1
00:00:00,710 --> 00:00:07,826
We have 7329 - 6278.

2
00:00:07,826 --> 00:00:09,225
So let's go place by place,

3
00:00:09,225 --> 00:00:10,580
and see if we can subtract.

4
00:00:10,580 --> 00:00:15,312
6278 is clearly less than 7329,

5
00:00:15,312 --> 00:00:17,180
so we should be able to do this.

6
00:00:17,180 --> 00:00:18,676
So, first we go to the ones place.

7
00:00:18,676 --> 00:00:21,012
We're subtracting an 8 from a 9.

8
00:00:21,012 --> 00:00:22,504
That seems pretty straightforward.

9
00:00:22,504 --> 00:00:24,121
That's just going to be a 1--

10
00:00:24,121 --> 00:00:25,167
a 1 in the ones place.

11
00:00:25,167 --> 00:00:26,997
It literally just represents 1.

12
00:00:27,012 --> 00:00:28,504
Then we go to the the 10s place.

13
00:00:28,520 --> 00:00:31,004
And we’re trying to subtract a 7 from a 2.

14
00:00:31,004 --> 00:00:32,489
And this is really representing 70.

15
00:00:32,489 --> 00:00:34,278
And this is really representing 20.

16
00:00:34,278 --> 00:00:37,110
Well now, we’re hitting a bit of a stumbling block.

17
00:00:37,110 --> 00:00:39,719
So we’re going to have to regroup or borrow.

18
00:00:39,719 --> 00:00:41,598
And to understand what we're doing,

19
00:00:41,598 --> 00:00:44,269
let’s rewrite both of these numbers.

20
00:00:44,269 --> 00:00:47,290
So 7329.

21
00:00:47,290 --> 00:00:52,585
7 we can rewrite as being equal to 7000.

22
00:00:52,585 --> 00:00:54,851
+ plus 300.

23
00:00:54,851 --> 00:00:58,258
So this 3 in the hundreds place is representing 300.

24
00:00:58,258 --> 00:01:00,486
The 7 in the thousands place is 7000,

25
00:01:00,486 --> 00:01:03,330
The 3 in the hundreds place is 300.

26
00:01:03,330 --> 00:01:07,801
The 2 in the tens place, that’s two 10’s, or 20.

27
00:01:07,801 --> 00:01:10,022
And then the 9 in the ones place

28
00:01:10,022 --> 00:01:12,275
is just going to be 9.

29
00:01:12,275 --> 00:01:16,362
So this is another way of representing 7329.

30
00:01:16,362 --> 00:01:18,705
And then down here, we have the 6

31
00:01:18,705 --> 00:01:20,218
in the thousands place.

32
00:01:20,218 --> 00:01:22,147
Well that's going to be 6000.

33
00:01:22,147 --> 00:01:25,817
We’re subtracting, so minus 6000.

34
00:01:25,817 --> 00:01:28,827
And then here, we have a 2 in the hundreds place.

35
00:01:28,827 --> 00:01:30,575
And once again, we are going to be subtracting

36
00:01:30,575 --> 00:01:32,323
all of these.

37
00:01:32,323 --> 00:01:34,072
So we're going to be subtracting 200.

38
00:01:34,072 --> 00:01:37,150
And then here in the tens place, we have our 7,

39
00:01:37,150 --> 00:01:39,109
we have our 7, and we're subtracting it.

40
00:01:39,109 --> 00:01:41,716
So 7 tens, that's 70.

41
00:01:41,716 --> 00:01:43,091
And then we have --

42
00:01:43,091 --> 00:01:46,726
We're subtracting that 8.

43
00:01:46,726 --> 00:01:48,566
And what we've already done --

44
00:01:48,566 --> 00:01:50,962
What we've already done is say,

45
00:01:50,962 --> 00:01:53,443
"Hey, look. Subtracting 8 from 9?

46
00:01:53,443 --> 00:01:56,723
That’s just going to be 1.”

47
00:01:56,723 --> 00:01:58,035
But then we got over here and we said,

48
00:01:58,035 --> 00:02:01,679
“Hey! How are we going to subtract 70 from 20?”

49
00:02:01,679 --> 00:02:03,001
And the key here is to regroup

50
00:02:03,001 --> 00:02:04,476
some of the value up here,

51
00:02:04,476 --> 00:02:05,645
and give it to the tens place,

52
00:02:05,645 --> 00:02:08,137
so that we can then subtract 70 from it.

53
00:02:08,137 --> 00:02:09,574
And the most natural place to go

54
00:02:09,574 --> 00:02:11,965
is one place value above.

55
00:02:11,965 --> 00:02:15,388
So we could take 100 from the 300 --

56
00:02:15,388 --> 00:02:18,670
so we could take 100 from the 300.

57
00:02:18,670 --> 00:02:20,896
So then it will become 200.

58
00:02:20,896 --> 00:02:23,834
We're going to give 100 to --

59
00:02:23,834 --> 00:02:26,142
We are going to give that 100 to the tens place.

60
00:02:26,142 --> 00:02:31,532
So it is going to become-- It is going to become 120.

61
00:02:31,532 --> 00:02:35,467
Notice, 200 + 120 is 320.

62
00:02:35,467 --> 00:02:37,410
300 + 20 is 320.

63
00:02:37,410 --> 00:02:39,321
We have not changed the value of the number.

64
00:02:39,321 --> 00:02:40,904
We've just changed what place

65
00:02:40,904 --> 00:02:42,458
we're representing it in.

66
00:02:42,473 --> 00:02:44,674
If we wanted to do it here, we could say --

67
00:02:44,674 --> 00:02:46,132
And this is kind of the --

68
00:02:46,132 --> 00:02:47,239
When you think of it this way,

69
00:02:47,239 --> 00:02:48,344
this is really regrouping --

70
00:02:48,344 --> 00:02:49,820
and this is really what's happening.

71
00:02:49,820 --> 00:02:50,659
But if you want to think of it

72
00:02:50,659 --> 00:02:51,917
in a borrowing framework,

73
00:02:51,933 --> 00:02:55,485
you could say, “Hey let's take 1 from the 3 --

74
00:02:55,485 --> 00:02:57,947
although that’s a 300 -- So you’re really taking 100.

75
00:02:57,947 --> 00:02:59,172
That becomes a 2.

76
00:02:59,172 --> 00:03:01,613
-- and you give that 1 to the tens place.

77
00:03:01,613 --> 00:03:05,124
And so that becomes a 12.

78
00:03:05,124 --> 00:03:07,761
Now, what was really happening is you took 100,

79
00:03:07,761 --> 00:03:10,163
and you gave it to the 20, so it became 120.

80
00:03:10,163 --> 00:03:11,341
But now you can subtract.

81
00:03:11,341 --> 00:03:14,430
Here, you’d say, "Well, what’s 120 minus 70?"

82
00:03:14,430 --> 00:03:17,989
Well, 120 minus 70 is going to be 50.

83
00:03:17,989 --> 00:03:20,711
Over here you could say, “Well what's 12 - 7?”

84
00:03:20,711 --> 00:03:22,177
Well that's 5.

85
00:03:22,177 --> 00:03:23,932
But it’s still representing the same thing.

86
00:03:23,932 --> 00:03:25,719
12 tens is 120.

87
00:03:25,719 --> 00:03:27,638
7 tens is 70.

88
00:03:27,638 --> 00:03:29,495
and they give you 5 tens –

89
00:03:29,495 --> 00:03:30,896
which is the same thing as 50.

90
00:03:30,896 --> 00:03:33,427
This 5 represents that 50.

91
00:03:33,427 --> 00:03:35,067
And then we can go to the other places.

92
00:03:35,067 --> 00:03:38,009
You say 2 minus 2. Well that's 0 hundreds.

93
00:03:38,009 --> 00:03:42,178
And then 7000 - 6000 is 1000.

94
00:03:42,178 --> 00:03:43,655
And once again, right over here,

95
00:03:43,655 --> 00:03:47,719
200 - 200 is 0 hundreds.

96
00:03:47,719 --> 00:03:52,713
And then 7000 - 6000 is 1000.

97
00:03:52,713 --> 00:03:56,345
So this is going to be 1000 + 0 + 50 + 1 ...

98
00:03:56,345 --> 00:03:59,769
which is the exact same thing as 1051.

99
00:03:59,769 --> 00:04:01,085
The important thing is to visualize --

100
00:04:01,085 --> 00:04:02,729
You don't have to write this out every time.

101
00:04:02,729 --> 00:04:03,991
[The important thing is] to make sure you visualize

102
00:04:03,991 --> 00:04:06,670
in your head that this 3 is representing 300 –

103
00:04:06,670 --> 00:04:08,490
that this 2 represents 20 --

104
00:04:08,490 --> 00:04:11,640
that when you're taking 100 from the 300,

105
00:04:11,640 --> 00:04:13,342
then you'd represent that as a 2

106
00:04:13,342 --> 00:04:14,566
in the hundreds place.

107
00:04:14,566 --> 00:04:16,748
And then when you give a 100 to the tens place,

108
00:04:16,748 --> 00:04:18,533
it's essentially like adding –

109
00:04:18,533 --> 00:04:22,448
it's essentially that the 2 tens will become 12 tens

110
00:04:22,448 --> 00:04:23,940
-- because you're giving it 10 more tens.

111
00:04:23,940 --> 00:04:25,256
You’re giving it a 100.

112
00:04:25,256 --> 00:04:27,445
So hopefully that makes some sense.