589 --> 00:04:26,909
well, let me give you an example where this will start

82
00:04:26,910 --> 00:04:28,810
to become difficult doing it this way.

83
00:04:28,810 --> 00:04:29,910
I'll do one more example like this.

84
00:04:29,910 --> 00:04:37,890
So let's say I had 95 minus 31.

85
00:04:37,889 --> 00:04:40,589
Just like that, 5 minus 1 is 4.

86
00:04:40,589 --> 00:04:42,269
9 minus 3 is 6.

87
00:04:42,269 --> 00:04:44,699
95 minus 31 is 64.

88
00:04:44,699 --> 00:04:47,279
You're probably saying, Sal, subtraction is easy.

89
00:04:47,279 --> 00:04:50,579
I can just look at each place, the ones place and subtract,

90
00:04:50,579 --> 00:04:52,240
tens places and subtract.

91
00:04:52,240 --> 00:04:54,620
But I'm about to show you that it's not always

92
00:04:54,620 --> 00:04:55,560
at least that easy.

93
00:04:55,560 --> 00:04:57,449
With a little bit of practice hopefully you'll realize

94
00:04:57,449 --> 00:05:00,699
that it's also not too bad.

95
00:05:00,699 --> 00:05:08,509
So what if I were to ask you what 22 minus 17 is.

96
00:05:08,509 --> 00:05:11,409


97
00:05:11,410 --> 00:05:14,400
Now once again, I could draw 22 oranges or apples and take away

98
00:05:14,399 --> 00:05:16,769
17 of them and you could count what's left and you would get

99
00:05:16,769 --> 00:05:18,729
the right answer, but that would take you forever.

100
00:05:18,730 --> 00:05:21,140
Is there any way I could do that maybe just on

101
00:05:21,139 --> 00:05:22,889
the paper right here?

102
00:05:22,889 --> 00:05:25,360
Now your reaction might say let me just do what

103
00:05:25,360 --> 00:05:26,780
you just did before.

104
00:05:26,779 --> 00:05:31,279
But if you look here, if I try to subtract 7 from 2, if I have

105
00:05:31,279 --> 00:05:34,129
two things, at least for the mathematics that we know right

106
00:05:34,129 --> 00:05:35,959
now, I can't give away 7.

107
00:05:35,959 --> 00:05:37,169
I only have 2 to give away.

108
00:05:37,170 --> 00:05:39,900
This would give me something smaller than 0 which

109
00:05:39,899 --> 00:05:40,959
we don't know about.

110
00:05:40,959 --> 00:05:42,639
That's a negative number.

111
00:05:42,639 --> 00:05:46,560
As far as we know right now, we can't subtract 7 from 2.

112
00:05:46,560 --> 00:05:49,540
But we know that 17 is smaller than 22.

113
00:05:49,540 --> 00:05:52,870
So what can we do here to actually do this

114
00:05:52,870 --> 00:05:54,670
subtraction problem?

115
00:05:54,670 --> 00:05:57,980
So what we do here, and you might call it borrowing, you

116
00:05:57,980 --> 00:06:00,090
might call it regrouping.

117
00:06:00,089 --> 00:06:05,250
This 2 right here, this 22 is the same thing as 20 plus 2.

118
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That's the 22 right there.

119
00:06:07,199 --> 00:06:08,979
It's 20 plus 2.

120
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The 17 is 10 plus 7.

121
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That's just another way to write 17.

122
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Now we have a 2 here.

123
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We want something larger than a 7 to subtract from.

124
00:06:19,990 --> 00:06:24,240
So what we can do is we can borrow from this 2 or from this

125
00:06:24,240 --> 00:06:26,660
20, they're the same thing.

126
00:06:26,660 --> 00:06:29,230
Let me do that in another color.

127
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This 2 right here is the same thing as that 20.

128
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A 2 in the tens place means two $10 bills.

129
00:06:37,149 --> 00:06:40,529
Two $10 bills is the same thing as $20.

130
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That's what that 2 represents.

131
00:06:42,279 --> 00:06:45,500
So if I want to make this 2 into something larger, why

132
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don't I take a $10 bill from here.

133
00:06:48,129 --> 00:06:51,709
If I take a $10 bill from here and I turn it into ones -- I

134
00:06:51,709 --> 00:06:54,579
go to the cashier and say give me a bunch of ones.

135
00:06:54,579 --> 00:06:57,769
So if I take a $10 bill from here, then this

136
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will become $10.

137
00:06:59,500 --> 00:07:02,300
And then I cash into a bunch of ones and put it here.

138
00:07:02,300 --> 00:07:05,020
So then this will become $12.

139
00:07:05,019 --> 00:07:08,689
If we look over here, what it looks like I did is I took a 1

140
00:07:08,689 --> 00:07:12,250
from this 2, so this 2 will now become a 1, right?

141
00:07:12,250 --> 00:07:15,269
We went from two $10s to one $10 and it became

142
00:07:15,269 --> 00:07:17,240
just one $10 bill.

143
00:07:17,240 --> 00:07:19,759
Then I gave that 1 to this 2.

144
00:07:19,759 --> 00:07:22,259
This 2 then becomes a 12.

145
00:07:22,259 --> 00:07:24,649
And now we can actually subtract.

146
00:07:24,649 --> 00:07:28,769
12 minus 7 is 5.

147
00:07:28,769 --> 00:07:32,219
12 minus 7 -- I'm just doing the same problem just written

148
00:07:32,220 --> 00:07:36,340
slightly different on this right hand side -- is also 5.

149
00:07:36,339 --> 00:07:39,289
Then we have 1 minus 1 is 0.

150
00:07:39,290 --> 00:07:41,250
I could write this as 05, but that's just

151
00:07:41,250 --> 00:07:42,660
the same thing as 5.

152
00:07:42,660 --> 00:07:46,310
And here I'd have 10 minus 10 -- well, 10 minus 10 is just 0.

153
00:07:46,310 --> 00:07:47,480
So it's just 05.

154
00:07:47,480 --> 00:07:51,140
So 22 minus 17 is 5.

155
00:07:51,139 --> 00:07:55,019
Let's try to extend this to an even harder problem.

156
00:07:55,019 --> 00:07:57,659
Hopefully you'll get the hang of how this borrowing or

157
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regrouping, depending and how you want to view it,

158
00:07:59,529 --> 00:08:00,989
actually works.

159
00:08:00,990 --> 00:08:07,225
So let's say that we have 703 minus 67.

160
00:08:07,225 --> 00:08:09,890


161
00:08:09,889 --> 00:08:12,159
So if I tried the technique that we learned earlier in

162
00:08:12,160 --> 00:08:14,040
this video, I immediately hit a roadblock.

163
00:08:14,040 --> 00:08:18,050
I say 3 minus 7 -- well if I have 3 apples, I can't

164
00:08:18,050 --> 00:08:19,389
take away 7 from there.

165
00:08:19,389 --> 00:08:21,469
So I'm at an impasse.

166
00:08:21,470 --> 00:08:22,590
I don't know what to do next.

167
00:08:22,589 --> 00:08:24,429
And you say well, maybe I can borrow.

168
00:08:24,430 --> 00:08:27,069
But I look to the left, well gee, there's a 0 there,

169
00:08:27,069 --> 00:08:29,389
how can I borrow from a 0?

170
00:08:29,389 --> 00:08:31,669
Then well, there's a 7 there, but then how do I borrow

171
00:08:31,670 --> 00:08:33,120
from the 7, all of that.

172
00:08:33,120 --> 00:08:35,370
And the best way to think about it and the more practice you do

173
00:08:35,370 --> 00:08:41,560
the better, remember this 703 is seven $100 bills plus zero

174
00:08:41,559 --> 00:08:45,389
$10 bills plus three $1 bills.

175
00:08:45,389 --> 00:08:50,939
And 67 is six $10 bills or $60 plus 7.

176
00:08:50,940 --> 00:08:53,860
So if we can't borrow from here because I have no $10 bills,

177
00:08:53,860 --> 00:08:58,269
what we want to do is break one of the $100 bills.

178
00:08:58,269 --> 00:09:01,519
So what I do is I take $100 bill from here, so now

179
00:09:01,519 --> 00:09:03,860
I'm left with $600.

180
00:09:03,860 --> 00:09:06,279
So this 7 becomes a 6, right?

181
00:09:06,279 --> 00:09:09,509
It's a 6 in the hundredths place and it represents six

182
00:09:09,509 --> 00:09:12,610
hundredths, six $100 bills.

183
00:09:12,610 --> 00:09:15,610
So, remember, I took out a $100 bill.

184
00:09:15,610 --> 00:09:19,050
And then what I can do is I can split that $100 bill, I can

185
00:09:19,049 --> 00:09:22,949
give $10 to this guy -- or sorry, I can give $90 to this

186
00:09:22,950 --> 00:09:29,980
guy right here, and then I can give $1 to this guy -- sorry, I

187
00:09:29,980 --> 00:09:34,340
could give $90 to this guy and I can give $10 to that

188
00:09:34,340 --> 00:09:34,850
guy right there.

189
00:09:34,850 --> 00:09:37,279
I have $100 to work with, right?

190
00:09:37,279 --> 00:09:38,350
So what happens?

191
00:09:38,350 --> 00:09:41,470
If I do that, if I take that $100 bill that I took out

192
00:09:41,470 --> 00:09:43,519
from here, went to the cash register, I got

193
00:09:43,519 --> 00:09:45,620
nine 10s or $90.

194
00:09:45,620 --> 00:09:48,139
So now I have nine 10s here.

195
00:09:48,139 --> 00:09:53,960
And then I have ten 1s here, so I add 10 plus 3, it becomes 13.

196
00:09:53,960 --> 00:09:56,800
And just like that, all my numbers in each column, if I

197
00:09:56,799 --> 00:09:59,639
were to draw columns like this, divide them up.

198
00:09:59,639 --> 00:10:02,129
Everything on top is bigger than everything on the bottom

199
00:10:02,129 --> 00:10:04,090
so now I can subtract.

200
00:10:04,090 --> 00:10:06,960
So 13 minus 7 is 6.

201
00:10:06,960 --> 00:10:11,230
9 minus 6 is 3.

202
00:10:11,230 --> 00:10:13,840
6 minus nothing is 6.

203
00:10:13,840 --> 00:10:17,620
So 703 minus 67 is 636.

204
00:10:17,620 --> 00:10:19,570
Now you might be saying, OK Sal, I kind of get what you

205
00:10:19,570 --> 00:10:23,140
did, you took 100 from here, you put 90 here, so that

206
00:10:23,139 --> 00:10:24,539
became a 9, you gave 10 here.

207
00:10:24,539 --> 00:10:26,629
But how did you know to do that or what's a more

208
00:10:26,629 --> 00:10:28,480
systematic way of doing.

209
00:10:28,480 --> 00:10:30,659
This kind of is a conceptual way, which is, in my

210
00:10:30,659 --> 00:10:32,350
mind, the most important way to understand it.

211
00:10:32,350 --> 00:10:36,080
But let me show you kind of a mechanical way to do that.

212
00:10:36,080 --> 00:10:40,060
So let's say we have 700 -- I'll do the same problem

213
00:10:40,059 --> 00:10:43,489
over again -- 703 minus 67.

214
00:10:43,490 --> 00:10:45,789
I look at all of the numbers on the top and I say are they all

215
00:10:45,789 --> 00:10:47,149
larger than the numbers on the bottom?

216
00:10:47,149 --> 00:10:50,189
I said well, 3 -- well, 7 is larger than 3, that's not good.

217
00:10:50,190 --> 00:10:51,695
6 is larger than 0, that's not good.

218
00:10:51,695 --> 00:10:53,200
So I need to do something.

219
00:10:53,200 --> 00:10:56,170
So what I do is I start with this 3 right here, and I say

220
00:10:56,169 --> 00:10:59,539
well, can I borrow from this number to the left?

221
00:10:59,539 --> 00:11:01,469
And I look to the number to the left and I can

222
00:11:01,470 --> 00:11:02,639
not borrow from 0.

223
00:11:02,639 --> 00:11:04,720
So then I look to the two numbers to the left and

224
00:11:04,720 --> 00:11:07,740
say can I borrow from 70?

225
00:11:07,740 --> 00:11:10,500
I say well gee, I can definitely borrow from 70 --

226
00:11:10,500 --> 00:11:12,330
we know this is actually 700.

227
00:11:12,330 --> 00:11:14,840
So if I borrow from 70 what happens?

228
00:11:14,840 --> 00:11:23,200
If I borrow one 10 from 70, 70 becomes 69, right?

229
00:11:23,200 --> 00:11:26,910
If I borrow one from 70, it becomes 69.

230
00:11:26,909 --> 00:11:30,969
And I take that 1 and it's essentially a 10, right?

231
00:11:30,970 --> 00:11:33,850
So that 10 plus 3 is now 13.

232
00:11:33,850 --> 00:11:35,710
And now these are my columns.

233
00:11:35,710 --> 00:11:38,120
Just just like.

234
00:11:38,120 --> 00:11:41,950
You have 13 minus 7 is 6, 9 minus 6 is 3.

235
00:11:41,950 --> 00:11:44,800
And then 6 right down here.

236
00:11:44,799 --> 00:11:48,179
Now, another way you can think about it, I'll do

237
00:11:48,179 --> 00:11:50,049
the exact same problem.

238
00:11:50,049 --> 00:11:54,799
703 minus 67.

239
00:11:54,799 --> 00:11:56,209
You could start at the left.

240
00:11:56,210 --> 00:11:58,269
You could say look, 7 is, well, it's larger

241
00:11:58,269 --> 00:11:58,860
than what's below it.

242
00:11:58,860 --> 00:12:01,100
Nothing is below it, so I'm cool there.

243
00:12:01,100 --> 00:12:02,769
And then you go 1 right to the right of it.

244
00:12:02,769 --> 00:12:07,039
And you say well, 0 -- well, 0 is not bigger than what's

245
00:12:07,039 --> 00:12:10,799
below it; it's not bigger than the 6 below it.

246
00:12:10,799 --> 00:12:12,829
So I'm going to need to borrow.

247
00:12:12,830 --> 00:12:16,030
So what I can do is I can borrow 1 from the 7 -- I'm

248
00:12:16,029 --> 00:12:18,220
essentially borrowing 100, right?

249
00:12:18,220 --> 00:12:22,259
So if I borrow -- this is 700, let me make it 600.

250
00:12:22,259 --> 00:12:24,110
Now if I take 100 away and I turn it to

251
00:12:24,110 --> 00:12:27,090
tens, that's 10 tens.

252
00:12:27,090 --> 00:12:29,450
It looks like we took a 1 away and we just put the 1 in front

253
00:12:29,450 --> 00:12:32,390
of 0, but we essentially added 10 tens to it.

254
00:12:32,389 --> 00:12:35,360
But if it helps your mind, we took a 1 away from this,

255
00:12:35,360 --> 00:12:38,480
put it right in front of the 0 just like that.

256
00:12:38,480 --> 00:12:42,129
This is the same 0 as that 0 right there.

257
00:12:42,129 --> 00:12:44,220
And this 1 we took from this guy.

258
00:12:44,220 --> 00:12:46,600
He became 6 and we have a 1 there.

259
00:12:46,600 --> 00:12:48,720
And then we say OK, 10 is definitely greater than

260
00:12:48,720 --> 00:12:50,019
6, we're cool there.

261
00:12:50,019 --> 00:12:53,299
But all of a sudden here on the 3 we're still not good.

262
00:12:53,299 --> 00:12:54,899
3 is smaller than 7.

263
00:12:54,899 --> 00:12:56,029
Still not cool.

264
00:12:56,029 --> 00:12:58,689
I won't be able to subtract, so let me borrow again.

265
00:12:58,690 --> 00:13:00,490
Now I have something to borrow from.

266
00:13:00,490 --> 00:13:02,560
Remember we went from the left to right this time instead

267
00:13:02,559 --> 00:13:03,659
of from the right to left.

268
00:13:03,659 --> 00:13:05,669
All of these are valid ways of doing it.

269
00:13:05,669 --> 00:13:07,860
So we say let me borrow 1 from the 10.

270
00:13:07,860 --> 00:13:13,680
So 10 minus 1 is 9, and let me give that 1 to the 3 to go 13.

271
00:13:13,679 --> 00:13:15,049
Remember, it's not a 1.

272
00:13:15,049 --> 00:13:16,169
I added 10 to it.

273
00:13:16,169 --> 00:13:18,909
If I take 1 from the tens place, that's like adding

274
00:13:18,909 --> 00:13:20,569
10 to the ones place.

275
00:13:20,570 --> 00:13:21,480
Don't want to confuse you.

276
00:13:21,480 --> 00:13:24,110
Hopefully you see the system here.

277
00:13:24,110 --> 00:13:26,610
I want you to be able to do the problems before you have to get

278
00:13:26,610 --> 00:13:28,960
the real deep understanding of what's going on.

279
00:13:28,960 --> 00:13:35,620
So 13 minus 7 is 6, 9 minus 6 is 3, 6 minus 0 is 6.

280
00:13:35,620 --> 00:13:36,620
636.

281
00:13:36,620 --> 00:13:38,820
Let's do a couple more problems, because the

282
00:13:38,820 --> 00:13:41,060
subtraction sometimes with the borrowing it can come a little

283
00:13:41,059 --> 00:13:43,509
bit confusing on what to do next.

284
00:13:43,509 --> 00:13:52,330
Let's say 953 minus 754.

285
00:13:52,330 --> 00:13:55,629
Maybe we'll do it in all of the different ways that you can

286
00:13:55,629 --> 00:13:58,189
actually do this type of problem.

287
00:13:58,190 --> 00:14:00,990
First, one of the ways I talked about is to start at the right.

288
00:14:00,990 --> 00:14:02,519
Let's see, is 3 larger than 4?

289
00:14:02,519 --> 00:14:03,230
No, it's not.

290
00:14:03,230 --> 00:14:04,970
So we're going to have to make it larger than 4.

291
00:14:04,970 --> 00:14:10,310
So let's borrow from this 5 over here.

292
00:14:10,309 --> 00:14:16,959
So if I borrow from the 5, the 5 will become a 4, and I'd

293
00:14:16,960 --> 00:14:20,210
borrowed 1, the 3 becomes a 13.

294
00:14:20,210 --> 00:14:22,129
Remember, if I borrow 1 from the tens place,

295
00:14:22,129 --> 00:14:23,539
that's actually a 10.

296
00:14:23,539 --> 00:14:25,019
This is 5 tens.

297
00:14:25,019 --> 00:14:28,350
I took one of the 10s away, so I'm left with four 10s, and I

298
00:14:28,350 --> 00:14:31,480
added that 10 to the 3, so I have 13.

299
00:14:31,480 --> 00:14:32,300
So this looks good.

300
00:14:32,299 --> 00:14:35,309
13 minus 4, I'll be able to subtract there.

301
00:14:35,309 --> 00:14:36,879
But here I have a problem.

302
00:14:36,879 --> 00:14:38,559
4 is less than 5.

303
00:14:38,559 --> 00:14:41,089
It was cool before but now all of a sudden it's messed up.

304
00:14:41,090 --> 00:14:42,920
So I'm going to have to borrow again.

305
00:14:42,919 --> 00:14:45,589
I'm going to say well, let me take a 1 from the

306
00:14:45,590 --> 00:14:48,180
hundredths place, so that will become an 8.

307
00:14:48,179 --> 00:14:50,939
And let me give that 100 to my tens place.

308
00:14:50,940 --> 00:14:52,800
100 is 10 tens.

309
00:14:52,799 --> 00:14:57,379
So I'm going to add a 10 here, so it's going to become 14.

310
00:14:57,379 --> 00:14:59,950
I took the 1 from there and I borrowed it, or

311
00:14:59,950 --> 00:15:01,759
I rearranged that 100.

312
00:15:01,759 --> 00:15:04,850
I could re-write that 100 as one 10, and so that's what

313
00:15:04,850 --> 00:15:08,470
got us to that from 9 to 8 -- or sorry, 100.

314
00:15:08,470 --> 00:15:11,470
I took away 100 from the 900 to get 800.

315
00:15:11,470 --> 00:15:16,440
And when I re-wrote the 100 in the tens place, it's ten 10s.

316
00:15:16,440 --> 00:15:19,990
So that's why I added a 10 to the 4 that I had before.

317
00:15:19,990 --> 00:15:22,889
I could have just scratched it out and put the 14 like that to

318
00:15:22,889 --> 00:15:25,519
show that I had to re-write the 4.

319
00:15:25,519 --> 00:15:26,819
But now all of a sudden I'm cool.

320
00:15:26,820 --> 00:15:29,930
13 minus 4 is 9.

321
00:15:29,929 --> 00:15:32,489
14 minus 5 is 9.

322
00:15:32,490 --> 00:15:34,210
8 minus 7 is 1.

323
00:15:34,210 --> 00:15:40,220
953 minus 754 is 199.

324
00:15:40,220 --> 00:15:42,660
Now let's do it the left to right way.

325
00:15:42,659 --> 00:15:50,469
953 -- let me use a different color -- minus 754.

326
00:15:50,470 --> 00:15:52,990
Now this is will be a little bit different

327
00:15:52,990 --> 00:15:53,470
than I did last time.

328
00:15:53,470 --> 00:15:56,509
I say well 9 is definitely larger than 7.

329
00:15:56,509 --> 00:16:00,240
5 is definitely larger -- well, at least it's equal to 5, so

330
00:16:00,240 --> 00:16:02,549
if I subtract maybe I'll get a 0 there.

331
00:16:02,549 --> 00:16:03,979
And 3 is less than 4.

332
00:16:03,980 --> 00:16:07,100
So maybe I'll just have to borrow here.

333
00:16:07,100 --> 00:16:09,795
If I borrow here than this is going to become a 4 and I'm

334
00:16:09,794 --> 00:16:11,629
going to have to borrow from there and give me 14.

335
00:16:11,629 --> 00:16:14,100
It'll essentially boil down to what we did on this

336
00:16:14,100 --> 00:16:15,720
left hand side right here.

337
00:16:15,720 --> 00:16:19,710
Instead, one thing you can do is say OK, 9 is larger than 7.

338
00:16:19,710 --> 00:16:20,590
That's cool.

339
00:16:20,590 --> 00:16:24,389
Or even better you could say 953 is larger than 754.

340
00:16:24,389 --> 00:16:25,029
You know that.

341
00:16:25,029 --> 00:16:27,159
You know that this is going to be a positive number.

342
00:16:27,159 --> 00:16:28,919
That this number is larger than that.

343
00:16:28,919 --> 00:16:31,339
Then you shift over one to the left.

344
00:16:31,340 --> 00:16:34,090
Is 53 larger than 54?

345
00:16:34,090 --> 00:16:37,410
Well no, 53 is not larger than 54.

346
00:16:37,409 --> 00:16:42,250
And because 53 is not larger than 54, let's borrow.

347
00:16:42,250 --> 00:16:45,000
Let's borrow from the hundredths place.

348
00:16:45,000 --> 00:16:49,840
So this will become an 8, and we have 100 to work with.

349
00:16:49,840 --> 00:16:52,290
So maybe we'll just throw that 100 right here.

350
00:16:52,289 --> 00:16:55,959
So if we throw the 100 into the tens place, it's ten 10s.

351
00:16:55,960 --> 00:16:59,170
So the 5 becomes 15.

352
00:16:59,169 --> 00:17:01,029
We're going from left to right.

353
00:17:01,029 --> 00:17:04,700
So now we say 8 is larger than 7.

354
00:17:04,700 --> 00:17:06,930
Well, 8 is definitely larger than 7, 15 is definitely

355
00:17:06,930 --> 00:17:08,250
larger than 5.

356
00:17:08,250 --> 00:17:10,809
And then here, once again, we see 3 is less than 4.

357
00:17:10,809 --> 00:17:13,119
But now we can borrow from the 15.

358
00:17:13,119 --> 00:17:16,589
So if we borrow from the 15, the 15 becomes a 14, and

359
00:17:16,589 --> 00:17:18,449
then the 3 becomes a 13.

360
00:17:18,450 --> 00:17:21,500
Because you take 1 away from the tens place, one $10

361
00:17:21,500 --> 00:17:23,210
bill is equal to 10 ones.

362
00:17:23,210 --> 00:17:26,110
So that's why you added 10 to the 3 and you got 13.

363
00:17:26,109 --> 00:17:28,549
And notice, we ended up really with the same thing no matter

364
00:17:28,549 --> 00:17:30,389
how we did this problem.

365
00:17:30,390 --> 00:17:33,680
So just like that you get 13 minus 4 is 9.

366
00:17:33,680 --> 00:17:35,820
14 minus 5 is 9.

367
00:17:35,819 --> 00:17:39,059
8 minus 7 is 1.

368
00:17:39,059 --> 00:17:41,549
Hopefully you found that pretty straightforward.

369
00:17:41,549 --> 00:17:44,289
These are, frankly, as hard as the borrowing problems get.

370
00:17:44,289 --> 00:17:46,349
The ones where you don't have something to borrow from or

371
00:17:46,349 --> 00:17:50,589
when you do borrow from it, all of a sudden you get a number

372
00:17:50,589 --> 00:17:52,789
that -- then you need to borrow from something else.

373
00:17:52,789 --> 00:17:55,460
If you ever get really confused about it, you should

374
00:17:55,460 --> 00:17:56,759
always go back to this.

375
00:17:56,759 --> 00:18:00,619
You should always go back to this notion of regrouping.

376
00:18:00,619 --> 00:18:04,169
This notion of OK, if these things are all too small, let

377
00:18:04,170 --> 00:18:08,470
me take $100 bill over here, so I have six $100 bills left.

378
00:18:08,470 --> 00:18:12,759
And let me regroup that $100 bills into the other spaces.

379
00:18:12,759 --> 00:18:17,509
In this case, we took the $100 bill and we put 90 here or nine

380
00:18:17,509 --> 00:18:21,619
10s, nine $10 bills, and then $10 of it right there to make

381
00:18:21,619 --> 00:18:24,059
everything in the numerator larger than everything

382
00:18:24,059 --> 00:18:24,740
in the denominator.

383
00:18:24,740 --> 00:18:26,039