Eyona ndlela yokwazi itafile yokuphindaphinda kukuqonda inkqubo yayo. Ngaphambili, bekuyimfuneko ukuhombisa itheyibhile yokuphindaphinda esikolweni, nangona kunjalo, namhlanje indlela yokufunda itafile yokuphindaphinda isuke ekuphindweni nje ukuya ekuqondeni ukuba isebenza njani.

Ngesi sizathu, ngoku kukho imidlalo emininzi kunye nokuzilolonga okwenza kube lula ukukhumbula ngeziphumo zetheyibhile yokuphindaphinda.

## Ukuphindaphinda kwetafile

Phakathi kweentlobo ze ukuphindaphinda iitafile, okona kubalulekileyo kukuphindaphinda. Hambisa imveliso phakathi kwamanani. Kumfanekiso ongezantsi sineetafile ukusuka kwi-1 kuye kwi-10:

Ukuba sifuna ukwazi ukuba yeyiphi i-9 x 5 exabisekileyo, sinokufikelela kwiziphumo ngokudibanisa. Oko kukuthi, 9 + 9 + 9 + 9 + 9 = 45.

Ke ngoko, kufuneka sikhumbule ukuba ukuphindaphinda kuyahambelana nesixa seepasile ezilinganayo.

Ukuqala ngeetafile ezilula zokuphindaphinda, umzekelo, 2, 5 no-10, kunokuba yindlela elungileyo yokufunda ukukhumbula iitafile zokuphindaphinda.

Enye indlela yokwazi itafile yamaxesha alithoba kukwenza oku kubalwe ngokujoyina inani langaphambili lezinto eziphindaphindwayo, enye elahlekileyo ifike kwi-XNUMX.

Umzekelo: 9 x 7 = 63 (kuba ngaphambi kokuba u-7 eze u-6 kwaye aphulukane no-3 ukuya ku-9).

Enye indlela etafileni yamaxesha ali-9 kukusebenzisa iminwe yakho kunye nokuthoba umnwe ngamnye ukusuka ekhohlo ukuya ekunene. Ke ukuba sifuna ukwazi ukuba yintoni u-9 x 7, kufuneka sihlise umnwe wesixhenxe ukusuka ekhohlo ukuya ekunene. Kukho ii-6 kwelinye icala kwaye ezi-3 kwelinye icala, nto leyo ibangele ama-63.

Ngokufanayo, ukuba sifuna ukwazi ukuba ingakanani i-3 x 9, sihlisa umnwe wesithathu kwaye sino: 2 kwelinye icala kunye no-7 kwelinye: 27.

QaphelaKhumbula ukuba naliphi na inani eliphindaphindwe ngo-zero (0) lihlala lililo, umzekelo, 0 x 5 = 0. Kwakhona, naliphi na inani eliphindaphindwe ngo-1 liya kuba lilodwa, umzekelo: 1 x 4 = 4.

## Itafile yokuphindaphinda iCartesian

Enye indlela yokubhala isiphumo sokuphindaphinda amanani kukusebenzisa itheyibhile yokuphindaphindeka kweCartesian. Ngokungafaniyo netafile yokuphindaphinda eqhelekileyo, yona yakhiwe ngokubeka amanani ngokuthe nkqo nangokuthe tye.

Ngoku siza kufunda ukwakha itafile yokuphindaphinda yeCartesian. Kuqala zoba isikwere esikhulu esinemiqolo eli-11 kunye neekholamu ezili-11.

Kwibhokisi yokuqala yomgca wokuqala siza kubeka u-X kwaye sibhale amanani ukusuka ku-1 ukuya ku-10 kwibhokisi nganye yalo mgca. Phinda okufanayo kwikholamu yokuqala.

Okwangoku, itafile yethu yokuphindaphinda iya kujongeka njengalo mzobo ulandelayo:

Kwikholamu yesibini siza kubhala itheyibhile yokuphindaphinda ka-1. Ukwenza oku, phinda ubhale amanani ukusuka ku-1 ukuya ku-10.

Kwikholamu yesithathu siza kugcwalisa ngetheyibhile yokuphindaphinda ka-2 .Ngoku, ungadibanisa amanani amabini abhalwe kumgca ofanayo, njengoko kubonisiwe kumzobo:

Kwikholamu yesine siza kubhala itheyibhile yokuphindaphinda ka-3. Sinokuqhubeka ngendlela efanayo xa sibhala itafile yokuphindaphinda ka-2, oko kukuthi, yongeza amaxabiso amabini angaphambili akumgca omnye.

Siyaqaphela ukuba u-4 ulingana no-2 × 2. Ke ngoko, singabhala kwikholamu yetafile yokuphindaphinda 4 iziphumo zamaxabiso etafile yokuphindaphinda 2 iphindaphindwe ngo-2.

Ukubhala itafile yokuphindaphinda ka-5, sinokongeza iziphumo zetheyibhile yokuphindaphinda ka-2 ngesiphumo setafile yokuphindaphinda ka-3, kuba 2 + 3 = 5.

Siyaqaphela ukuba u-6 ulingana no-2 × 3, ngoko ke siza kubeka iziphumo zamaxabiso etafile ka-3 ephindaphindwe ngo-2 kwikholamu ebhekisa kwitafile ka-6, njengoko kubonisiwe kumfanekiso ukuqhubeka.

Singafumana amaxabiso kwitafile yokuphindaphinda ka-7, ukudibanisa amaxabiso etafile yokuphindaphinda ka-2 naleyo ka-5 (2 + 5 = 7), itheyibhile yokuphindaphinda ka-3 kunye no-4 (3 + 4 = 7), okanye kwitheyibhile yokuphindaphinda ka-6 kunye no-1 (6 + 1 = 7).

Kwitheyibhile ka-8, singadibanisa iitafile apho amanani adibanisa ukuya ku-8 (1 no-7, 2 no-6, no-3 ngo-5), okanye usebenzise inyani yokuba u-8 ulingana no-2 x 4.

Kwitheyibhile yamaxesha u-9 singasebenzisa inani lamanani adibanisa ukuya ku-9, okanye sinokugcwalisa itafile yamaxesha sisebenzisa oku kulandelayo: ngokufanayo, ubeka nje amanani, ukuqala ku-0, ezantsi phezulu.

Okokugqibela, siyigcwalisa itafile ngetafile yokuphindaphinda ka-10. Ukwenza oku, beka nje amanani ukusuka ku-1 ukuya ku-10 kwikholamu yokugqibela emva koko ubeke u-0 ekupheleni kwelinye ngalinye.

Ke, sigqiba itafile yokuphindaphinda yeCartesian. Ukufumana umphumo wokuphindaphinda amanani amabini, usebenzisa le tafile yokuphindaphinda, kufuneka sidibanise amanani kumqolo kunye nabo kwikholamu.

Umzekelo, ukuba sifuna ukwazi ukuba yintoni u-7 x 9, landela nje ikholamu yenani lesi-7 ngomgca wenombolo 9, apho badibana khona sisiphumo sokuphindaphinda.

Kumzobo ongezantsi, sibona itheyibhile yokuphindaphinda ukusuka ku-1 ukuya ku-10. Qaphela ukuba amanani aboniswe kwidayagonal amele izikwere ezigqibeleleyo.

Ukujonga kwitafile engentla, siyaqaphela ukuba idiagonal enezikwere ezigqibeleleyo yahlula itafile yophinda-phindo ibe ngamacandelo amabini, amaxabiso aphindaphinda ngokulinganayo.

Kungenxa yenyani yokuba xa uphinda-phinda Umyalelo wezinto awutshintshi imvelisoOko kukuthi: 9 x 5 = 5 x 9. Ke ngoko, kufuneka uhombise kuphela isiqingatha setafile yokuphindaphinda ukusuka ku-1 kuye ku-10.

## Itafile yokwahlulahlula

Itheyibhile yokwahlula inceda ekubaleni izibalo, kuba ngalo msebenzi sinokufumana iziphumo zetheyibhile yokuphindaphinda. Kungenxa yokuba ukuphindaphinda kunye nabahluli benani banxulumene.

Umzekelo:

8 x 4 = 32 (itheyibhile yokuphindaphinda)
32: 8 = 4 (iitafile zokwahlula)

Jonga itafile yokuphindaphinda apha ngezantsi:

## Itafile zokongeza

Kwitheyibhile yokongezwa sinokwenza izibalo ezahlukeneyo kwimathematics. Jonga umfanekiso ongezantsi:

## Itheyibhile yokuthabatha

Ukongeza kwitafile yokongeza, sinetafile yokuthabatha:

Kufanelekile ukuba sikhumbule ukuba ngokudibanisa nokukhupha amanani, sinokukhumbula ngentloko kwaye siqonde ubudlelwane phakathi kwabo.

### Ubusazi

Itheyibhile yokuphindaphinda yinkqubo esetyenziswa kwimathematics edibanisa ukuphindaphinda kunye nabahluli bamanani ngendlela elungelelanisiweyo.

Inceda kwimisebenzi eyahlukeneyo yemathematics (ukudibanisa, ukuthabatha, ukuphinda-phinda nokwahlulahlula), ngaloo ndlela kuququzelelwa ukubalwa.

Itheyibhile yokuphindaphinda ibizwa ngokuba Itheyibhile yamaxesha kaPythagoras, ngewonga kwisazi ngezibalo nesithandi sobulumko esingumGrike uPythagoras.