Kufunika kwa Kulinganiza mu Ma Equation
Mu masamu, mawu oti "equation" amamveka osavuta: chizindikiro chofanana (=) chosonyeza kuti manambala awiri ali ndi phindu lofanana. Komabe, kumbuyo kwa chizindikiro chimenecho kuli lingaliro lalikulu lomwe limatsimikizira momwe timaganizira mwanzeru, kuthetsa mavuto, komanso kupanga zisankho motsatira deta. Lingaliro lalikulu limenelo ndi kulinganiza. Kulinganiza mu ma equation si lamulo laukadaulo lokha losuntha manambala kuchokera kumanzere kupita kumanja; ndi mfundo yofunika kwambiri yomwe imatsimikizira kuti gawo lililonse la kuwerengera limakhala lolondola komanso lodalirika.
Equation ngati "Kulemera" kwa Malingaliro Amtengo Wapatali
Njira yosavuta yomvetsetsa equation ndi kulingalira sikelo yokhala ndi manja awiri. Mbali yakumanzere imanyamula kulemera, ndipo mbali yakumanja imanyamula kulemera kwina. Ngati sikeloyo ili yolinganizidwa, misa mbali zonse ziwiri ndi yofanana. Mofananamo, ndi equation, mbali yakumanzere ndi yakumanja zimakhala ndi miyezo yofanana.
Mwachitsanzo, mu equation:
x +3 = 10
Mbali yakumanzere "ili ndi" x kuphatikiza 3, pomwe mbali yakumanja ili ndi 10. Bola ngati equation ndi yoona, mbali zonse ziwiri ziyenera kukhala zofanana. Ntchito yathu ndikupeza mtengo wa x womwe umapangitsa kuti zinthu zikhale zofanana. Mwachidziwitso, ngati mbali yakumanzere yawonjezeka ndi 3, ndiye kuti kuti ikhale yofanana kufika pa 10, x iyenera kukhala 7. Ichi ndiye chofunikira pakuthetsa ma equation: kupeza zinthu zomwe zimasunga bwino.
N’chifukwa chiyani Kusamala N’kofunika?
Kulinganiza ndikofunikira chifukwa ma equation ndi mawu a choonadi cha masamu. Ngati kulinganiza kwasweka, mawuwo amakhala abodza. Mwachizolowezi, "kuphwanya kulinganiza" kumachitika tikamachita opaleshoni mbali imodzi yokha.
Chitsanzo chosavuta:
x +3 = 10
Ngati tichotsa 3 kumanzere kokha:
x = 10
Izi sizolondola, chifukwa tikusintha mtengo wa mbali yakumanzere koma tikusiya mbali yakumanja yosasinthika. Kuti tisunge bwino, ntchitoyi iyenera kuchitika mbali zonse ziwiri mofanana:
Chotsani 3 kuchokera mbali zonse ziwiri:
x + 3 − 3 = 10 − 3
x = 7
Mfundo imeneyi ingaoneke ngati yopanda pake, koma kwenikweni imagwira ntchito ngati "woteteza umphumphu" wa kuganiza kwa masamu. Imatiphunzitsa kukhala okhazikika, achilungamo pa zochita zathu, komanso kupewa kusankha ntchito zomwe zimapindulitsa mbali imodzi yokha.
Ntchito Zosunga Bwino
Pali ntchito zingapo zoyambira zomwe, zikachitika mbali zonse ziwiri za equation, zimasunga bwino:
1. Onjezani nambala yomweyi mbali zonse ziwiri
Ngati a = b , ndiye kuti a + c = b + c .
2. Chotsani manambala omwewo mbali zonse ziwiri
Ngati a = b , ndiye kuti a − c = b − c .
3. Chulukitsani mbali zonse ziwiri ndi nambala yomweyi (kupatula ziro m'malo ena)
Ngati a = b , ndiye kuti a·c = b·c .
4. Gawani mbali zonse ziwiri ndi nambala yomweyi (sizingatheke kukhala zero)
Ngati a = b ndi c ≠ 0 , ndiye kuti a/c = b/c .
Chitsanzo cha ntchito:
2x = 16
Kuti mugwirizane, gawani mbali zonse ziwiri ndi 2:
2x/2 = 16/2
x = 8
Kufanana kumagwiranso ntchito pamene ma equation akukhala ovuta kwambiri, mwachitsanzo:
3x − 5 = 2x + 7
Kuti tigwirizane, tikhoza kuchotsa 2x kuchokera mbali zonse ziwiri:
3x − 2x − 5 = 2x − 2x + 7
x - 5 = 7
Kenako onjezani 5 mbali zonse ziwiri:
x - 5 + 5 = 7 + 5
x = 12
Zotsatira zake ndi zolondola chifukwa pa gawo lililonse, timasunga mbali zonse ziwiri kukhala zofanana.
Kulinganiza ndi Zolakwika Zofala
Zolakwika zambiri pakuthetsa ma equation zimachitika chifukwa mfundo ya equilibrium imanyalanyazidwa kapena kugwiritsidwa ntchito mopanda chidwi. Zitsanzo zina zodziwika bwino:
1. Kusuntha mawu popanda kusintha zizindikiro molondola
Kawirikawiri anthu amamva kuti "kusuntha magawo kumatanthauza kusintha zizindikiro." Zoona zake n'zakuti timachita opaleshoni yomweyo mbali zonse ziwiri, osati kusamutsa kwamatsenga. Mwachitsanzo, kuchokera ku
x +5 = 12
imakhala x = 12 − 5
Ndikofanana ndi kuchotsa 5 mbali zonse ziwiri. Ngati anthu sakumvetsa bwino momwe zinthu zilili, amatha kusintha zizindikiro molakwika kapena kuchita zinthu zosasinthasintha.
2. Kugawa ndi variable popanda kutsimikizira kuti mtengo wake si zero
Mu ma equation ena, kugawa ndi mawu omwe angakhale zero kumatha kuchotsa mayankho kapena kuwonjezera mayankho abodza. Mwachitsanzo, ngati pali chinthu (x − 2), tiyenera kusamala chifukwa x ikhoza kukhala 2. Kufanana sikungokhudza "kuchita chinthu chomwecho," komanso kuonetsetsa kuti ntchitozo zikugwira ntchito moyenera.
3. Kuchotsa mizu kapena mabwalo popanda kutsimikizira
Mwachitsanzo, mu ma equation okhudzana ndi masikweya, tingapeze mayankho omwe amafunika kufufuzidwanso chifukwa ntchito yoyika masikweya mbali zonse ziwiri imatha kukulitsa zomwe zingatheke.
Zolakwitsa izi zikusonyeza kuti kulinganiza zinthu si njira yokha, koma njira yosungira choonadi.
Kufanana monga Maziko a Algebra ndi Sayansi
Ma equation ndi chilankhulo cha algebra, fizikisi, chemistry, zachuma, ndi uinjiniya. Kufanana komwe ali nako nthawi zambiri kumayimira zochitika zenizeni:
– Mu fizikisi, equation ya mphamvu (monga equilibrium) imasonyeza kuti mphamvu yochokerapo ndi zero. Equilibrium ya masamu imasonyeza equilibrium ya thupi.
– Mu chemistry, equation ya reaction iyenera kukhala ndi maatomu ofanana mbali yakumanzere ndi yakumanja. Umenewo ndi mtundu weniweni wa balance.
- Mu zachuma, ma equation amatha kufotokoza bwino pakati pa kufunikira ndi kupezeka, kapena ubale pakati pa ndalama ndi ndalama zomwe zapezedwa.
Tikasunga bwino ma equation a masamu, kwenikweni tikuchita njira yomweyo yoganizira yomwe imagwiritsidwa ntchito kumvetsetsa machitidwe enieni: kusintha kulikonse kumakhala ndi zotsatira zake, ndipo kuyenera "kulipiridwa" ndi kusintha kofanana kuti chitsanzocho chikhale chovomerezeka.
Kuchokera ku Masamu Kupita ku Kuganiza Mozama
Phindu lalikulu lomvetsetsa kufanana mu ma equation sikuti ndi luso lokha lothana ndi mafunso a mayeso, komanso luso loganiza mozama. Kufanana kumatiphunzitsa kuchita izi:
- Sungani kusinthasintha pang'onopang'ono.
- Pewani "njira zachidule" zomwe zimafooketsa chowonadi.
- Onetsetsani kuti kusintha kulikonse kuli ndi chifukwa chomveka bwino.
- Yang'ananinso zotsatira zomaliza ndi kusintha kuti mutsimikizire kuti equationyo ikupitirirabe kukhala yofanana.
Mwachitsanzo, titapeza x = 12 kuchokera ku equation 3x − 5 = 2x + 7 , tikhoza kuwona:
Kumanzere: 3(12) − 5 = 36 − 5 = 31
Kumanja: 2(12) + 7 = 24 + 7 = 31
Zonsezi ndi zofanana: equation ndi yowona, kulinganiza kumasungidwa.
Kutseka
Kulinganiza mu ma equation ndiko maziko a masamu monga sayansi yokonzedwa bwino komanso yodalirika. Imaphunzitsa kuti chizindikiro chofanana sichimalekanitsa "sitepe" ndi "yankho," koma chizindikiro cha kufanana chomwe chiyenera kulemekezedwa. Tikathetsa ma equation, kwenikweni timakhala ndi "mlingo wa chowonadi" womwe sunagwedezeke ndi zolakwika zogwirira ntchito kapena malingaliro osalondola.
Mwa kumvetsetsa ndi kugwiritsa ntchito mfundo ya kulinganiza, sitingokhala aluso kwambiri mu algebra, komanso timaganiza molondola kwambiri. Kulinganiza kumapangitsa ma equation kukhala zida zamphamvu—osati zizindikiro zokha m'buku lophunzirira, komanso maziko omvetsetsa dziko lapansi kudzera mu logic, muyeso, ndi maubwenzi omveka bwino.
