Kuenzanisa pakati peRatio neProportion
Mumasvomhu nehupenyu hwezuva nezuva, tinowanzo enzanisa zvinhu zviviri: mutengo uchienzaniswa nehuwandu, daro uchienzaniswa nenguva, kana huwandu hwevadzidzi vechirume nevechikadzi. Pfungwa mbiri dzinowanzo shandiswa kukurukura kuenzanisa kwakadaro ireshiyo nechiyero. Kunyange zvazvo zvingaita sezvine kufanana, uye zvichiwanzo kanganiswa nechinhu chimwe chete, zvine mabasa akasiyana uye mashandisirwo akasiyana. Chinyorwa chino chinotsanangura zvakajeka kuenzanisa pakati pechiyero nechiyero, nemienzaniso yekunzwisiswa zviri nyore.
Kunzwisisa Ratio
Chiyero kuenzanisa pakati pehuwandu huviri hwakafanana kana hwakafanana. Chinoratidza kuti kangani kukosha kumwe kunoenzaniswa nechimwe. Zviyero zvinogona kunyorwa mumhando dzakasiyana-siyana, semuenzaniso:
– a : b (verenga “a anoenzanisa b”)
– a/b
- muchimiro chemashoko, semuenzaniso "a zvichienzaniswa na b"
Semuenzaniso, kana mukirasi muine vadzidzi vechirume gumi nevaviri nevadzidzi vechikadzi gumi nevasere, saka chiyero chevarume nevakadzi ndeichi:
– 12:18
Chiyero ichi chinogona kurerutswa nekukamura zvese ne6:
– 2:3
Izvi zvinoreva kuti pavadzidzi vaviri vechirume, pane vadzidzi vechikadzi vatatu.
Hunhu hweZviyero
1. Enzanisa huwandu huviri (kana kupfuura, asi kazhinji huviri).
2. Inogona kurerutswa sechikamu.
3. Hazvirevi nguva dzose kuti "kuenzana"; chiyero chinoratidza kuenzanisa chete.
Kunzwisisa Kuenzana
Kuenzana ndiko kuenzana kwezviyero zviviri. Kana chiyero cheA kusvika B chakafanana nechiyero cheC kusvika D, saka hukama hunonzi chiyero. Kazhinji chinonyorwa kuti:
– a : b = c : d
kana
– a/b = c/d
Muenzaniso:
Kana 2/3 = 4/6, saka ichi chikamu nekuti zviyero zviviri zvakaenzana.
Muhupenyu chaihwo, zviyero zvinowanzo shandiswa kugadzirisa matambudziko ane chekuita nekuyera, mabikirwo, kumhanya, mitengo yeyuniti, nezvimwewo.
Hunhu hweChikamu
1. Nguva dzose inosanganisira zviyero zviviri zvinoenzaniswa.
2. Inoratidza kuenzana (kukosha kwekuenzanisa kwakafanana).
3. Kazhinji inoshandiswa kuwana zvinhu zvisingazivikanwe (zvinoshandiswa).
Kusiyana Kwakakosha Pakati Pehuwandu uye Kuenzana
Kunyangwe zvakabatana, chiyero uye chiyero zvine musiyano mukuru mutsananguro nebasa. Heino kuenzanisa kukuru:
1. Tsananguro yepfungwa
- Chiyero: kuenzanisa huwandu huviri.
- Kuenzana: kuenzana kwezviyero zviviri.
Chiyero chakafanana ne "kuenzanisa", nepo chiyero chakafanana ne "kuenzanisa zviyero zviviri".
2. Fomu reChirevo
– Chiyero chinongonyorwa se: b.
– Chikamu chinonyorwa se: b = c: d kana a/b = c/d.
3. Tujuan Penggunaan
- Zviyero zvinoshandiswa kuratidza mamiriro kana kuumbwa.
- Kuenzana kunoshandiswa kugadzirisa matambudziko anoda kuenzana kwakaenzana.
4. Kuti kuenzana kuripo here kana kuti kwete
- Chiyero ichi hachidi kuenzana nezvimwe zviyero.
- Kuenzana kunogara kuchiratidza kuenzana kwezviyero zviviri.
Mienzaniso yeZviyero muhupenyu hwezuva nezuva
Muenzaniso 1: Kuumbwa kweMusanganiswa
Chinwiwa chinogadzirwa kubva munyuchi nemvura muchiyero che1:5. Izvi zvinoreva:
– chikamu chimwe nechimwe chesiropu chakasanganiswa nezvikamu zvishanu zvemvura.
Ireshiyo nekuti inongoratidza kuenzanisa kwezvimisikidzo.
Muenzaniso 2: Kuenzanisa Kureba Nenguva
Munhu anofamba makiromita zana nemakumi maviri mumaawa maviri. Chiyero chedaro nenguva ndeichi:
– 120 : 2 = 60 : 1
Kazhinji inobatanidzwa nekumhanya, asi chinhu chekutanga i ratio.
Mienzaniso yeZviyero muhupenyu hwezuva nezuva
Muenzaniso 1: Chikero cheMepu
Chikero chemepu 1:100.000 zvinoreva 1 cm pamepu = 100.000 cm muhupenyu chaihwo.
Kana daro riri pamepu riri 3 cm, daro racho chairo nderei?
Tinoita chikamu:
– 1/100.000 = 3/x
Saka:
– x = 3 × 100.000 = 300.000 cm = 3 km
Ichi chikamu nekuti chinosanganisira kuenzana kwezviyero zviviri uye chinoshandiswa kuwana kukosha kwa x.
Muenzaniso 2: Resipi yekubika
Resipi yevanhu vana inoda magiramu mazana maviri efurawa. Magiramu mangani anodiwa kuvanhu gumi?
Tinoita chikamu:
– 200/4 = x/10
x = (200 × 10) / 4 = 500 magiramu
Uyu muenzaniso wekare wehuwandu mukuenzanisa kwakatarisana kana kwakaenzana.
Hukama huripo pakati pehuwandu hwevanhu (Ratio) nehuwandu hwevanhu (Proportion)
Chiyero nechipimo hazvienderane. Chiyero chakavakirwa papfungwa yechiyero. Pasina kunzwisisa chiyero, zvichave zvakaoma kunzwisisa chiyero. Zvisinei, kuva nechiyero chega hazvina kukwana kuti tizive chiyero; tinoda chimwe chiyero chakaenzana.
Chiyero ndicho "chinhu chikuru", chiyero ndicho "hukama hwekuenzana" pakati pekuenzanisa kuviri.
Misalnya:
- Chiyero che2: 3 ndicho chiyero.
– Kana tikataura 2 : 3 = 4 : 6, zvinova chikamu.
Maitiro Ekutarisa Kana Chikamu Chakarurama
Kuti tione kana a/b = c/d iri chikamu chakakodzera, tinogona kushandisa cross multiplication:
– a × d = b × c
Muenzaniso:
– 2/3 = 4/6
Tarisa:
– 2 × 6 = 12
– 3 × 4 = 12
Sezvo zvakafanana, chiyero chacho chakarurama.
Kana mhedzisiro yacho isina kufanana, zvinoreva kuti zviyero zviviri izvi hazvina kufanana uye hazvisi chikamu chakakodzera.
Zvikanganiso Zvakajairika Mukunzwisisa Zviyero uye Zviyero
1. Ngatitii zviyero zvese zve otomatiki zviyero.
Chiyero chitsva chinova chikamu kana chichienzaniswa nezvimwe zviyero zvakaenzana.
2. Usatanga warerutsa chiyero.
Zviyero zve12: 18 na2: 3 zvakafanana, asi kana zvikasagadziriswa, zvinogona kuvhiringidza.
3. Kuisa huwandu zvisirizvo.
Pakuenzanisa, kurongeka kwakakosha. Kana kurongeka kwakashata, mhedzisiro yekuverenga ichavewo isiriyo.
Mhedziso
Chiyero nechipimo zvose zvinokurukura kuenzanisa, asi zvakasiyana muchimiro nebasa. Chiyero kuenzanisa pakati pehuwandu huviri, nepo chiyero chiri chirevo chekuti huwandu huviri hwakaenzana. Chiyero chinowanzo shandiswa kutsanangura kuumbwa kana kuenzanisa zvakananga, nepo chiyero chinoshandiswa kugadzirisa matambudziko ane chekuita nekuenzana uye kuwana kukosha kusingazivikanwe.
Kunzwisisa musiyano uripo pakati pezviviri izvi kuchabatsira mumamiriro ezvinhu akawanda, kubva pamasvomhu echikoro nekuverenga mepu kusvika pakuverenga mabikirwo uye kugadzira zvirongwa zvemitengo nechiyero. Nepfungwa dzakakodzera, tinogona kushandisa zviyero nezvikamu nemazvo uye zvinobudirira.
