WEBVTT 00:00:00.145 --> 00:00:03.553 Nipo hapa na Jesse ambae ni Mwalimu wa hesabu 00:00:03.553 --> 00:00:05.160 kwenye chuo cha Khan 00:00:05.160 --> 00:00:08.403 na una maswali mazuri au mawazo. 00:00:08.403 --> 00:00:11.599 Swali ambalo wanafunzi wamekuwa wanauliza wanapojifunza algebra 00:00:11.599 --> 00:00:16.106 ni kwa nini tunatumia herufi, kwa nini tuisitumie namba kwenye kila kitu? 00:00:16.106 --> 00:00:18.076 Kwa nini tunatumia herufi?kwa nini tuna hizi 00:00:18.076 --> 00:00:21.811 X, Y na Z na ABC tunapoanza kufanya algebra? 00:00:21.811 --> 00:00:22.680 sawa. 00:00:22.680 --> 00:00:28.286 Inafurahisha, tunawaacha mtafakari kwa mda kidogo. 00:00:28.286 --> 00:00:30.232 Hivyo Sal, utajibuje hili swali? 00:00:30.232 --> 00:00:32.193 Kwa nini tunahitaji herufi kwenye Algebra? 00:00:32.193 --> 00:00:35.824 Kuna sababu naweza kuzieleza. 00:00:35.824 --> 00:00:38.026 Moja ni ukiwa huna kitu. 00:00:38.026 --> 00:00:44.239 Hivyo kama nikiandika X jumlisha tatu in sawa na kumi. 00:00:44.239 --> 00:00:46.577 tunafanya hivi kwa sababu hatujui X ni nini 00:00:46.577 --> 00:00:48.298 ni kitu kisichojulikana. 00:00:48.298 --> 00:00:50.197 Hivyo tunaanza kuitafuta kwa njia tofauti. 00:00:50.197 --> 00:00:51.710 Ila haitakiwi kuwa X. 00:00:51.710 --> 00:00:55.703 Tunaweza kuweka nafasi wazi jumlisha tatu ni sawa na kumi. 00:00:55.703 --> 00:00:59.725 Au tunaweza kuweka alama ya ulizo jumlisha tatu ni sawa na kumi. 00:00:59.725 --> 00:01:03.147 Hivyo sio lazima iwe herufi, ila kinachohitajika ni alama tu. 00:01:03.147 --> 00:01:07.434 Inaweza kuwekwa hata uso jumlisha tatu ni sawa na kumi. 00:01:07.434 --> 00:01:12.181 Ila mpaka ufahamu, unahitaji alama kuwakilisha hiyo namba tusiyoijua. 00:01:12.181 --> 00:01:15.700 Sasa tunafanya hili swali na kisha tujue hiyo alama inawakilisha nini. 00:01:15.700 --> 00:01:17.916 Kama tulijua kabla ya muda, isingekuwa ni kitu tusichokifahamu. 00:01:17.916 --> 00:01:20.387 Isingekuwa ni kitu tusichokifahamu. 00:01:20.387 --> 00:01:23.576 Hivyo hiyo ni moja ya sababu ya kutumia herufi 00:01:23.576 --> 00:01:26.489 na sehemu ambayo namba zenyewe haziwezi kusaidia. 00:01:26.489 --> 00:01:28.942 Nyingine ni wakati unatazama mahusiano ya namba. 00:01:28.942 --> 00:01:32.286 Hivyo nitafanya kitu kama- ninaweza kusema 00:01:32.286 --> 00:01:38.021 ukinipa tatu, nitakupa nne. 00:01:38.021 --> 00:01:43.762 Na naweza kusema, kama ukinipa tano, nitakupa sita. 00:01:43.762 --> 00:01:46.050 Ninaweza kuendelea mpaka mwisho. 00:01:46.050 --> 00:01:51.626 Ukinipa 7.1, nitakupa 8.1. 00:01:51.626 --> 00:01:54.431 Ninaweza kuendelea kuainisha mpaka mwisho. 00:01:54.431 --> 00:01:57.477 Unaweza kunipa namba yeyote na nitakuambia nitakupa ngapi. 00:01:57.477 --> 00:02:00.879 Ila nitaishiwa na sehemu na muda kama nikiziorodhesha zote. 00:02:00.879 --> 00:02:06.259 Tutafanya vizuri kama tutatumia herufi kutambua namba. 00:02:06.259 --> 00:02:11.296 Pengine ulichonipa tunakiita X na ninachokupa tunakiita Y. 00:02:11.296 --> 00:02:14.678 Ninaweza kuisema chochote unachonipa nitajumlisha na moja. 00:02:14.678 --> 00:02:16.867 Na ndicho nitakacho kurudishia. 00:02:16.867 --> 00:02:20.670 Sasa, huu ni mlinganyo mrahisi hapa 00:02:20.670 --> 00:02:24.717 unaweza kugundua namba inayowakilisha mahusiano baina ya X 00:02:24.717 --> 00:02:28.219 na Y. 00:02:28.219 --> 00:02:31.497 Sasa inajulikana X yeyote utakayonipa 00:02:31.497 --> 00:02:34.612 umenipa tatu, nina jumlisha moja na nitakupa nne. 00:02:34.627 --> 00:02:38.200 Ukinipa 7.1, nitajumlisha moja na nitakupa 8.1. 00:02:38.200 --> 00:02:41.166 Hakuna njia ya kuwakilisha zaidi ya kutumia alama. 00:02:41.166 --> 00:02:43.959 Kwahiyo, sihitaji kutumia X na Y. 00:02:43.959 --> 00:02:46.648 Hizi zimezoeleka kutumika tangu zamani 00:02:46.648 --> 00:02:49.725 Ninaweza kusema ulichonipa ni nyota 00:02:49.725 --> 00:02:54.827 na nilichokupa ni sura 00:02:54.827 --> 00:02:57.733 na hii pia inaweza kuwa njia sahihi ya kuwakilisha. 00:02:57.733 --> 00:03:01.733 Hivyo herufi ni alama tu, Hakuna cha ziada.