Ukuqhathanisa phakathi kwesilinganiso kanye nesilinganiso
Ezibalweni nasekuphileni kwansuku zonke, sivame ukuqhathanisa izinto ezimbili: intengo uma kuqhathaniswa nobuningi, ibanga uma kuqhathaniswa nesikhathi, noma inani labafundi besilisa uma kuqhathaniswa nabesifazane. Imibono emibili evame ukusetshenziswa kakhulu ukuxoxa ngokuqhathanisa okunjalo isilinganiso kanye nesilinganiso. Nakuba zingase zibonakale zifana, futhi zivame ukuphambaniswa nento efanayo, empeleni zinezindima kanye nokusetshenziswa okuhlukile. Lesi sihloko sixoxa ngokusobala ngokuqhathanisa isilinganiso kanye nesilinganiso, ngezibonelo zokuziqonda kalula.
Ukuqonda Isilinganiso
Isilinganiso siwukuqhathanisa phakathi kwamanani amabili afanayo noma afanayo. Sibonisa ukuthi inani elilodwa liqhathaniswa kangaki nelinye. Izilinganiso zingabhalwa ngezindlela eziningana, isibonelo:
– a : b (funda “u-a uqhathanisa u-b”)
– a/b
– ngesimo samagama, isibonelo “u-a uma kuqhathaniswa no-b”
Isibonelo, uma ekilasini kunabafundi besilisa abayi-12 kanye nabafundi besifazane abayi-18, khona-ke isilinganiso sabesilisa nabesifazane yilesi:
– 12: 18
Lesi silinganiso singenziwa lula ngokuhlukanisa kokubili ngo-6:
– 2: 3
Lokhu kusho ukuthi kubafundi besilisa ababili, kunabafundi besifazane abathathu.
Izici zezilinganiso
1. Qhathanisa amanani amabili (noma ngaphezulu, kodwa ngokuvamile amabili).
2. Kungenziwa lula njengengxenyana.
3. Akubonisi njalo "ukulingana"; isilinganiso sibonisa ukuqhathanisa kuphela.
Ukuqonda Ukulingana
Isilinganiso siwukulingana kwezilinganiso ezimbili. Uma isilinganiso sika-A kuya ku-B sifana nesilinganiso sika-C kuya ku-D, khona-ke ubudlelwano bubizwa ngokuthi isilinganiso. Ngokuvamile kubhalwa kanje:
– a : b = c : d
noma
– a/b = c/d
Isibonelo:
Uma u-2/3 = 4/6, khona-ke lokhu kuyisilinganiso ngoba izilinganiso ezimbili ziyalingana.
Empilweni yangempela, izilinganiso zivame ukusetshenziswa ukuxazulula izinkinga ezihlobene nosayizi, izindlela zokupheka, isivinini, amanani eyunithi, njalo njalo.
Izici Zokulingana
1. Kuhlala kuhilela ukuqhathaniswa kwezilinganiso ezimbili.
2. Kubonisa ukulingana (inani lokuqhathanisa liyafana).
3. Ngokuvamile isetshenziselwa ukuthola amanani angaziwa (iziguquguquko).
Umehluko Obalulekile Phakathi Kwesilinganiso Nokulingana
Nakuba kuhlobene, isilinganiso kanye nesilinganiso kunemehluko eyisisekelo encazelweni nasemsebenzini. Nasi isiqhathaniso esibalulekile:
1. Incazelo Yomqondo
– Isilinganiso: ukuqhathanisa amanani amabili.
– Isilinganiso: ukulingana kwezilinganiso ezimbili.
Isilinganiso sifana “nokuqhathanisa”, kanti isilinganiso sifana “nokuqhathanisa izilinganiso ezimbili”.
2. Uhlobo Lwesitatimende
– Isilinganiso sibhalwe kalula ngokuthi a : b .
– Isilinganiso sibhalwe kanje: b = c: d noma a/b = c/d.
3. Tujuan Penggunaan
– Izilinganiso zisetshenziselwa ukuveza izimo noma ukwakheka.
– Izilinganiso zisetshenziselwa ukuxazulula izinkinga ezidinga ukulingana okuqhathanisayo.
4. Ukuthi kukhona ukulingana noma cha
– Isilinganiso asidingi ukulingana nezinye izilinganiso.
– Isilinganiso sihlala sibonisa ukulingana kwezilinganiso ezimbili.
Izibonelo Zezilinganiso Ekuphileni Kwansuku Zonke
Isibonelo 1: Ukwakheka Kwengxube
Isiphuzo senziwe ngesiraphu namanzi ngesilinganiso esingu-1:5. Lokhu kusho ukuthi:
– ingxenye ngayinye yesiraphu exutshwe nezingxenye ezi-5 zamanzi.
Kuyisilinganiso ngoba sibonisa kuphela ukuqhathaniswa kwezakhi.
Isibonelo 2: Ukuqhathaniswa Kwebanga Nesikhathi
Umuntu uhamba amakhilomitha ayi-120 ngamahora ama-2. Isilinganiso sebanga nesikhathi yilesi:
– 120: 2 = 60: 1
Ngokuvamile kuhlotshaniswa nesivinini, kodwa i-essence yokuqala iyisilinganiso.
Izibonelo Zokulingana Ekuphileni Kwansuku Zonke
Isibonelo 1: Isikali Semephu
Isikali semephu esingu-1:100.000 sisho ukuthi i-1 cm kumephu = i-100.000 cm empilweni yangempela.
Uma ibanga elikumephu lingu-3 cm, liyini ibanga langempela?
Senza isilinganiso:
– 1/100.000 = 3/x
Ngakho-ke:
– x = 3 × 100.000 = 300.000 cm = 3 km
Lena yi-proportion ngoba ihilela ukulingana kwezilinganiso ezimbili futhi isetshenziselwa ukuthola inani lika-x.
Isibonelo 2: Iresiphi Yokupheka
Iresiphi yabantu abane ibiza amagremu angu-200 kafulawa. Mangaki amagremu adingekayo kubantu abayi-10?
Senza isilinganiso:
– 200/4 = x/10
x = (200 × 10) / 4 = 500 amagremu
Lesi yisibonelo esivamile sesilinganiso ekuqhathaniseni okuphambene noma okulinganayo.
Ubudlelwano phakathi kwesilinganiso kanye nesilinganiso
Isilinganiso kanye nesilinganiso azihlukani. Isilinganiso empeleni sakhiwe ngomqondo wesilinganiso. Ngaphandle kokuqonda isilinganiso, kuzoba nzima ukuqonda isilinganiso. Kodwa-ke, ukuba nesilinganiso kukodwa akwanele ukusungula isilinganiso; sidinga esinye isilinganiso esilinganayo.
Isilinganiso “yisithako esiyisisekelo”, isilinganiso “ubudlelwano bokulingana” phakathi kokuqhathanisa okubili.
I-Misalnya:
– Isilinganiso 2: 3 yisilinganiso.
– Uma sithi 2: 3 = 4: 6, kuba yisilinganiso.
Indlela Yokuhlola Ukuthi Ingxenye Ilungile
Ukuze sihlole ukuthi i-a/b = c/d iyisilinganiso esifanele, singasebenzisa ukuphindaphinda okuphambene:
– a × d = b × c
Isibonelo:
– 2/3 = 4/6
Isheke:
- 2 × 6 = 12
- 3 × 4 = 12
Njengoba zifana, isilinganiso silungile.
Uma imiphumela ingafani, kusho ukuthi izilinganiso ezimbili azifani futhi aziyona isilinganiso esifanele.
Amaphutha Avamile Ekuqondeni Izilinganiso kanye Nokulingana
1. Ake sithi zonke izilinganiso ezizenzakalelayo ziyizilinganiso.
Isilinganiso esisha siba yisilinganiso uma siqhathaniswa nezinye izilinganiso ezilinganayo.
2. Ungaqali wenze isilinganiso sibe lula.
Izilinganiso 12: 18 kanye no-2: 3 empeleni ziyafana, kodwa uma zingenziwa lula, zingadida.
3. Ukubeka inani ngendlela engafanele.
Ngokwezilinganiso, ukuhleleka kubalulekile. Uma ukuhleleka kungalungile, imiphumela yokubala nayo izoba yiphutha.
Isiphetho
Isilinganiso kanye nesilinganiso kokubili kuxoxa ngokuqhathanisa, kodwa kuyahluka ngesakhiwo kanye nomsebenzi. Isilinganiso siwukuqhathanisa phakathi kwamanani amabili, kuyilapho isilinganiso siwukuchaza ukuthi amanani amabili ayalingana. Izilinganiso zivame ukusetshenziswa ukuchaza ukwakheka noma ukuqhathanisa okuqondile, kuyilapho izilinganiso zisetshenziselwa ukuxazulula izinkinga ezihilela ukulingana kanye nokuthola amanani angaziwa.
Ukuqonda umehluko phakathi kwalokhu okubili kuzosiza ezimweni eziningi, kusukela ezibalweni zesikole nasekufundweni kwemephu kuya ekubaleni izindlela zokupheka kanye nokudala izinhlelo zezindleko nezikali. Ngemiqondo efanele, singasebenzisa izilinganiso nezilinganiso ngokunembile nangendlela ephumelelayo.
