Indlela ukuqonda ukuba kutheni i "dibanisa" "ezimbi 'ukuba unika i' thabatha '?

Ukuphulaphula utitshala yemathematika, inkoliso yabafundi ziyifumanisa umbandela njengento saziwe. Kodwa bambalwa abantu bezama ukuya ezantsi uze ufumanise ukuba kutheni 'thabatha' ukuya 'dibanisa' unika umqondiso "thabatha", yaye xa phinda amanani amabini athabathayo uyaphuma ezintle.

imithetho yemathematika

Uninzi abadala abakwazi ukuchazela ngokwabo okanye abantwana babo ukuba kutheni kunjalo. Ngokungagungqiyo baqonde imathiriyeli esikolweni, kodwa loo nto ayithethi bazame ukufumanisa apho wenza le mithetho. Ngenxa yesizathu esibalulekileyo. Amaxesha amaninzi, aba bantwana namhlanje abafazazana abazono ziziimfumba kunjalo, kufuneka ukuya ezantsi ukuqonda, umzekelo, kutheni 'dibanisa' ukuya 'ezimbi "unika" thabatha ". Kwaye ngamanye amaxesha urchins ukubuza ngqo imibuzo edidayo, ukuze banandiphe ixesha xa abadala akanako ukunika impendulo ecacileyo. Kwaye ngokwenene kubalulekile ukuba utitshala oselula kokuba sibanjwe ...

Phela, kufanele kuqatshelwe ukuba ulawulo ikhankanywe ngentla olusebenzayo-phindo kunye ngokucandeka. Imveliso yamanani ezimbi nezilungileyo kuphela "ukunikeza thabatha. Ukuba kukho amanani amabini kunye umqondiso "-", ngoko umphumo uya kuba linani elidibanisayo. Kukwasebenza kwanjalo kuyo eli candelo. Ukuba omnye manani kuya kuba embi, ngoko ke QUOTIENT uya kuba ngumqondiso "-".

Ukuba achaze ukuchaneka umthetho kwimathematika, kuyimfuneko ukuqulunqa amakhonkco saziwe. Kodwa ukuqonda kufuneka kuqala ukuba yintoni na. Kwimathematika ebizwa ring iseti apho imisebenzi ezimbini ndalala izinto ezimbini. Kodwa ukuze siqonde ngcono kunye umzekelo.

ring saziwe

Kukho imithetho eziliqela zezibalo.

• Eyokuqala kwezi aluguquki, ngokutsho kwakhe, C + V = V + C.
• Eyesibini kuthiwa associative (V + C) + D = V + (C + D).

Baya elandela Kwakhona phinda (V x C) x D = V x (C x D).

Akukho mntu irhoxisiwe kunye nemigaqo ngayo isibiyeli evulekileyo (V + C) x D = V x D + C x D, kuyinyaniso kananjalo ukuba C x (V + D) = C x V + C x D.

Ngaphezulu, kufunyaniswe ukuba umsesane Ungangena cala ezizodwa ngokuthi kongezwe i element, ukusetyenziswa apho zilandelayo kuyinyaniso: C + 0 = C. Ukongeza, kuba nganye C esahlukileyo i element ezinokuthi okhethiweyo njengo (-C). Ngaloo ndlela C + (-C) = 0.

elikuwo Deducing for amanani akhabayo

? Ngokwamkela iingxelo ngentla, kunokwenzeka ukuba uphendule lo mbuzo: " 'dibanisa' ukuya 'ezimbi" unika naluphi uphawu' Ukwazi saziwe malunga phindo lwamanani awunayo, kufuneka uqinisekise ukuba okunene (-C) x V = - (x V C). Kananjalo, oko kuyinyaniso ilingana: (- (- C)) = C.

Ukuze wenze oku, kuqala kufuneka angqine ukuba nganye kwezi zinto kukho enye malunga naye nje "mzalwana." Qwalasela ubungqina alandelayo. Makhe uzame ukucinga ukuba C malunga amanani amabini - V kunye D. Ukusuka oku kulandela ukuba C + V = 0 no C + D = 0, okt C + V = 0 = C + D. Ekhumbula umthetho properties and phezu iimpawu amanani 0, singakwazi ingqalelo isiphumo zontathu amanani: C, V, kwaye zama ukufumana phandle i ixabiso D. V. Ngoko kusengqiqweni, V = V + 0 = V + (C + D) = V + C + D, ukususela ixabiso C + D, yamkelwa nje ngentla, nto ilingana no0 yoko, V = V + C + D.

Ngokufanayo, ixabiso imveliso kunye D: D = V + C + D = (V + C) + D = 0 + D = D. Ukusuka oku, kuye kucace ukuba V = D.

Ukuze siqonde isizathu sokuba zonke i 'dibanisa' ukuya 'ezimbi "unika i" thabatha ", kuyimfuneko ukuba ukuqonda oku kulandelayo. Ngenxa yoko, i-elementi (-C) ephikisanayo kunye C (- (- C)), ngamanye amazwi ke lingana omnye komnye.

Ngoko ke kucacile ukuba 0 x V = (C + (-C)) = C x V x V + (-C) x V. Ukusuka oku kulandela ukuba C x V oppositely (-) C x V, ke ngoko, (- C) x V = - (x V C).

Kuba okukhulu epheleleyo zezibalo kufuneka uqinisekise ukuba 0 x V = 0 naziphi element. Ukuba landela ingqiqo, ngoko 0 x V = (0 + 0) x 0 x V = V + 0 x V. Oku kuthetha ukuba kongezwe imveliso 0 x V ayitshintshi imali emiselweyo. Emva kwako konke oku msebenzi ngu zero.

Ukwazi zonke ezi elikuwo anokuzuzwa nje kuphela ngokuthi 'dibanisa' ukuya 'ezimbi "unika, kodwa efunyanwa phinda amanani akhabayo.

Uphinda-phindo nokwahlula amanani amabini kunye umqondiso "-"

Ngaphandle wangena bokuqonda zemathematika, unga zama indlela elula ukucacisa imithetho amanyathelo kunye amanani akhabayo.

Ucinge ukuba C - (-V) = D, phezu kwesi sisekelo, C = D + (-V), ngamanye C = D - V. We transfer V sibona ukuba C + V = D. Oko kukuthi, i C + V = C - (-V). Lo mzekelo ichaza isizathu sokuba ibinzana elithi, apho kukho ezimbini 'thabatha' emgceni, uthi imiqondiso kufuneka itshintshwe ukuze "dibanisa". Ngoku makhe ukujamelana nophindaphindo.

(-C) x (-V) = D, kweli binzana ukudibanisa nokuthabatha ziqwenga zibini twatse engayi ukutshintsha ixabiso layo: (-C) x (-V) + (C x V) - (x V C) = D.

Masikhumbule imithetho yokusebenza kutyiwa le, sifumana:

1) (x V -C) x (-V) + (C) + (-C) x V = D;

2) (-C) x ((-V) V +) + C x V = D;

3) (-C) + C x 0 x V = D;

4) C x V = D.

Kulo kulandela ukuba C x V = (-C) x (-V).

Ngokufanayo, umntu unakho ukubonisa ukuba ngenxa yale ukwahlulwa amanani amabini athabathayo, nakanjani.

imithetho jikelele lwezibalo

Kakade ke, le ngcaciso ezingafanelekanga abantwana besikolo samabanga abo ekuqaleni nje ukuba bafunde amanani akhabayo abstract. Bafuna chaza ngcono ukuba into ebonakalayo, ukusebenzisa gama kubo esipilini. Umzekelo, nini, kodwa akukho zokudlala esele zikhona. Uyakwazi ukubonisa nabo umqondiso "-". Uphindaphindo yezinto ezimbini transmirror ohambisa zweni ehlabathini, nto leyo ilingana ngoku, oko kukuthi, ngenxa yoko, sinalo samanani avumelanayo. Kodwa phindo yenani abstract zingathandekiyo elihle unika kuphela iziphumo kubo bonke. Ngapha koko, le "dibanisa" liphindaphindwe 'thabatha' unikeza 'thabatha'. Noko ke, kule kwisikolo samabanga yobudala abantwana abalindelekanga kakhulu ozama ukungena zonke bokuqonda zemathematika.

Nangona, xa ujamelene inyaniso, abantu abaninzi, ewe imfundo ephakamileyo yaqhubeka iyimfihlelo imithetho emininzi. Konke oku kuthatha lula ukuba ootitshala bafundisa kuzo, ungazikhathazi kakhulu lokumba zonke iingxaki ezendeleyo imathematika. "Okugwenxa" kwi "ezimbi" unika "dibanisa" - wonke umntu uyayazi loo nto, ngaphandle kokukhetha. Oku kuyinyaniso ukuba wonke, nangenxa amanani iqhezu.