1
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Hebu tuseme kwamba
tuna sehemu 9/10,

2
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na mimi nataka kuongeza sehemu 1/6.

3
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Hii itakuwa sawa na nini?

4
00:00:13,839 --> 00:00:14,827
Hivyo wakati unaangalia hii, unaweza kusema,

5
00:00:14,827 --> 00:00:16,602
"Oh, nina asili tofauti hapa.

6
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Siyo kawaida kufanya hesabu kama hizi. "

7
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Na njia sahihi ya kufanya hii ni

8
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kuanza kwa kutafuta kigawe cha shirika,

9
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kubadili sehemu zote hizi mbili kuwa

10
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sehemu zenye asili sawa.

11
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Hivyo ni jinsi gani unaweza kupata asili ya shirika?

12
00:00:30,498 --> 00:00:32,125
Naam, asili ya shirika itakuwa ni

13
00:00:32,125 --> 00:00:36,478
kigawe cha shirika cha asili 10 na 6.

14
00:00:36,478 --> 00:00:38,638
Hivyo kigawe cha shirika cha 10 na 6 ni kipi?

15
00:00:38,638 --> 00:00:41,436
Na ni rahisi kutafuta kigawe kidogo cha shirika,

16
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na njia nzuri ya kufanya hii ni kuanza na

17
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asili kubwa, 10, na ujiulize, je 10 inagawanyika kwa 6?

18
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Hapana. Je 20 inagawanyika kwa 6?

19
00:00:51,588 --> 00:00:56,005
Hapana. Je 30 inagawanyika kwa 6?

20
00:00:56,005 --> 00:00:57,722
Hapa tulikuwa tunaangalia vigawe vya 10

21
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na ni kigawe gani kidogo cha 10

22
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ambacho kinagawanyika kwa 6? Na hiko kitakuwa ni 30.

23
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Hivyo naweza kuziandika upya hizi sehemu

24
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kama namba fulani juu ya 30.

25
00:01:07,605 --> 00:01:10,296
Hivyo 9 juu ya 10. Nitaandika vipi hiyo

26
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kama kitu fulani juu ya 30? Nitazidisha

27
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asili kwa 3.

28
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Hivyo nimezidisha asili kwa 3.

29
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Kwa hiyo kama sihitaji kubadili thamani ya sehemu ,

30
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ninatakiwa kufanya vivyo hivyo kwa kiasi.

31
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Nitazidisha kiasi kwa tatu

32
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kwa sababu nilizidisha kiasi kwa tatu

33
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na asili kwa tatu, na hiyo haitabadili

34
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thamani ya sehemu.

35
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Hivyo sita mara tatu ni 27.

36
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Na hivyo, 9/10 na 27/30

37
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zinawakilisha kitu sawa.

38
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Nimeandika hii ikiwa na asili 30,

39
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na pia naweza kuandika 1/6

40
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ikiwa na asili 30. Hebu tufanye hiyo.

41
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Hivyo 1/6 ni nini juu ya 30?

42
00:01:51,621 --> 00:01:52,724
Nakushauri usimamishe hii video

43
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na ujaribu kufanya hiyo.

44
00:01:53,850 --> 00:01:56,149
Hivyo tutafanya nini kutoka 6 mpaka 30?

45
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Tunatakiwa kuzidisha kwa tano.

46
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hivyo kama tukizidisha asili kwa tano,

47
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pia tunatakiwa kuzidisha kiasi kwa tano,

48
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hivyo moja mara tano ni tano.

49
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Hivyo 9/10 ni sawa na 27/30,

50
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na 1/6 ni sawa na 5/30.

51
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Na sasa tunaweza kujumlisha

52
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na iko wazi.

53
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Tuna namba fulani juu ya 30,

54
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na tunajumlisha namba fulani juu ya 30,

55
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hivyo 27/30 + 5/30, hiyo itakuwa sawa na

56
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27 jumlisha 5,

57
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27 + 5,

58
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ambayo

59
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itakuwa sawa na 32/30.

60
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32 juu ya 30, na

61
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kama tukitaka, tunaweza kurahisisha hii sehemu.

62
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Tuna kigawo cha 32 na 30,

63
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zote zinagawanyika kwa 2.

64
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Hivyo kama tukigawanya kiasi na asili kwa 2,

65
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kiasi gawa kwa mbili ni 16,

66
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asili gawa kwa 2 ni 15.

67
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Hivyo, hii ni sawa na 16/15, na kama tukitaka

68
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kuandika hii kama namba mchanganyiko, 15 inaingia mara moja katika 16

69
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na baki moja.

70
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Hivyo hii ni sawa na 1 1/15.

71
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Hebu tufanye hesabu nyingine.

72
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Hebu tuseme tunahitaji kujumlisha

73
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1/2 na

74
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11/12.

75
00:03:36,893 --> 00:03:38,033
Nakushauri usimamishe video

76
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na ujaribu kufanya hii.

77
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Kama tulivyoona mwanzo, tunatakiwa kutafuta

78
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kigawe cha shirika.

79
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Kama hizi zina asili sawa,

80
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tunaweza kuzijumlisha moja kwa moja,

81
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lakini tunatakiwa kutafuta asili ya shirika

82
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kwa sababu haziko sawa.

83
00:03:50,902 --> 00:03:53,468
Tunachotakiwa kutafuta ni rahisi,

84
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kigawe cha shirika cha 2 na12,

85
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na ni vizuri kutafuta kigawe kidogo cha shirika cha 2 na 12,

86
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na kama tulivyofanya mwanzoni, hebu tuanze na kubwa

87
00:04:00,264 --> 00:04:01,901
kati ya hizi mbili, ambayo ni 12.

88
00:04:01,901 --> 00:04:05,291
Na sasa tunachukua 12 mara moja ambayo ni 12,

89
00:04:05,291 --> 00:04:07,949
na hivyo tunaweza kuona kuwa ni kigawe kidogo cha 12.

90
00:04:07,949 --> 00:04:10,632
Na je hiyo inagawanyika kwa mbili? Ndiyo, hakika.

91
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12 inagawanyika kwa mbili.

92
00:04:12,790 --> 00:04:15,855
Hivyo 12 ni kigawe kidogo cha shirika cha mbili na 12,

93
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tunaweza kuandika hizi sehemu mbili

94
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kama kitu fulani juu ya 12.

95
00:04:19,013 --> 00:04:21,625
Hiyo 1/2 ni nini juu ya 12?

96
00:04:21,625 --> 00:04:24,446
Kutoka mbili mpaka 12, utazidisha kwa sita,

97
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pia tutazidisha kiasi kwa sita.

98
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Sasa tunaona 1/2, na 6/12, hizi ni kitu sawa.

99
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Moja ni nusu ya mbili, sita ni nusu ya 12.

100
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Na tutaandikaje 11/12 kama kitu fulani juu ya 12?

101
00:04:38,485 --> 00:04:40,855
Hii tayari imekwisha andikwa juu ya 12,

102
00:04:40,855 --> 00:04:43,258
11/12 tayari ina 12 kama asili,

103
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hivyo hatuna sababu ya kubadili hiyo.

104
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11/12, sasa tuko tayari kujumlisha.

105
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Hivyo hii itakuwa sawa na sita,

106
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hii itakuwa sawa na sita jumlisha 11,

107
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sita jumlisha 11 juu ya 12.

108
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Tuna 6/12 jumlisha 11/12,

109
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itakuwa sita jumlisha 11 juu ya 12,

110
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ambayo itakuwa sawa, na sita jumlisha 11 ni 17/12.

111
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Kama tukitaka kuandika hii kama namba mchanganyiko,

112
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12 inaingia mara moja katika 17

113
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na baki tano, hivyo ni 1 5/12.

114
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Hebu tufanye nyingine kama hii.

115
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Hii ni tofauti kidogo.

116
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Hebu tuseme tunataka kujumlisha,

117
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3/4 na,

118
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1/5.

119
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Na moja juu ya tano.

120
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Hii itakuwa sawa na nini?

121
00:05:44,659 --> 00:05:46,157
Na kwa mara nyingine tena, simamisha hii video na

122
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ujaribu kufanya mwenyewe.

123
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Tuna asili tofauti,

124
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na tunataka kuandika hizi

125
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zikiwa na asili sawa,

126
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hivyo tunatakiwa kutafuta kigawe cha shirika,

127
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ni vizuri kiwe kigawe kidogo cha shirika.

128
00:05:57,095 --> 00:05:59,738
Je, kipi ni kigawe kidogo cha shirika cha nne na tano?

129
00:06:00,548 --> 00:06:01,862
Hebu tuanze na namba kubwa,

130
00:06:01,862 --> 00:06:04,718
na tuangalie vigawe vyake

131
00:06:04,718 --> 00:06:07,061
mpaka tutakapopata kigawe kitakacho gawanyika kwa nne.

132
00:06:07,061 --> 00:06:10,064
Hivyo tano haigawanyiki kwa nne.

133
00:06:10,064 --> 00:06:13,622
10 haigawanyiki kwa nne, bila kubaki

134
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ndio kitu tunachoangalia zaidi.

135
00:06:14,702 --> 00:06:17,059
15 haigawanyiki kwa nne bila kubaki.

136
00:06:17,059 --> 00:06:20,763
20 inagawanyika kwa nne, hiyo ni sawa na tano mara nne.

137
00:06:20,763 --> 00:06:23,514
Kigawe ni 20. Hivyo tunachotakiwa kufanya ni kuandika

138
00:06:23,514 --> 00:06:27,460
sehemu zote mbili zikiwa na asili 20,

139
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au 20 kama asili.

140
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Hivyo tunaweza kuandika 3/4 kama kitu fulani juu ya 20.

141
00:06:32,996 --> 00:06:35,319
Hivyo kutoka nne mpaka 20 katika asili,

142
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tunazidisha kwa tano.

143
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Pia tutazidisha katika kiasi .

144
00:06:38,466 --> 00:06:41,398
Tunazidisha tatu mara tano kupata 15.

145
00:06:41,398 --> 00:06:44,183
Tulichofanya ili kupata 20 ni kuzidisha kwa tano.

146
00:06:44,183 --> 00:06:45,820
Pia tunatakiwa kufanya sawa kwa kiasi,

147
00:06:45,820 --> 00:06:47,736
tatu mara tano ni 15.

148
00:06:47,736 --> 00:06:52,658
3/4 ni sawa na 15/20.

149
00:06:52,658 --> 00:06:55,004
1/5. Itakuwa sawa na nini juu ya 20?

150
00:06:55,004 --> 00:06:58,358
Hivyo kutoka tano mpaka 20, unatakiwa kuzidisha kwa nne.

151
00:06:58,358 --> 00:06:59,995
Pia tunatakiwa kufanya sawa na kwa kiasi.

152
00:06:59,995 --> 00:07:03,861
Tunatakiwa kuzidisha kiasi kwa nne ili kupata 4/20.

153
00:07:04,451 --> 00:07:07,181
Hivyo nimeandika hii badala ya 3/4 jumlisha 1/5,

154
00:07:07,181 --> 00:07:10,815
sasa tumeandika 15/20 jumlisha 4/20.

155
00:07:10,815 --> 00:07:12,973
Na hiyo itakuwa sawa na nini?

156
00:07:12,973 --> 00:07:17,932
Hiyo itakuwa sawa na 15 jumlisha nne ambayo ni 19/20.

157
00:07:17,932 --> 00:07:22,024
19/20, na tumemaliza.