Ratio thiab kev faib ua feem yog dav siv nyob rau hauv algebra los nrhiav kev faib thiab x lub sij hawm. Qhov piv yog qhov cuam tshuam tag nrho rau cov feem ntau vim tias txhua qhov sib piv tuaj yeem sau ua daim ntawv p / q. Ntawm qhov tod tes, qhov kev faib ua feem muaj ob qhov piv nrog rau qhov sib npaug ntawm lawv.
Ratio & proportions yog siv nyob rau hauv ntau yam kev ua lej xws li algebra, geometry, triangles, thiab lwm yam. nws feem ntau yog siv los sib piv ob nqe lus xws li qhov siab, qhov deb, qhov loj, thiab lwm yam.
Hauv tsab xov xwm no, peb yuav tham txog lub ntsiab lus thiab hom piv & piv nrog rau ntau yam piv txwv.
Qhov ratios & proportions yog dab tsi?
Cia peb tham txog proportions thiab proportions luv luv.
Piv
Hauv kev ua lej, lo lus siv los sib piv ob qhov tseem ceeb yog hu ua piv txwv. Kev sib piv ntawm cov ntsiab lus qhia peb ntau npaum li cas ib lub sij hawm muaj piv rau lwm lub sij hawm. Hauv kev sib piv, cov ntsiab lus yuav tsum muaj tib lub units.
Nws yog feem ntau denoted los ntawm ":” kos npe. Piv txwv tuaj yeem sau rau hauv daim ntawv ntawm u / v, qhov twg v tsis sib npaug rau xoom.
Piv txwv li, los sib piv cov txiv neej thiab poj niam cov tub ntxhais kawm nyob rau hauv ib chav kawm sib piv yog siv. Yog tias muaj plaub caug tus tub ntxhais kawm hauv chav kawm, qhov twg 16 yog txiv neej cov tub ntxhais kawm thiab 24 yog cov tub ntxhais kawm poj niam. Tom qab ntawd daim ntawv piv txwv yog txiv neej cov tub ntxhais kawm: poj niam cov tub ntxhais kawm = 16 : 24.
Hauv daim ntawv ntawm ib feem, nws tuaj yeem sau ua 16/24. Tam sim no yooj yim cov ntsiab lus los sib piv cov txiv neej & poj niam cov tub ntxhais kawm, 2 : 3 lossis 2/3. Txhawm rau piv cov txiv neej cov tub ntxhais kawm rau poj niam cov tub ntxhais kawm tsuas yog sau rov qab piv nrog cov poj niam ua ntej li 3: 2 lossis 3/2.
Kev faib ua feem
Hauv algebra, qhov kev faib ua feem yog qhov sib npaug ntawm ob qhov sib piv los qhia koj tias ob qhov sib npaug sib npaug li cas. Qhov sib npaug kuj tuaj yeem sau ua cov feem. Ob txoj hauv kev los sau ib feem yog:
- s :t::v
- s / t = u / v
Hom piv
Hauv algebra, muaj ob hom kev siv feem ntau.
- Ib feem rau tag nrho qhov ratio
- Ib feem rau ib feem ratio
1. Ib feem rau tag nrho qhov piv
Yog hais tias ob nqe lus los yog tej yam raug muab piv rau hauv txoj kev uas ib yam yog coj los ntawm tag nrho, ces nws yuav yog ib feem rau tag nrho cov piv. Piv txwv li, yog tias koj nqa ib daim khob cij los ntawm tag nrho cov pob ntawv, ces nws yuav yog ib feem rau tag nrho qhov piv.
2. Ib feem rau ib feem piv
Ib feem rau ib feem piv yog hom piv uas sib txawv cov ntsiab lus los yog khoom sib piv. Nws tuaj yeem muab qhov sib piv ntawm ob pawg. Piv txwv li, qhov piv ntawm cov tub rog thiab tub ceev xwm, qhov piv ntawm cov tub ntxhais kawm poj niam hauv chav kawm 8 rau cov tub ntxhais kawm poj niam hauv chav kawm 9 yog ob peb yam piv txwv ntawm hom piv txwv no,
Hom kev faib ua feem
Feem ntau yog ob hom.
- Ncaj ncaj
- Inverse proportion
1. Kev faib ua feem ncaj qha
Kev faib ua feem ncaj yog ib hom kev faib ua feem uas qhov nce hauv ib qho khoom ua rau muaj kev nce ntxiv hauv lwm yam khoom lossis kev txo qis hauv ib qho khoom ua rau txo qis hauv lwm yam khoom. Piv txwv li, koj muaj ob yam khoom u & v qhov twg u yog tus naj npawb ntawm cov neeg ua haujlwm thiab v yog kev ua haujlwm ntawm kev tsim kho ntawm phab ntsa.
Yog tias tus naj npawb ntawm cov neeg ua haujlwm nce ntxiv, kev ua haujlwm nrawm ntawm phab ntsa nce, lossis yog tias koj ntiav cov neeg ua haujlwm tsawg lossis txo tus neeg ua haujlwm, kev ua haujlwm yuav tsum txo qis. Nws yog ib qho piv txwv ncaj qha raws li ob qho tib si u & v nce lossis txo nrog nce lossis txo hauv ib qho.
2. Inverse proportions
Inverse proportion yog lwm hom kev faib ua feem uas qhov nce hauv ib qho ua rau txo qis hauv lwm qhov ntau lossis txo qis hauv ib qho ua rau txo qis rau lwm qhov. Piv txwv li, x thiab y yog ob nqe lus, qhov twg x yog tus naj npawb ntawm cov neeg nyob hauv ib qho chaw pw hav zoov thiab y yog zaub mov rau 40 hnub.
Yog tias cov khoom noj nce ntxiv, cov zaub mov rau 40 hnub yuav txo qis, lossis yog tias tus neeg txo qis ces cov zaub mov yuav tsum tau nce ntxiv.
Piv txwv piv txwv thiab proportions
Hauv qab no yog ob peb yam piv txwv ntawm qhov piv txwv thiab kev faib ua feem kom kawm paub xam lawv li cas.
Piv txwv 1: Rau qhov piv txwv
Hauv ib lub thawv ntoo, muaj 16 balloons. Los ntawm cov 16 balloons, 7 yog liab, 5 yog ntshav, thiab 4 yog dawb. Xam qhov ratio ntawm:
- Paj yeeb balloons rau cov paj liab liab
- ntshav balloons rau tag nrho cov balloons
- dawb balloons mus rau liab balloons
tshuaj
Kauj ruam 1: Sau cov ntaub ntawv muab ntawm balloons.
Total balloons = 16
Paj yeeb = 7
liab qab balloons = 5
Pob tshab dawb = 4
Kauj ruam 2: Nrhiav cov paj liab paj rau cov paj liab liab
Tus naj npawb ntawm cov paj liab liab = 7
Number of ntshav balloons = 6
Qhov ratio yog,
7: 6
or
7/6
Kauj ruam 3: Nrhiav qhov piv ntawm cov paj liab liab rau tag nrho cov balloons
Number of balloons = 16
Number of ntshav balloons = 5
Qhov sib txawv ntawm tag nrho cov balloons thiab ntshav balloons = 16 - 5 = 11
Tam sim no qhov ratio yog,
5: 11
Or
5 / 11
Kauj ruam 4: Tam sim no pom qhov piv ntawm cov zais pa dawb rau cov paj liab paj yeeb
Number of white balloons = 4
Tus naj npawb ntawm cov paj liab liab = 7
Ratio yog,
4: 7
Or
4 / 7
Piv txwv 2: Rau qhov kev faib ua feem
15 tus neeg ua haujlwm yuav tsum tsim tus choj hauv 30 hnub, yuav tsum muaj pes tsawg tus neeg ua haujlwm los tsim tus choj tib yam hauv 14 hnub.
tshuaj
Kauj ruam 1: Sau cov ntaub ntawv muab ntawm cov neeg ua haujlwm & hnub.
Cov neeg ua haujlwm yuav tsum ua tus choj = 15
Hnub = 30
Cov neeg ua haujlwm yuav tsum tsim tib tus choj hauv 14 hnub = x
Kauj ruam 2: Sau cov neeg ua haujlwm thiab hnub nyob rau hauv daim ntawv ntawm kev faib ua feem.
cov neeg ua haujlwm : hnub : : cov neeg ua haujlwm : hnub
15 : 30 : : x : 14
Kauj ruam 3: Sau cov piv txwv nyob rau hauv daim ntawv ntawm cov feem nrog ib tug sib npaug zos kos npe rau ntawm lawv los xam tus nqi ntawm x.
15/30 = x/14
Kauj ruam 4: Txhawm rau nrhiav tus nqi ntawm x, siv tus lej sib npaug thiab ua kom yooj yim rau cov lus hais saum toj no.
15/30 = x/14
1/2 = x/14
1 x 14 = x²
14 x = 2
2x = 14
x = 14/2 hli
x = 7 os
Cov neeg ua hauj lwm yuav tsum tau tsim ib tug choj nyob rau hauv 14 hnub = 15 + 7 = 22
Yog li, 7 tus neeg ua haujlwm ntxiv yuav tsum tsim tus choj hauv 14 hnub.
Koj kuj tuaj yeem siv a lub laij lej proportion txhawm rau nrhiav qhov x qhov tseem ceeb ntawm cov teeb meem muab hauv ib feem ntawm cov vib nas this. Ua raws li cov kauj ruam hauv qab no los xam tus nqi x.
Kauj ruam 1: Muab cov ntaub ntawv muaj nqis.
Kauj ruam 2: Nias lub laij lej.
Kauj ruam 3: Nias lub khawm qhia ntxiv kom pom cov kev daws teeb meem nrog cov kauj ruam.
Ntsiab lus
Tam sim no koj tau pom tias qhov sib piv thiab cov proportions tsis yog lub ntsiab lus nyuaj. Koj tuaj yeem rub tag nrho cov hauv paus ntawm qhov piv & kev faib ua feem los ntawm kev kawm cov lus saum toj no. Tam sim no koj tuaj yeem daws txhua qhov teeb meem ntawm qhov sib piv & proportions yooj yim los ntawm kev ua raws li cov piv txwv saum toj no.
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