Isilinganiso nesilinganiso sisetshenziswa kakhulu ku-algebra ukuze kutholwe ukuhlukanisa kanye nethemu elithi x. Isilinganiso sihambisana ngokuphelele namafrakshini njengoba zonke izilinganiso zingabhalwa ngendlela ethi p/q. ngakolunye uhlangothi, ingxenye inezilinganiso ezimbili ezinophawu olulinganayo phakathi kwazo.
Isilinganiso nesilinganiso sisetshenziswa emikhakheni eyahlukene yezibalo njenge-algebra, i-geometry, onxantathu, njll. ngokuvamile isetshenziswa ukuqhathanisa amagama amabili afana nobude, ibanga, ubukhulu, njll.
Kulesi sihloko, sizoxoxa ngencazelo nezinhlobo zesilinganiso nesilinganiso kanye nezibonelo eziningi.
Ayini ama-ratios nezilinganiso?
Ake sixoxe izilinganiso nezilinganiso kafushane.
Izilinganiso
Kumathematika, igama elisetshenziswa ukuqhathanisa amanani amabili laziwa ngokuthi ama-ratios. Ukuqhathaniswa kwamagama kusitshela ukuthi lingakanani ithemu elilodwa uma liqhathaniswa nelinye. Ngokulinganisa, imigomo kufanele ibe namayunithi afanayo.
Ngokuvamile kuchazwa ngokuthi “:” uphawu. Izilinganiso zingabhalwa ngendlela ethi u/v, lapho u-v engalingani noziro.
Isibonelo, ukuqhathanisa abafundi besilisa nabesifazane ngezilinganiso zekilasi kusetshenziswa. Uma kunabafundi abangamashumi amane ekilasini, lapho abafundi besilisa abangu-16 bese kuthi abangama-24 kube ngabesifazane. Khona-ke ifomu lesilinganiso ngabafundi besilisa : abafundi besifazane = 16 : 24.
Ngendlela yengxenyana, ingabhalwa ngokuthi 16/24. Manje yenza amagama abe lula ukuze uqhathanise abafundi besilisa nabesifazane, 2 : 3 noma 2/3. Ukuqhathanisa abafundi besilisa nabafundi besifazane vele ubhale kabusha izilinganiso nenani labesifazane kuqala njengo-3:2 noma 3/2.
Ingxenye
Ku-algebra, ingxenye iyisibalo sezilinganiso ezimbili ukukutshela ukuthi izilinganiso ezimbili zilingana kanjani nesinye. I-Proportion ingabuye ibhalwe ngendlela yamafrakshini. Izindlela ezimbili ezingenzeka zokubhala isilinganiso yilezi:
- s: ::u :v
- s / t = wena / v
Izinhlobo zesilinganiso
Ku-algebra, kunezinhlobo ezimbili ezivame ukusetshenziswa zezilinganiso.
- Ingxenye kuyo yonke isilinganiso
- Isilinganiso sengxenye nengxenye
1. Ingxenye kuyo yonke isilinganiso
Uma amagama amabili noma izinto ziqhathaniswa ngendlela yokuthi into eyodwa ithathwe kuyo yonke, khona-ke iyoba yingxenye yesilinganiso sonke. Isibonelo, uma uthatha ucezu lwesinkwa kulo lonke iphakethe, khona-ke kuyoba yingxenye yokulinganisa okuphelele.
2. Isilinganiso sengxenye nengxenye
Isilinganiso sengxenye nengxenye yilolo hlobo lwesilinganiso lapho amagama ahlukene noma izinto ziqhathaniswa khona. Inganikeza ukuqhathanisa kwamaqembu amabili. Isibonelo, isilinganiso phakathi kwamasosha namaphoyisa, isilinganiso sabafundi besifazane ekilasini lesi-8 kubafundi besifazane ekilasini lesi-9 yizibonelo ezimbalwa zalolu hlobo lwesilinganiso,
Izinhlobo zesilinganiso
Izilinganiso ziyizinhlobo ezimbili.
- Isilinganiso esiqondile
- Isilinganiso esiphambene
1. Isilinganiso esiqondile
I-Direct proportion uhlobo lwesilinganiso lapho ukwanda kwento eyodwa kubangela ukwanda kwenye into noma ukuncipha kwento eyodwa kubangela ukuncipha kwenye into. Isibonelo, unezinto ezimbili u & v lapho u-inombolo yabasebenzi futhi v kuwumsebenzi wokwakhiwa kodonga.
Uma isibalo sabasebenzi sikhuphuka isivinini sokusebenza sodonga siyakhula, noma uma uqasha abasebenzi abambalwa noma wehlisa isisebenzi umsebenzi kufanele wehliswe. Kuyisilinganiso esiqondile njengoba kokubili u & v enyuka noma ehla ngokunyuka noma ukwehla ngenani elilodwa.
2. Isilinganiso esiphambene
Ingxenye ephambene ingolunye uhlobo lwengxenye lapho ukwanda kwenani elilodwa kubangela ukwehla kwelinye noma ukuncipha kwenani elilodwa kubangela ukwehla kwelinye. Isibonelo, u-x kanye no-y amagama amabili, lapho u-x eyinani labantu ekamu futhi u-y ewukudla kwezinsuku ezingu-40.
Uma inani lokudla likhuphuka khona-ke ukudla kwezinsuku ezingama-40 kuzokwehla, noma uma inani labantu lincipha kufanele kwandiswe inani lokudla.
Izibonelo zezilinganiso nezilinganiso
Okulandelayo izibonelo ezimbalwa zesilinganiso nezilinganiso zokufunda ukuthi zibalwa kanjani.
Isibonelo 1: Ngezilinganiso
Ebhokisini lamapulangwe, kunamabhaluni angu-16. Kula mabhaluni angu-16, angu-7 anombala obomvana, angu-5 anonsomi, angu-4 amhlophe. Bala isilinganiso:
- Amabhaluni apinki ukuya kumabhaluni ansomi
- amabhaluni ansomi kumabhaluni esewonke
- amabhaluni amhlophe kuya kumabhaluni apinki
Isixazululo
Isinyathelo 1: Bhala idatha enikeziwe yamabhaluni.
Amabhaluni aphelele = 16
Amabhaluni aphinki = 7
amabhaluni ansomi = 5
Amabhaluni amhlophe = 4
Isinyathelo 2: Thola amabhaluni apinki ukuya kumabhaluni ansomi
Inani lamabhaluni aphinki = 7
Inani lamabhaluni ansomi = 6
Isilinganiso sithi,
7: 6
or
7/6
Isinyathelo 3: Thola isilinganiso samabhaluni ansomi kumabhaluni esewonke
Inani lamabhaluni esewonke = 16
Inani lamabhaluni ansomi = 5
Umehluko phakathi kwamabhaluni aphelele namabhaluni ansomi = 16 – 5 = 11
Manje isilinganiso sithi,
5: 11
Or
5 / 11
Isinyathelo 4: Manje thola isilinganiso samabhaluni amhlophe namabhaluni aphinki
Inani lamabhaluni amhlophe = 4
Inani lamabhaluni aphinki = 7
Isilinganiso sithi,
4: 7
Or
4 / 7
Isibonelo sesi-2: Ngokwesilinganiso
Kudingeka abasebenzi abangu-15 ukuze bakhe ibhuloho ngezinsuku ezingu-30, bangaki abasebenzi abadingekayo ukuze bakhe ibhuloho elifanayo ezinsukwini ezingu-14.
Isixazululo
Isinyathelo 1: Bhala idatha enikeziwe yabasebenzi nezinsuku.
Kudingeka abasebenzi bakhe ibhuloho = 15
Izinsuku = 30
Abasebenzi kwakudingeka bakhe ibhuloho elifanayo ngezinsuku eziyi-14 = x
Isinyathelo 2: Bhala abasebenzi nezinsuku ngendlela yesilinganiso.
abasebenzi : izinsuku :: abasebenzi : izinsuku
15 : 30 : : x : 14
Isinyathelo 3: Bhala izilinganiso ngendlela yamafrakhishini anophawu lokulingana phakathi kwazo ukuze ubale inani lika-x.
15/30 = x/14
Isinyathelo 4: Ukuze uthole inani lika-x, sebenzisa ukuphindaphinda futhi wenze lula inkulumo engenhla.
15/30 = x/14
1/2 = x/14
1 * 14 = x * 2
14 = 2x
2x 14
x = 14/2
x = i-7
Abasebenzi kwakudingeka bakhe ibhuloho elifanayo ngezinsuku eziyi-14 = 15 + 7 = 22
Ngakho-ke, kudingeka abasebenzi abangu-7 abengeziwe ukuze kwakhiwe leli bhuloho ngezinsuku ezingu-14.
Ungasebenzisa futhi i- isilinganiso wokubala ukuthola amanani angu-x ezinkinga ezinikeziwe engxenyeni yamasekhondi. Landela lezi zinyathelo ezingezansi ukuze ubale inani lika-x.
Isinyathelo 1: Faka amanani edatha.
Isinyathelo 2: Cindezela inkinobho yokubala.
Isinyathelo 3: Cindezela inkinobho ethi show more ukuze ubuke isixazululo ngezinyathelo.
Isifinyezo
Manje usufakazelwa ukuthi izilinganiso nezilinganiso akusona isihloko esinzima. Ungathola zonke izisekelo zesilinganiso nesilinganiso ngokufunda okuthunyelwe ngenhla. Manje usungakwazi ukuxazulula noma iyiphi inkinga yezilinganiso nezilinganiso kalula ngokulandela izibonelo ezishiwo ngenhla.
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