1
00:00:00,000 --> 00:00:00,690
Alama za Kubwa kuliko na Ndogo kuliko

2
00:00:00,690 --> 00:00:04,730
Wengi wetu tuna uzoefu na alama ya sawa sawa tangu

3
00:00:04,730 --> 00:00:06,330
siku za mwanzo za kujifunza hesabu.

4
00:00:06,330 --> 00:00:10,480
unaweza kuona kitu kama moja jumlisha moja ni sawa sawa na mbili.

5
00:00:10,480 --> 00:00:14,180
Sasa,watu wengi wanaweza kuwaza wanapoona kitu

6
00:00:14,180 --> 00:00:17,440
kama hiki kwamba kwanamna fulani sawa sawa ina maana ya kunipa mimi jibu.

7
00:00:17,440 --> 00:00:19,100
moja jumlisha moja ni tatizo.

8
00:00:19,100 --> 00:00:22,540
Sawa sawa maana yake kunipa mimi jibu na moja jumlisha moja ni mbili.

9
00:00:22,540 --> 00:00:24,940
Hiyo sio maana ya neno sawa sawa.

10
00:00:24,940 --> 00:00:28,860
Sawa sawa ni uhalisia wa kujaribu kulinganisha viwango viwili.

11
00:00:28,860 --> 00:00:32,250
Ninapoandika moja jumlisha moja sawa na mbili ,kwahiyo

12
00:00:32,250 --> 00:00:34,640
ina maana kwamba nilichonacho upande wa mkono wa kushoto

13
00:00:34,640 --> 00:00:39,370
wa alama ya sawa sawa ni viwango sawa kabisa

14
00:00:39,370 --> 00:00:42,420
Na vile nilivyonavyo upande wa kulia wa alama ya kujumlisha.

15
00:00:42,420 --> 00:00:48,990
Ningeweza pia kuandika kiurahisi mbili ni sawa na moja jumlisha moja.

16
00:00:48,990 --> 00:00:50,950
Hivi vitu viwili ni sawa.

17
00:00:50,950 --> 00:00:54,250
Ningeweza kuandika mbili sawa sawa na mbili.

18
00:00:54,250 --> 00:00:56,040
Hii ni ni tamko lenye ukweli uliokamili.

19
00:00:56,040 --> 00:00:57,500
Hivi vitu viwili ni sawa.

20
00:00:57,500 --> 00:01:02,970
Ningeweza kuandika moja jumlisha moja ni sawa na moja jumlisha moja.

21
00:01:02,970 --> 00:01:12,650
Ningeweza kuandika moja jumlisha moja ni sawa sawa na tatu toa mbili.

22
00:01:12,650 --> 00:01:14,860
Hivi vyote ni viwango sawa.

23
00:01:14,860 --> 00:01:18,880
Nilichonacho hapa upande wa mkono wa kushoto,

24
00:01:18,880 --> 00:01:23,680
ni moja jumlisha moja kutoa moja ni moja na hii hapa kulia ni moja.

25
00:01:23,680 --> 00:01:26,580
Hivi vyote ni viwango sawa .

26
00:01:26,580 --> 00:01:29,600
Sasa,nitawatambulisha kwa jinsi nyingine

27
00:01:29,600 --> 00:01:31,520
ya kulinganisha namba.

28
00:01:31,520 --> 00:01:34,760
Alama ya sawa sawa ni wakati nina viwango sawia kabisa

29
00:01:34,760 --> 00:01:35,805
kwa pande zote mbili.

30
00:01:35,805 --> 00:01:37,180
Sasa tutatafakari juu ya nini

31
00:01:37,180 --> 00:01:40,430
tutafanya tukiwa na viwango tofauti katika pande zote

32
00:01:40,430 --> 00:01:47,780
Kwahiyo tuseme nina namba tatu na namba moja

33
00:01:47,780 --> 00:01:50,140
na nataka kulinganisha zote.

34
00:01:50,140 --> 00:01:53,130
Kwahiyo kiuhalisia tatu na moja sio sawa sawa.

35
00:01:53,130 --> 00:01:54,630
Kwa uhakika ,ninaweza kutamka

36
00:01:54,630 --> 00:01:56,080
bila alama ya sawa sawa.

37
00:01:56,080 --> 00:01:59,740
Kwahiyo naweza kusema tatu haitoweza kuwa sawa na moja.

38
00:01:59,740 --> 00:02:02,410
Lakini tuseme nataka kujua ipi kati yao ni kubwa ya

39
00:02:02,410 --> 00:02:03,860
na ipi ni ndogo ya

40
00:02:03,860 --> 00:02:08,210
Kwahiyo nataka kuwa na baadhi ya alama ambapo naweza kuzilinganisha,

41
00:02:08,210 --> 00:02:12,900
ambapo nitasema , wapi nitatamka zipi kati ya hizi ni kubwa.

42
00:02:12,900 --> 00:02:16,536
Na alama itakayo onesha kwamba hii ni alama ya kubwa kuliko.

43
00:02:16,536 --> 00:02:20,230


44
00:02:20,230 --> 00:02:26,130
Hii itasoma tatu ni kubwa kuliko moja.

45
00:02:26,130 --> 00:02:28,450
Tatu ni kiwango kikubwa.

46
00:02:28,450 --> 00:02:31,580
Na kama kutakuwa na tatizo kukumbuka hii inamaana gani--

47
00:02:31,580 --> 00:02:36,105
kubwa kuliko -kiwango kikubwa kipo kwenye uwazi.

48
00:02:36,105 --> 00:02:38,740


49
00:02:38,740 --> 00:02:41,200
Nahisi kama utaangalia hii kama aina ya mshale,

50
00:02:41,200 --> 00:02:45,370
au kama aina ya alama, lakini huu ni upande mkubwa.

51
00:02:45,370 --> 00:02:47,540
Hapa , una upande mdogo,nukta ndogo

52
00:02:47,540 --> 00:02:49,895
na hapa una upande mkubwa,kwahiyo kiwango kikubwa

53
00:02:49,895 --> 00:02:50,850
kipo ubande mkubwa.

54
00:02:50,850 --> 00:02:52,860
Hii itakuwa inasomeka kama tatu

55
00:02:52,860 --> 00:02:55,550
ni kubwa kuliko-nikiandika

56
00:02:55,550 --> 00:03:02,420
hapa chini-kubwa kuliko,tatu ni kubwa kuliko moja.

57
00:03:02,420 --> 00:03:05,100
Na baadae tena, haiotokuwa tena namba kama ilivyokuwa hivi.

58
00:03:05,100 --> 00:03:06,470
Ninaweza kutoa maelezo.

59
00:03:06,470 --> 00:03:18,130
Naweza kuandika moja jumlisha moja jumlisha moja ni kubwa kuliko,tuseme ,vema,

60
00:03:18,130 --> 00:03:20,110
ni moja upande wa kulia tu.

61
00:03:20,110 --> 00:03:21,800
Hii inafanya mlinganisho.

62
00:03:21,800 --> 00:03:23,910
Lakini ikitokea tuna vitu kwa namna nyingine.

63
00:03:23,910 --> 00:03:28,620
Nini kama nataka kufanya mlinganisho kati ya tano

64
00:03:28,620 --> 00:03:33,040
na ,kusema,kumi na tisa.

65
00:03:33,040 --> 00:03:35,500
Kwahiyo sasa hapa alama ya kubwa kuliko haito tumika.

66
00:03:35,500 --> 00:03:38,320
sio kweli kwamba tano ni kubwa kuliko kumi na tisa.

67
00:03:38,320 --> 00:03:40,800
Naweza kusema kwamba tano sio sawa na kumi na tisa.

68
00:03:40,800 --> 00:03:43,647
Kwahiyo naweza kuendelea kusema hivi.

69
00:03:43,647 --> 00:03:45,980
Lakini ikitokea kama nataka kusema juu ya ipi

70
00:03:45,980 --> 00:03:48,124
ni kubwa na ipi ni ndogo?

71
00:03:48,124 --> 00:03:49,540
Vema,katika kiingereza cha kawaida, ninge

72
00:03:49,540 --> 00:03:53,110
taka kusema tano ni ndogo kuliko kumi na tisa.

73
00:03:53,110 --> 00:03:55,720
Kwahiyo ningetaka kusema -niandike hapa chini-

74
00:03:55,720 --> 00:04:08,890
nataka kuandika tano ni ndogo kuliko kumi na tisa.

75
00:04:08,890 --> 00:04:10,189
Nilitaka kusema .

76
00:04:10,189 --> 00:04:12,480
Na tunatakiwa kuwaza juu ya maandishi ya hesabati

77
00:04:12,480 --> 00:04:16,769
kwa kuandika "ndogo kuliko".

78
00:04:16,769 --> 00:04:19,010
Vema,hii kama ni kubwa kuliko ,

79
00:04:19,010 --> 00:04:21,329
inafanya maana kamili kwamba tulinganishe.

80
00:04:21,329 --> 00:04:23,292
Tufanye,tena,

81
00:04:23,292 --> 00:04:26,400
nukta katika kiwango kidogo na upande mkubwa

82
00:04:26,400 --> 00:04:28,710
wa nukta alama ya kiwango kikubwa.

83
00:04:28,710 --> 00:04:30,810
Kwahiyo hapa tano ni kiwango kidogo kwahiyo

84
00:04:30,810 --> 00:04:32,390
inafanya nukta hapa.

85
00:04:32,390 --> 00:04:37,050
Na kumi na tisa ni kiwango kikubwa,kwahiyo nitafanya hii wazi kama hivi.

86
00:04:37,050 --> 00:04:42,320
Na kwahiyo hii itasomeka kama tano ni ndogo kuliko kumi na tisa.

87
00:04:42,320 --> 00:04:46,160
tano ni kiwango kidogo kuliko kumi na tisa.

88
00:04:46,160 --> 00:04:52,700
Ninaweza pia kuandika moja jumlisha moja ni ndogo kuliko moja

89
00:04:52,700 --> 00:04:54,620
jumlisha moja jumlisha moja.

90
00:04:54,620 --> 00:04:56,830
Ni sawa na kusema kwamba hili tamko , ni kiwango,

91
00:04:56,830 --> 00:05:03,401
moja jumlisha moja ni ndogo kuliko moja jumlisha moja

92
00:05:03,401 --> 00:05:03,901