WEBVTT 00:00:00.000 --> 00:00:00.570 00:00:00.570 --> 00:00:03.110 Tuseme tuna namba 5 na tumeulizwa, 00:00:03.110 --> 00:00:07.870 ni namba gani tukijumlisha na namba 5 tunapata 0? 00:00:07.870 --> 00:00:10.620 Unaweza ukawa umeshafahamu, ila nitachora. 00:00:10.620 --> 00:00:13.900 Tunamstari wa namba hapa. 00:00:13.900 --> 00:00:16.300 Na 0 imekaa hapo. 00:00:16.300 --> 00:00:19.740 Na tayari tupo hapa kwenye 5. 00:00:19.740 --> 00:00:23.995 Hivyo kutoka kwenye 5 mpaka 0, inatakiwa twende nafasi 5 kushoto. 00:00:23.995 --> 00:00:27.710 00:00:27.710 --> 00:00:29.550 Na kama tunaenda nafasi 5 kushoto, 00:00:29.550 --> 00:00:32.400 Inamaanisha tunajumlisha hasi 5. 00:00:32.400 --> 00:00:34.780 Tukiongeza hasi 5 hapa, 00:00:34.780 --> 00:00:38.250 hii itaturudisha kwenye 0. 00:00:38.250 --> 00:00:40.750 hii itaturudisha hapa kwenye 0. 00:00:40.750 --> 00:00:42.680 Pengine ulikuwa umeshajua. 00:00:42.680 --> 00:00:45.900 Nafikiri hii hapa inaingia akilini. 00:00:45.900 --> 00:00:49.170 Ila tunaweza kuita kinyume cha 00:00:49.170 --> 00:00:50.070 kujumlisha. 00:00:50.070 --> 00:00:52.060 Na zakujumlisha-- ninaiandika. 00:00:52.060 --> 00:00:53.768 nafikiri inachanganya 00:00:53.768 --> 00:00:55.940 kutoa jina gumu kwenye jambo rahisi-- 00:00:55.940 --> 00:00:58.600 kinyume cha kujumlisha. 00:00:58.600 --> 00:01:00.650 Na ni wazo kwamba kama una namba 00:01:00.650 --> 00:01:03.920 na ujumlishe kinyume cha hiyo namba, ambayo 00:01:03.920 --> 00:01:06.320 watu wengi wanaita hasi ya namba -- 00:01:06.320 --> 00:01:08.530 ukijumlisha hasi ya namba kwenye namba yako 00:01:08.530 --> 00:01:10.920 utapata 0 kwa sababu 00:01:10.920 --> 00:01:13.860 zinalingana, unaweza kuona hivyo. 00:01:13.860 --> 00:01:16.190 Zote zina ukubwa wa 5, ila hii inaongeza tano 00:01:16.190 --> 00:01:20.060 kulia na kisha unapunguza tano kwa kwenda kushoto. 00:01:20.060 --> 00:01:24.860 Ni sawa, na kama ukianza kwenye- ngoja nichore mstari mwingine wa namba 00:01:24.860 --> 00:01:29.310 hapa-- kama ukianza kwenye hasi 3. 00:01:29.310 --> 00:01:31.570 Kama ukianza hapa kwenye hasi 3, 00:01:31.570 --> 00:01:34.040 utakuwa umeshasogea nafasi tatu kwenda kushoto, 00:01:34.040 --> 00:01:39.030 mmoja kasema, ninatakiwa kuongeza ngapi kwenye hasi 3 00:01:39.030 --> 00:01:39.920 ili nirudi kwenye 0? 00:01:39.920 --> 00:01:42.660 Itatakiwa nisogee nafasi tatu kwenda kulia. 00:01:42.660 --> 00:01:45.160 Na nafasi tatu kwenda kulia ni upande chanya. 00:01:45.160 --> 00:01:47.540 Hivyo natakiwa kuongeza chanya 3. 00:01:47.540 --> 00:01:51.270 Hivyo kama nimejumlisha chanya 3 kwenye hasi 3 ninapata 0. 00:01:51.270 --> 00:02:00.030 Kwa ujumla, kama nina namba yeyote-- kama nina 1,725,314 00:02:00.030 --> 00:02:03.170 na nikajiuliza natakiwa nijumlishe ngapi ili nirudi kwenye 0? 00:02:03.170 --> 00:02:07.010 Nitatakiwa kwenda uelekeo kinyume. 00:02:07.010 --> 00:02:09.180 Nitakwenda kwenye uelekeo wa kushoto. 00:02:09.180 --> 00:02:11.000 Hivyo natakiwa kutoa kiasi kilekile. 00:02:11.000 --> 00:02:13.880 Au ninaweza kusema ninajumlisha namba kinyume, 00:02:13.880 --> 00:02:16.270 au ninajumlisha kinyume cha hiyo namba. 00:02:16.270 --> 00:02:18.690 Hivyo hii itakuwa ni sawa na kujumlisha 00:02:18.690 --> 00:02:26.230 hasi 1,725,314 na hapa nitapata 0. 00:02:26.230 --> 00:02:29.850 Ni sawa na nikisema, ni namba gani natakiwa nijumlishe na hasi 7 00:02:29.850 --> 00:02:30.410 nipate 0? 00:02:30.410 --> 00:02:33.430 Kama tayari niko kwenye hasi 7, natakiwa niende mara saba kulia 00:02:33.430 --> 00:02:35.510 hivyo ninaongeza chanya 7. 00:02:35.510 --> 00:02:39.080 Na hii itakuwa sawa na 0. 00:02:39.080 --> 00:02:41.460 Na hii inatokana na uelewa wa jumla 00:02:41.460 --> 00:02:44.970 5 jumlisha hasi 5, 00:02:44.970 --> 00:02:47.410 au 5 jumlisha kinyume cha 5, 00:02:47.410 --> 00:02:51.314 unaweza kusema ni namna nyingine ya kusema 5 toa 5. 00:02:51.314 --> 00:02:52.730 Na kama una 5 ya kitu, 00:02:52.730 --> 00:02:55.540 na ukaondoa tano, umejifunza miaka mingi iliyopita 00:02:55.540 --> 00:02:58.524 kwamba hiyo itakuwa ni sawa na 0. 00:02:58.524 --> 00:02:59.024