Ukudibanisa/Ukongeza

Ukongeza yindlela yakwamathematika ekuqokolelwa izinto zibe ndawonye.  

 IZIBALO 
Kwizibalo, xa kudityaniswa kuyongezwa. Oko kukuthi xa kusongezwa inani kwinani elikhoyo, kuphuma inani elinye, nanku umzekelo, xa u-5 ( esongezwa ku-4 . Kuphuma inani elilingana nala manani omabini xa edibene. Nalu uphawu olubonisa ukongeza inani kwinani elikhoyo +  enye into kwenyeinto kwenye into kufunyanwa inani elisisiphumo laxa kudityaniswe amanani  amabini nangaphezulu. uphawu lokudibanisa nali "+". Igama loluphawu lithi "+" is "dibanisa". Elinye igama lesiphumo samanani adityanisiweyo kuthiwa y-isum.

 Imizekelo yokubala 
Umzekelo, kukho ii-objects kumaqela amabini. Ezi objects zizangqa ezincinane: "o". Ezi-5 kwezi zangqa zekwelinye iqela. Ukanti ezi-3 zikwelinye iqela. Ukuze sifumane inani elufumaneka lezi-objects kula maqela mabini, kufuneka zibalwe ezi objects. Enye indlela yokufumana inani lee-objects kumaqela omabini, kukudibanisa laa manani eqela ngalinye.  

 Ukudibanisa 
Enye indlela kukudibanisa amanani ezi-objects kwiqela A nakwiqela B, kuba sele zibaliwe.  Kwezi mpawu:

kukho imigaqo elandelwayo xa kudityaniswa amanani afundwa ngabantu. Kukwakho nemigaqo yokudibanisa amanani akhelwe koomathsini.   (binary adder). Le migaqo ithi: 

komnye umzekelo wokubala, uSally noBill banabantwana aba-2. U-Sally no-Bill baye baphinda balizwa ngabantwana aba-3.   U-Sally noBill bongeze abantwana abathathu kubantwana babo ababini. Ngoku banabantwana abahlanu.  

Le animation engasentla ibonisa udityaniswa  kwamakhulu asixhenxe anamashumi asibhozo anesithandathu kunye namakhulu amane anamashumi amathandathu anesixhenxe, ii-digits ezikulomdibaniso wokubala zahlulwahlulwe zazii-units, zangamashumi kunye namakhulu, (i-place value).  Okokuqala ii-units u-6 no-7 bayadityaniswa benze u-13, oko kuthetha okokuba benza ishumi eli-1 kunye nee-units ezi-3, u-3 ubhalwa ngaphantsi aze ke yena u-1 olishumi athwalwe aye kubekwa kwikholam yamashumi.  Okulandelayo, kwikholam yamashumi kukho u-1, 8 no-6 bathi badityaniswe benze i-15 yamashumi, goko ke i-1 yekhulu kunye nesi-5 samashumi,  isi-5 sibhalwa ngaphantsi lize ikhulu eli-1 lithwalwe liye kubekwa kwikholam yamakhulu. Okokugqibela, kwikholam yamakhulu engu 1, 7 kunye no-4 bayadityaniswa baze benze i-12 lamakhulu, ngoko ke iwaka eli-1 kunye namakhulu ama-2, u-2 ubhalwa ngaphantsi aze u-1 wewaka athwalwe aye kubekwa phantsi kwekholam yamawaka.  Nasi ke isiphumo soku kubala liwaka namakhulu amabini anamashumi amahlanu anesithathu.  

Lo mdibaniso ungasentla ubonisa umdibaniso wamakhulu asixhenxe anamashumi asibhozo anesithandathu kunye namakhulu amane anamashumi amathandathu nesixhenxe, iingxaki yeyokokuba ii-digits zahluliwe zayimivo, amashumi, kunye namakhulu (place value).  Okokuqala imivo yesi-6 neyesi-7 idityanisiwe yaza yenza u-13, ibe ke ngoko lishumi eli-1 nemivo emi-3, isi-3 sibhalwe apha ngaphantsi laza lona ishumi eli-1 lathwalwa lasiwa kwikholum yamashumi. Okulandelayo kwikholam yeshumi isi-1, isi-8 nesi-6 zidityanisiwe zize zenze ishumi i-15, ngoko ke ikhulu esli-1 kunye namashumi ama-5, isi-5 sibhalwe ngaphantsi, lize lona ikhulu lithwalwe lisiwe kwikholam yamakhulu. xa sifika kwikhom yokugqibela, ikholam yamakhulu  eli-1, asi-7 nama-4 ayadityaniswa atsho enze amakhulu ali-12, ngoko ke iwaka eli-1 namakhulu ama-2, isi-2 sibhalwa ngaphantsi lize iwaka eli-1 lithwalwe lisiwe kwikholam yamawaka. Sitsho sibe nesiphumo esithi iwaka namakhulu amabini anamashumi amahlanu anesithathu.  

U-Tom ufuna ukwazi umgama ophakathi kwendlu yakhe nendlu ka Sally. Indlu kaBob  ingumgama oziimitha ezingama- 300 kumntla wendlu kaTom. indlu kaSally izimitha ezingama-120 eemitha kumantla endlu kaBob:

 umzekelo womlinganiselo  
 Indlu kaTom<------------300 iimitha-------------->Bob's indlu<-----120 iimitha----->indlu kaSally
Umgama osuka kwindlu kaTom oya kwindlu kaSally ungafumaneka ngokudibanisa imigama esele ibaliwe imilinganiselo yawo. Umgama osuka kwindlu kaTom ukuya kwindlu kaBob  udityaniswe kumgama osuka kwindlu kaBob usiya kwindlu kaSally uyafana nomgama osuka kwindlu kaTom ukuya kwekaSally. Oko kuthetha ukuthi, iimitha ezingamakhulu amathathu (300) zidityaniswe neemitha ezili-120. 

Ukudibanisa kusenokuthatha okokuba wenza nkulu into. 

 Ukudibanisa kuyandisa 

 Umzekelo wokudibanisa ngeenjongo zokwandisa  
 Umzekelo, uTom unendlu. UTom wakha indlu entsha emzini wakhe. Le ndlu intsha kuthiwa iyongeza.  

 UJohn wenza ukutya. Ukuze ukutya akwenze kunambitheke kangcono, UJohn ugalela ityuwa ekutyeni. Oko kuthetha okokuba, uJohn wongeza ityuwa ekutyeni. Ityuwa le yongezwa ekutyeni.  

 Amanani okudibanisa 
 + 1  2  3  4  5  6  7  8  9  10 1 2  3  4  5  6  7  8  9   10  11 2 3  4  5  6  7  8  9  10  11  12 3 4  5   6  7  8  9  10  11  12  13 4 5  6   7  8  9  10  11  12  13  14 5 6  7  8  9  10  11  12  13  14  15 6 7  8  9  10  11  12  13  14  15  16 7 8  9  10  11  12  13  14  15  16  17 8 9  10  11  12  13  14  15  16  17  18 9 10  11  12  13  14  15  16  17  18  19 10 11  12  13  14  15  16  17  18  19  20

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