WEBVTT 00:00:00.000 --> 00:00:00.690 Alama za Kubwa kuliko na Ndogo kuliko 00:00:00.690 --> 00:00:04.730 Wengi wetu tuna uzoefu na alama ya sawa sawa tangu 00:00:04.730 --> 00:00:06.330 siku za mwanzo za kujifunza hesabu. 00:00:06.330 --> 00:00:10.480 unaweza kuona kitu kama moja jumlisha moja ni sawa sawa na mbili. 00:00:10.480 --> 00:00:14.180 Sasa,watu wengi wanaweza kuwaza wanapoona kitu 00:00:14.180 --> 00:00:17.440 kama hiki kwamba kwanamna fulani sawa sawa ina maana ya kunipa mimi jibu. 00:00:17.440 --> 00:00:19.100 moja jumlisha moja ni tatizo. 00:00:19.100 --> 00:00:22.540 Sawa sawa maana yake kunipa mimi jibu na moja jumlisha moja ni mbili. 00:00:22.540 --> 00:00:24.940 Hiyo sio maana ya neno sawa sawa. 00:00:24.940 --> 00:00:28.860 Sawa sawa ni uhalisia wa kujaribu kulinganisha viwango viwili. 00:00:28.860 --> 00:00:32.250 Ninapoandika moja jumlisha moja sawa na mbili ,kwahiyo 00:00:32.250 --> 00:00:34.640 ina maana kwamba nilichonacho upande wa mkono wa kushoto 00:00:34.640 --> 00:00:39.370 wa alama ya sawa sawa ni viwango sawa kabisa 00:00:39.370 --> 00:00:42.420 Na vile nilivyonavyo upande wa kulia wa alama ya kujumlisha. 00:00:42.420 --> 00:00:48.990 Ningeweza pia kuandika kiurahisi mbili ni sawa na moja jumlisha moja. 00:00:48.990 --> 00:00:50.950 Hivi vitu viwili ni sawa. 00:00:50.950 --> 00:00:54.250 Ningeweza kuandika mbili sawa sawa na mbili. 00:00:54.250 --> 00:00:56.040 Hii ni ni tamko lenye ukweli uliokamili. 00:00:56.040 --> 00:00:57.500 Hivi vitu viwili ni sawa. 00:00:57.500 --> 00:01:02.970 Ningeweza kuandika moja jumlisha moja ni sawa na moja jumlisha moja. 00:01:02.970 --> 00:01:12.650 Ningeweza kuandika moja jumlisha moja ni sawa sawa na tatu toa mbili. 00:01:12.650 --> 00:01:14.860 Hivi vyote ni viwango sawa. 00:01:14.860 --> 00:01:18.880 Nilichonacho hapa upande wa mkono wa kushoto, 00:01:18.880 --> 00:01:23.680 ni moja jumlisha moja kutoa moja ni moja na hii hapa kulia ni moja. 00:01:23.680 --> 00:01:26.580 Hivi vyote ni viwango sawa . 00:01:26.580 --> 00:01:29.600 Sasa,nitawatambulisha kwa jinsi nyingine 00:01:29.600 --> 00:01:31.520 ya kulinganisha namba. 00:01:31.520 --> 00:01:34.760 Alama ya sawa sawa ni wakati nina viwango sawia kabisa 00:01:34.760 --> 00:01:35.805 kwa pande zote mbili. 00:01:35.805 --> 00:01:37.180 Sasa tutatafakari juu ya nini 00:01:37.180 --> 00:01:40.430 tutafanya tukiwa na viwango tofauti katika pande zote 00:01:40.430 --> 00:01:47.780 Kwahiyo tuseme nina namba tatu na namba moja 00:01:47.780 --> 00:01:50.140 na nataka kulinganisha zote. 00:01:50.140 --> 00:01:53.130 Kwahiyo kiuhalisia tatu na moja sio sawa sawa. 00:01:53.130 --> 00:01:54.630 Kwa uhakika ,ninaweza kutamka 00:01:54.630 --> 00:01:56.080 bila alama ya sawa sawa. 00:01:56.080 --> 00:01:59.740 Kwahiyo naweza kusema tatu haitoweza kuwa sawa na moja. 00:01:59.740 --> 00:02:02.410 Lakini tuseme nataka kujua ipi kati yao ni kubwa ya 00:02:02.410 --> 00:02:03.860 na ipi ni ndogo ya 00:02:03.860 --> 00:02:08.210 Kwahiyo nataka kuwa na baadhi ya alama ambapo naweza kuzilinganisha, 00:02:08.210 --> 00:02:12.900 ambapo nitasema , wapi nitatamka zipi kati ya hizi ni kubwa. 00:02:12.900 --> 00:02:16.536 Na alama itakayo onesha kwamba hii ni alama ya kubwa kuliko. 00:02:16.536 --> 00:02:20.230 00:02:20.230 --> 00:02:26.130 Hii itasoma tatu ni kubwa kuliko moja. 00:02:26.130 --> 00:02:28.450 Tatu ni kiwango kikubwa. 00:02:28.450 --> 00:02:31.580 Na kama kutakuwa na tatizo kukumbuka hii inamaana gani-- 00:02:31.580 --> 00:02:36.105 kubwa kuliko -kiwango kikubwa kipo kwenye uwazi. 00:02:36.105 --> 00:02:38.740 00:02:38.740 --> 00:02:41.200 Nahisi kama utaangalia hii kama aina ya mshale, 00:02:41.200 --> 00:02:45.370 au kama aina ya alama, lakini huu ni upande mkubwa. 00:02:45.370 --> 00:02:47.540 Hapa , una upande mdogo,nukta ndogo 00:02:47.540 --> 00:02:49.895 na hapa una upande mkubwa,kwahiyo kiwango kikubwa 00:02:49.895 --> 00:02:50.850 kipo ubande mkubwa. 00:02:50.850 --> 00:02:52.860 Hii itakuwa inasomeka kama tatu 00:02:52.860 --> 00:02:55.550 ni kubwa kuliko-nikiandika 00:02:55.550 --> 00:03:02.420 hapa chini-kubwa kuliko,tatu ni kubwa kuliko moja. 00:03:02.420 --> 00:03:05.100 Na baadae tena, haiotokuwa tena namba kama ilivyokuwa hivi. 00:03:05.100 --> 00:03:06.470 Ninaweza kutoa maelezo. 00:03:06.470 --> 00:03:18.130 Naweza kuandika moja jumlisha moja jumlisha moja ni kubwa kuliko,tuseme ,vema, 00:03:18.130 --> 00:03:20.110 ni moja upande wa kulia tu. 00:03:20.110 --> 00:03:21.800 Hii inafanya mlinganisho. 00:03:21.800 --> 00:03:23.910 Lakini ikitokea tuna vitu kwa namna nyingine. 00:03:23.910 --> 00:03:28.620 Nini kama nataka kufanya mlinganisho kati ya tano 00:03:28.620 --> 00:03:33.040 na ,kusema,kumi na tisa. 00:03:33.040 --> 00:03:35.500 Kwahiyo sasa hapa alama ya kubwa kuliko haito tumika. 00:03:35.500 --> 00:03:38.320 sio kweli kwamba tano ni kubwa kuliko kumi na tisa. 00:03:38.320 --> 00:03:40.800 Naweza kusema kwamba tano sio sawa na kumi na tisa. 00:03:40.800 --> 00:03:43.647 Kwahiyo naweza kuendelea kusema hivi. 00:03:43.647 --> 00:03:45.980 Lakini ikitokea kama nataka kusema juu ya ipi 00:03:45.980 --> 00:03:48.124 ni kubwa na ipi ni ndogo? 00:03:48.124 --> 00:03:49.540 Vema,katika kiingereza cha kawaida, ninge 00:03:49.540 --> 00:03:53.110 taka kusema tano ni ndogo kuliko kumi na tisa. 00:03:53.110 --> 00:03:55.720 Kwahiyo ningetaka kusema -niandike hapa chini- 00:03:55.720 --> 00:04:08.890 nataka kuandika tano ni ndogo kuliko kumi na tisa. 00:04:08.890 --> 00:04:10.189 Nilitaka kusema . 00:04:10.189 --> 00:04:12.480 Na tunatakiwa kuwaza juu ya maandishi ya hesabati 00:04:12.480 --> 00:04:16.769 kwa kuandika "ndogo kuliko". 00:04:16.769 --> 00:04:19.010 Vema,hii kama ni kubwa kuliko , 00:04:19.010 --> 00:04:21.329 inafanya maana kamili kwamba tulinganishe. 00:04:21.329 --> 00:04:23.292 Tufanye,tena, 00:04:23.292 --> 00:04:26.400 nukta katika kiwango kidogo na upande mkubwa 00:04:26.400 --> 00:04:28.710 wa nukta alama ya kiwango kikubwa. 00:04:28.710 --> 00:04:30.810 Kwahiyo hapa tano ni kiwango kidogo kwahiyo 00:04:30.810 --> 00:04:32.390 inafanya nukta hapa. 00:04:32.390 --> 00:04:37.050 Na kumi na tisa ni kiwango kikubwa,kwahiyo nitafanya hii wazi kama hivi. 00:04:37.050 --> 00:04:42.320 Na kwahiyo hii itasomeka kama tano ni ndogo kuliko kumi na tisa. 00:04:42.320 --> 00:04:46.160 tano ni kiwango kidogo kuliko kumi na tisa. 00:04:46.160 --> 00:04:52.700 Ninaweza pia kuandika moja jumlisha moja ni ndogo kuliko moja 00:04:52.700 --> 00:04:54.620 jumlisha moja jumlisha moja. 00:04:54.620 --> 00:04:56.830 Ni sawa na kusema kwamba hili tamko , ni kiwango, 00:04:56.830 --> 00:05:03.401 moja jumlisha moja ni ndogo kuliko moja jumlisha moja 00:05:03.401 --> 00:05:03.901