WEBVTT 00:00:00.283 --> 00:00:01.862 Hebu tufanye maswali ya 00:00:01.862 --> 00:00:03.650 kukokotoa milinganyo. 00:00:03.650 --> 00:00:08.421 Tuchukulie tuna mlinganyo huu, 1/3 jumlisha A 00:00:08.421 --> 00:00:10.905 ni sawa na 5/3. 00:00:10.905 --> 00:00:13.924 Je, thamani ya A ni ngapi kwenye mlinganyo? 00:00:13.924 --> 00:00:17.604 Kama nina 1/3 jumlisha A, je A inatakiwa kuwa ngapi 00:00:17.604 --> 00:00:22.604 ili tukiijumlisha kwa 1/3 iwe sawa na 5/3? 00:00:23.873 --> 00:00:27.135 Kuna njia nyingi za kufanya hii, 00:00:27.135 --> 00:00:29.735 na hiki ni kitu cha kufurahisha kuhusu mlinganyo 00:00:29.735 --> 00:00:32.835 na hakuna njia moja ya kukokotoa. 00:00:32.835 --> 00:00:34.831 Hivyo ngoja nifikirie, 00:00:34.831 --> 00:00:36.004 njia nyepesi ya kutumia. 00:00:36.004 --> 00:00:38.105 Na kabla sijafanya chochote, unaweza 00:00:38.105 --> 00:00:40.891 kusubirisha video, na ufanye mwenyewe. 00:00:40.891 --> 00:00:45.891 Hivyo nachotakiwa ni kuwa na A 00:00:46.313 --> 00:00:47.892 upande mmoja wa mlinganyo. 00:00:47.892 --> 00:00:49.536 Kwa kuwa A ipo tayari upande wa kushoto, 00:00:49.536 --> 00:00:51.440 tuone kama nitaweza kuendelea kuiweka upande wa kushoto, 00:00:51.440 --> 00:00:53.831 hivyo naiondoa 1/3. 00:00:53.831 --> 00:00:55.930 Vizuri, njia rahisi ya kuiondoa 00:00:55.930 --> 00:00:59.314 hii 1/3 ni kutoa 1/3 kutoka upande wa 00:00:59.314 --> 00:01:00.757 kushoto wa mlinganyo. 00:01:00.757 --> 00:01:02.661 Siwezi kutoa 00:01:02.661 --> 00:01:04.298 upande wa kushoto wa mlinganyo peke yake. 00:01:04.298 --> 00:01:06.759 Kama 1/3 jumlisha A ni sawa na 5/3, 00:01:06.759 --> 00:01:09.719 na kama nikitoa 1/3 kutoka upande wa kushoto tu, 00:01:09.719 --> 00:01:11.715 hivyo haiwezi kuwa sawa. 00:01:11.715 --> 00:01:13.699 Hivyo upande huu utakuwa pungufu ya 1/3, 00:01:13.699 --> 00:01:15.059 endapo upande huu hautobadilika. 00:01:15.059 --> 00:01:16.800 Hivyo basi upande wa kushoto utakuwa 00:01:16.800 --> 00:01:18.321 pungufu ya 5/3. 00:01:18.321 --> 00:01:20.862 Kwa hiyo ili kupata usawa, nitakachokifanya 00:01:20.862 --> 00:01:23.986 upande wa kushoto nitakifanya upande wa kulia pia. 00:01:23.986 --> 00:01:26.819 Hivyo nitatoa 1/3 pande zote. 00:01:26.819 --> 00:01:30.313 Na kama nikifanya hivyo, upande wa kushoto, 00:01:30.313 --> 00:01:32.391 1/3 toa 1/3, ndiyo maana 00:01:32.391 --> 00:01:35.190 nimetoa 1/3 ili kuondoa 1/3, 00:01:35.190 --> 00:01:40.190 na nimebakiwa na A ni sawa na 5/3 toa 1/3, 00:01:41.829 --> 00:01:46.055 5/3 toa 1/3, 00:01:46.055 --> 00:01:49.762 toa 1/3 , tutapata ngapi? 00:01:49.762 --> 00:01:53.268 Nina tano ya kitu hapa, kwenye hili swali nina 5/3, 00:01:53.268 --> 00:01:55.893 ninatoa kwa 1/3. 00:01:55.893 --> 00:01:58.902 Hivyo nitabakiwa na 4/3. 00:01:58.902 --> 00:02:03.902 Hivyo nitaandika A ni sawa na 4/3. 00:02:05.856 --> 00:02:07.482 Unaweza kuhakikisha kama ni sahihi. 00:02:07.482 --> 00:02:12.482 1/3 jumlisha 4/3 ni sawa na 5/3. 00:02:12.972 --> 00:02:14.853 Hebu tufanye mfano mwingine. 00:02:14.853 --> 00:02:19.853 Tuchukulie tuna mlinganyo huu, K toa nane 00:02:21.240 --> 00:02:24.920 ni sawa na 11.8. 00:02:24.920 --> 00:02:27.522 Kwa mara nyingine, natafuta thamani ya K. 00:02:27.522 --> 00:02:29.437 Nina K upande wa kushoto. 00:02:29.437 --> 00:02:33.477 Sihitaji kuwa na hii, toa nane hapa. 00:02:33.477 --> 00:02:36.011 Hivyo ili kuondoa hii nane, hivyo tuongeze nane 00:02:36.011 --> 00:02:36.795 upande wa kushoto. 00:02:36.795 --> 00:02:38.095 Hivyo, kama nafanya hivi upande wa kushoto, 00:02:38.095 --> 00:02:40.278 nitafanya hivyohivyo upande wa kulia. 00:02:40.278 --> 00:02:42.775 Hivyo tunaongeza nane pande zote. 00:02:42.775 --> 00:02:45.524 Upande wa kushoto, unatoa nane 00:02:45.524 --> 00:02:46.441 na pia unajumlisha nane. 00:02:46.441 --> 00:02:47.615 Hii inaisha, 00:02:47.615 --> 00:02:49.761 na unabakiwa na K. 00:02:49.761 --> 00:02:53.175 Na upande wa kulia, 11.8 jumlisha nane. 00:02:53.175 --> 00:02:58.175 Vizuri, 11 jumlisha nane ni 19, itakuwa 19.8. 00:02:58.758 --> 00:03:01.115 Na tumemaliza, 00:03:01.115 --> 00:03:03.413 Unaweza kuhakikisha kama umepata jibu sahihi. 00:03:03.413 --> 00:03:07.803 19.8 toa nane ni 11.8. 00:03:07.803 --> 00:03:10.542 Hebu tufanye nyingine, hii inavutia. 00:03:10.542 --> 00:03:15.542 Sawa, tuchukulie nina 5/13 ni sawa na 00:03:16.462 --> 00:03:20.259 T toa 6/13. 00:03:20.259 --> 00:03:22.362 Vizuri, hii inavutia kwa sababu sasa nina mtajo 00:03:22.362 --> 00:03:23.878 upande wa kulia. 00:03:23.878 --> 00:03:24.841 Hivyo naiacha hapa. 00:03:24.841 --> 00:03:27.545 Tuone kama tunaweza kutafuta thamani ya T kwa kuondoa 00:03:27.545 --> 00:03:29.263 namba yoyote upande wa kulia. 00:03:29.263 --> 00:03:33.663 Na kama tulivyofanya awali, kama natoa 6/13, 00:03:33.663 --> 00:03:35.602 kwa nini nisiijumlishe? 00:03:35.602 --> 00:03:37.424 Kwa nini nisijumlishe 6/13? 00:03:37.424 --> 00:03:38.776 Siwezi kufanya hivyo upande wa kushoto. 00:03:38.776 --> 00:03:41.110 Hizi pande mbili hazitakuwa sawa, 00:03:41.110 --> 00:03:43.106 nitafanya hivyo upande wa kulia kama ninataka 00:03:43.106 --> 00:03:45.289 kupata usawa. 00:03:45.289 --> 00:03:47.007 Hivyo nini kitatokea? 00:03:47.007 --> 00:03:47.832 Nini kitatokea? 00:03:47.832 --> 00:03:50.466 Upande wa kushoto nina 00:03:50.466 --> 00:03:52.126 ngoja niache nafasi kidogo, 00:03:52.126 --> 00:03:56.615 nina 5/13 jumlisha 6/13, 00:03:57.548 --> 00:04:01.880 jumlisha 6/13 ni sawa na , 00:04:01.880 --> 00:04:03.702 ni sawa na 00:04:03.702 --> 00:04:06.745 Nilitoa 6/13, sasa najumlisha 6/13. 00:04:06.745 --> 00:04:09.135 Hizi zitatupatia sifuri. 00:04:09.135 --> 00:04:12.943 6/13 toa 6/13 inabaki sifuri, hivyo umebakiwa na T. 00:04:12.943 --> 00:04:14.278 Hivyo T ni sawa na hii. 00:04:14.278 --> 00:04:17.401 Kama nina 5/13 na najumlisha na hii 6/13, 00:04:17.401 --> 00:04:19.304 Nitapata 11/13. 00:04:19.304 --> 00:04:24.018 Hivyo hii itakuwa 11/13 ni sawa na T, 00:04:24.018 --> 00:04:25.319 au naweza kuiandika kwa njia nyingine. 00:04:25.319 --> 00:04:30.319 Naandika T ni sawa na 11/13.