1
00:00:00,000 --> 00:00:03,410
I thought I would do another example of partial quotient method

2
00:00:03,410 --> 00:00:04,580
for long division

3
00:00:04,580 --> 00:00:07,180
So there actually has some positives to do

4
00:00:07,180 --> 00:00:08,510
It's actually kind of fun to do

5
00:00:08,510 --> 00:00:10,780
So let's say I want to do something really hairy

6
00:00:10,780 --> 00:00:18,270
like 291 divided into-- let me just throw some digits over here-

7
00:00:18,270 --> 00:00:21,690
actually let's stole another digit right over here-

8
00:00:21,690 --> 00:00:25,260
So this is- how many times does 291 go into- what is this-

9
00:00:25,260 --> 00:00:29,540
9,873,952

10
00:00:29,540 --> 00:00:31,740
And to just kind of get our bearings

11
00:00:31,740 --> 00:00:34,940
we know what 291 times 1 is. That's pretty easy

12
00:00:34,940 --> 00:00:38,750
291 times 1 is clearly just 291

13
00:00:38,750 --> 00:00:44,890
We know what 291 times 10 is. That's clearly 2,910

14
00:00:44,890 --> 00:00:46,960
Let's get some stuff in between here

15
00:00:46,960 --> 00:00:49,060
that will help us to try to approximate

16
00:00:49,060 --> 00:00:53,470
how many times 291 goes into this crazy thing over here

17
00:00:53,470 --> 00:00:56,800
So let's just pick- in the last example I picked 2 and 5-

18
00:00:56,800 --> 00:00:58,790
you could just pick 3 and 6 if you want

19
00:00:58,790 --> 00:01:00,790
You could pick 2 and 7. You could pick whatever you want

20
00:01:00,790 --> 00:01:01,880
You could even just do 1

21
00:01:01,880 --> 00:01:03,300
one of them, one of the above

22
00:01:03,300 --> 00:01:10,910
Let's just say 291 times- let's try 3 out. 291 times 3

23
00:01:10,910 --> 00:01:12,410
So I could do this in my head

24
00:01:12,410 --> 00:01:14,330
or I could just make sure I don't make a mistake

25
00:01:14,330 --> 00:01:15,460
Let me do it right over here

26
00:01:15,460 --> 00:01:23,100
So 291 times 3 is- 1 times 3 is 3. 9 times 3 is 27

27
00:01:23,100 --> 00:01:27,560
2 times 3 is 6. 6 plus 2 is 8

28
00:01:27,560 --> 00:01:31,340
So this is equal to 873

29
00:01:31,340 --> 00:01:33,980
It's actually strange that 873 showed up over there

30
00:01:33,980 --> 00:01:36,480
My brain is doing strange things in the back ground

31
00:01:36,480 --> 00:01:37,020
But anyway

32
00:01:37,020 --> 00:01:39,700
that has actually no relevance to the actual solution of this problem

33
00:01:39,700 --> 00:01:49,180
And let's also try 291 times 6. Let's figure out what that is

34
00:01:49,180 --> 00:01:51,570
So 291 times 6

35
00:01:51,570 --> 00:01:53,420
It's actually going to be this thing times 2

36
00:01:53,420 --> 00:01:56,660
But I'll just calculate it. 291 times 6-

37
00:01:56,660 --> 00:02:03,720
1 times 6 is 6. 9 times 6 is 54. 2 times 6 is 12, plus 5 is 17

38
00:02:03,720 --> 00:02:09,410
So it's 1746

39
00:02:09,410 --> 00:02:10,580
And you might say, Sal

40
00:02:10,580 --> 00:02:13,250
why did you go through the trouble of figuring out this and this?

41
00:02:13,250 --> 00:02:16,420
And I'm just using these as some of the approximation tools

42
00:02:16,420 --> 00:02:17,060
when we try to figure out

43
00:02:17,060 --> 00:02:20,280
how many times 291 goes through this whole crazy mess

44
00:02:20,280 --> 00:02:22,860
So first of all, let's just look at this whole thing

45
00:02:22,860 --> 00:02:25,380
This is 9873952

46
00:02:25,380 --> 00:02:31,760
So let's just say, how many times does 291 go into 9,000,000?

47
00:02:31,760 --> 00:02:36,430
So 291 times 3 would be 873

48
00:02:36,430 --> 00:02:40,860
We want to have a bunch of zeros after the 873

49
00:02:40,860 --> 00:02:43,600
So think of it this way- I'm picking 873

50
00:02:43,600 --> 00:02:46,970
because its leading digit is as closer than 9 as possible

51
00:02:46,970 --> 00:02:49,420
But it's definitely lower than the 9

52
00:02:49,420 --> 00:02:56,090
So you say, okay, 873- and I'm going to have 1,2,3,4 zeros behind it

53
00:02:56,090 --> 00:02:59,320
So 291 times 3 would give me 873

54
00:02:59,320 --> 00:03:06,560
But I have to multiply- times 3 with 1,2,3,4 zeros to get this number

55
00:03:06,560 --> 00:03:10,080
8.73 million

56
00:03:10,080 --> 00:03:11,770
I have to multiply by 30,000

57
00:03:11,770 --> 00:03:16,290
But I got this straight from this idea, that 291 times 3 is 873

58
00:03:16,290 --> 00:03:20,620
So let's subtract this right over here. Let's subtract this

59
00:03:20,620 --> 00:03:27,610
2 minus 0 is 2. 5, 9, 3, 7 minus 3 is 4, 8 minus 7 is 1

60
00:03:27,610 --> 00:03:30,280
9 minus 8 is 1

61
00:03:30,280 --> 00:03:35,850
So now we are left with 1,143,952

62
00:03:35,850 --> 00:03:40,140
So which of these just gets us right under that?

63
00:03:40,140 --> 00:03:45,140
So let's see, if we want to go to-

64
00:03:45,140 --> 00:03:47,820
we can't go straight to 1746

65
00:03:47,820 --> 00:03:49,580
That would be too big over here

66
00:03:49,580 --> 00:03:51,430
We might want to do 873 again

67
00:03:51,430 --> 00:03:57,480
But this time we are going to do 873,000

68
00:03:57,480 --> 00:04:03,280
That is equal to 3- and then you have 1,2,3 zeros. So 1,2,3

69
00:04:03,280 --> 00:04:08,310
3 times 291 is 873. 3000, is 873000

70
00:04:08,310 --> 00:04:10,200
Let me write this a little bit neater

71
00:04:10,200 --> 00:04:16,940
My handwriting is- so this is going to be 3000

72
00:04:16,940 --> 00:04:19,520
3000 times 291

73
00:04:19,520 --> 00:04:23,510
Let me make sure. This is a 2 right over here. 2 minus 0 is 2

74
00:04:23,510 --> 00:04:26,990
And then you subtract again

75
00:04:26,990 --> 00:04:34,180
2 minus 0 is 2. 5 minus 0 is 5. 9 minus 0 is 9. 3 minus 3 is 0

76
00:04:34,180 --> 00:04:37,560
And then you have 4 minus 7

77
00:04:37,560 --> 00:04:40,920
The way I like to do it when I have to start regrouping and borrowing

78
00:04:40,920 --> 00:04:42,860
is making sure I go from the left

79
00:04:42,860 --> 00:04:47,310
So this 1, I could borrow from there. So this becomes 11

80
00:04:47,310 --> 00:04:50,430
And then the 4, I can borrow 1 from here

81
00:04:50,430 --> 00:04:53,250
So that becomes a 10, and this becomes a 14

82
00:04:53,250 --> 00:04:58,420
So 14 minus 7 is 7. 10 minus 8 is 2

83
00:04:58,420 --> 00:05:04,690
Now 270,952. What's right below that?

84
00:05:04,690 --> 00:05:08,270
So it seems we can get pretty close if we do 291 times 6

85
00:05:08,270 --> 00:05:14,300
If we do a 1746, and then add two zeros to it

86
00:05:14,300 --> 00:05:17,890
This is going to be times 6 with two zeros

87
00:05:17,890 --> 00:05:20,210
So this is times 600

88
00:05:20,210 --> 00:05:22,880
Once again, you subtract

89
00:05:22,880 --> 00:05:24,950
We see I'm only using the 6 and 3

90
00:05:24,950 --> 00:05:26,260
because I figured those out ahead of time

91
00:05:26,260 --> 00:05:27,790
so I didn't have to do any extra math

92
00:05:27,790 --> 00:05:34,950
2 minus 0 is 2. 5 minus 0 is 5. 9 minus 6 is 3. 0 minus 4--

93
00:05:34,950 --> 00:05:38,460
Well, there are a couple of ways you can think about doing this

94
00:05:38,460 --> 00:05:41,130
You could borrow from here. That will become a 6

95
00:05:41,130 --> 00:05:44,660
This becomes a 10. 10 minus 4 is 6

96
00:05:44,660 --> 00:05:47,190
Now this one is lower, so it has to borrow as well

97
00:05:47,190 --> 00:05:51,120
Make this into a 16. 16 minus 7-

98
00:05:51,120 --> 00:05:53,290
I have multiple of videos on how to borrow

99
00:05:53,290 --> 00:05:54,760
if I'm doing that part too fast

100
00:05:54,760 --> 00:05:57,260
But the idea here is to show you a different way of long division

101
00:05:57,260 --> 00:05:59,610
So 16 minus 7 is 9

102
00:05:59,610 --> 00:06:02,680
So now, 96,352

103
00:06:02,680 --> 00:06:03,960
And once again

104
00:06:03,960 --> 00:06:07,300
it looks like the 873 is about the closest we can get

105
00:06:07,300 --> 00:06:11,040
So let me put a 873 over here with 2 zeros

106
00:06:11,040 --> 00:06:15,450
So that would literally be 291 times 3 with 2 zeros

107
00:06:15,450 --> 00:06:19,840
Times 300. And so once again, we want to subtract here

108
00:06:19,840 --> 00:06:26,130
2 minus 0- you get a 2. 5. 0. Make this a 16. Make this an 8

109
00:06:26,130 --> 00:06:28,480
16 minus 7 is 9

110
00:06:28,480 --> 00:06:31,830
And then we have to get close to 9,052

111
00:06:31,830 --> 00:06:35,450
Once again, that 873- those digits look pretty good

112
00:06:35,450 --> 00:06:40,800
873- we still want to multiply 3, and then 10

113
00:06:40,800 --> 00:06:43,730
So this is going to be times 30 right over here

114
00:06:43,730 --> 00:06:50,330
We subtract again. 2 minus 0 is 2. 5 minus 3 is 2

115
00:06:50,330 --> 00:06:52,850
And then you have 90 minus 87 is 3

116
00:06:52,850 --> 00:06:54,290
I'm doing the subtraction a little fast

117
00:06:54,290 --> 00:06:56,580
just so we can get the general idea

118
00:06:56,580 --> 00:07:00,310
Then we have to go into 322. How can we get close to that?

119
00:07:00,310 --> 00:07:03,230
Well, actually 291 is pretty darn close to that

120
00:07:03,230 --> 00:07:05,880
So it's 291. You go into it one time

121
00:07:05,880 --> 00:07:14,290
1 times 291 is 291. 2 minus 1 is 1. 32 minus 29 is 3

122
00:07:14,290 --> 00:07:15,720
So you have a remainder of 31

123
00:07:15,720 --> 00:07:20,010
291 cannot go into 31 any more. So that's our remainder

124
00:07:20,010 --> 00:07:23,290
But how many times does it actually go into this big beastly number?

125
00:07:23,290 --> 00:07:26,340
This 9,873,952

126
00:07:26,340 --> 00:07:29,180
Well, there, we just have to add up all of these right over here

127
00:07:29,180 --> 00:07:31,410
30000 plus 3000- we could even do it in our head

128
00:07:31,410 --> 00:07:41,910
30000 plus 3000 is 33,000. 33600. 33900. 33931

129
00:07:41,910 --> 00:07:45,720
33,931

130
00:07:45,720 --> 00:07:49,550
And we're done, assuming I haven't made some silly mistake

131
00:07:49,550 --> 00:07:55,580
291 goes into this thing 33,931 times with a remainder of 31