1
00:00:00,000 --> 00:00:00,570


2
00:00:00,570 --> 00:00:03,110
Tuseme tuna namba 5 na tumeulizwa,

3
00:00:03,110 --> 00:00:07,870
ni namba gani tukijumlisha na namba 5 tunapata 0?

4
00:00:07,870 --> 00:00:10,620
Unaweza ukawa umeshafahamu, ila nitachora.

5
00:00:10,620 --> 00:00:13,900
Tunamstari wa namba hapa.

6
00:00:13,900 --> 00:00:16,300
Na 0 imekaa hapo.

7
00:00:16,300 --> 00:00:19,740
Na tayari tupo hapa kwenye 5.

8
00:00:19,740 --> 00:00:23,995
Hivyo kutoka kwenye 5 mpaka 0, inatakiwa twende nafasi 5 kushoto.

9
00:00:23,995 --> 00:00:27,710


10
00:00:27,710 --> 00:00:29,550
Na kama tunaenda nafasi 5 kushoto,

11
00:00:29,550 --> 00:00:32,400
Inamaanisha tunajumlisha hasi 5.

12
00:00:32,400 --> 00:00:34,780
Tukiongeza hasi 5 hapa,

13
00:00:34,780 --> 00:00:38,250
hii itaturudisha kwenye 0.

14
00:00:38,250 --> 00:00:40,750
hii itaturudisha hapa kwenye 0.

15
00:00:40,750 --> 00:00:42,680
Pengine ulikuwa umeshajua.

16
00:00:42,680 --> 00:00:45,900
Nafikiri hii hapa inaingia akilini.

17
00:00:45,900 --> 00:00:49,170
Ila tunaweza kuita kinyume cha

18
00:00:49,170 --> 00:00:50,070
kujumlisha.

19
00:00:50,070 --> 00:00:52,060
Na zakujumlisha-- ninaiandika.

20
00:00:52,060 --> 00:00:53,768
nafikiri inachanganya

21
00:00:53,768 --> 00:00:55,940
kutoa jina gumu kwenye jambo rahisi--

22
00:00:55,940 --> 00:00:58,600
kinyume cha kujumlisha.

23
00:00:58,600 --> 00:01:00,650
Na ni wazo kwamba kama una namba

24
00:01:00,650 --> 00:01:03,920
na ujumlishe kinyume cha hiyo namba, ambayo

25
00:01:03,920 --> 00:01:06,320
watu wengi wanaita hasi ya namba --

26
00:01:06,320 --> 00:01:08,530
ukijumlisha hasi ya namba kwenye namba yako

27
00:01:08,530 --> 00:01:10,920
utapata 0 kwa sababu

28
00:01:10,920 --> 00:01:13,860
zinalingana, unaweza kuona hivyo.

29
00:01:13,860 --> 00:01:16,190
Zote zina ukubwa wa 5, ila hii inaongeza tano

30
00:01:16,190 --> 00:01:20,060
kulia na kisha unapunguza tano kwa kwenda kushoto.

31
00:01:20,060 --> 00:01:24,860
Ni sawa, na kama ukianza kwenye- ngoja nichore mstari mwingine wa namba

32
00:01:24,860 --> 00:01:29,310
hapa-- kama ukianza kwenye hasi 3.

33
00:01:29,310 --> 00:01:31,570
Kama ukianza hapa kwenye hasi 3,

34
00:01:31,570 --> 00:01:34,040
utakuwa umeshasogea nafasi tatu kwenda kushoto,

35
00:01:34,040 --> 00:01:39,030
mmoja kasema, ninatakiwa kuongeza ngapi kwenye hasi 3

36
00:01:39,030 --> 00:01:39,920
ili nirudi kwenye 0?

37
00:01:39,920 --> 00:01:42,660
Itatakiwa nisogee nafasi tatu kwenda kulia.

38
00:01:42,660 --> 00:01:45,160
Na nafasi tatu kwenda kulia ni upande chanya.

39
00:01:45,160 --> 00:01:47,540
Hivyo natakiwa kuongeza chanya 3.

40
00:01:47,540 --> 00:01:51,270
Hivyo kama nimejumlisha chanya 3 kwenye hasi 3 ninapata 0.

41
00:01:51,270 --> 00:02:00,030
Kwa ujumla, kama nina namba yeyote-- kama nina 1,725,314

42
00:02:00,030 --> 00:02:03,170
na nikajiuliza natakiwa nijumlishe ngapi ili nirudi kwenye 0?

43
00:02:03,170 --> 00:02:07,010
Nitatakiwa kwenda uelekeo kinyume.

44
00:02:07,010 --> 00:02:09,180
Nitakwenda kwenye uelekeo wa kushoto.

45
00:02:09,180 --> 00:02:11,000
Hivyo natakiwa kutoa kiasi kilekile.

46
00:02:11,000 --> 00:02:13,880
Au ninaweza kusema ninajumlisha namba kinyume,

47
00:02:13,880 --> 00:02:16,270
au ninajumlisha kinyume cha hiyo namba.

48
00:02:16,270 --> 00:02:18,690
Hivyo hii itakuwa ni sawa na kujumlisha

49
00:02:18,690 --> 00:02:26,230
hasi 1,725,314 na hapa nitapata 0.

50
00:02:26,230 --> 00:02:29,850
Ni sawa na nikisema, ni namba gani natakiwa nijumlishe na hasi 7

51
00:02:29,850 --> 00:02:30,410
nipate 0?

52
00:02:30,410 --> 00:02:33,430
Kama tayari niko kwenye hasi 7, natakiwa niende mara saba kulia

53
00:02:33,430 --> 00:02:35,510
hivyo ninaongeza chanya 7.

54
00:02:35,510 --> 00:02:39,080
Na hii itakuwa sawa na 0.

55
00:02:39,080 --> 00:02:41,460
Na hii inatokana na uelewa wa jumla

56
00:02:41,460 --> 00:02:44,970
5 jumlisha hasi 5,

57
00:02:44,970 --> 00:02:47,410
au 5 jumlisha kinyume cha 5,

58
00:02:47,410 --> 00:02:51,314
unaweza kusema ni namna nyingine ya kusema 5 toa 5.

59
00:02:51,314 --> 00:02:52,730
Na kama una 5 ya kitu,

60
00:02:52,730 --> 00:02:55,540
na ukaondoa tano, umejifunza miaka mingi iliyopita

61
00:02:55,540 --> 00:02:58,524
kwamba hiyo itakuwa ni sawa na 0.

62
00:02:58,524 --> 00:02:59,024