Ib qho nyuaj tshaj plaws rau cov tub ntxhais kawm kom nkag siab yog qhov sib txawv nrog cov feem yooj yim. Qhov no yog vim lub fact tias nws tseem nyuaj rau cov me nyuam xav abstractly, thiab feem, qhov tseeb, zoo li ntawd rau lawv. Yog li ntawd, thaum nthuav tawm cov ntaub ntawv, cov kws qhia ntawv feem ntau siv cov piv txwv thiab piav qhia qhov kev rho tawm thiab sib ntxiv ntawm cov feem ntawm cov ntiv tes. Txawm hais tias tsis yog ib zaj lus qhia ntawm tsev kawm ntawv lej tuaj yeem ua yam tsis muaj cov cai thiab cov ntsiab lus.
Basic concepts
Ua ntej koj pib ua haujlwm nrog cov feem, nws raug nquahu kom kawm ob peb lub ntsiab lus thiab cov cai. Thaum xub thawj, nws yog ib qho tseem ceeb kom nkag siab tias ib feem yog dab tsi. Los ntawm nws txhais tau tias tus lej sawv cev ib lossis ntau qhov feem ntawm ib chav. Piv txwv li, yog tias koj txiav ib lub ncuav rau hauv 8 qhov chaw thiab muab 3 daim ntawm lawv rau ntawm lub phaj, ces 3/8 yuav yog ib feem. Ntxiv mus, hauv qhov kev sau no nws yuav yog ib feem yooj yim, qhov twg tus lej saum kab yog tus lej, thiab hauv qab nws yog tus lej. Tab sis yog tias nws sau li 0.375, nws yuav yog tus lej feem pua.
Ntxiv rau, cov feem yooj yim muab faib ua kom raug, tsis raug thiab sib xyaw. Cov qub suav nrog txhua tus uas nws tus lej tsawg duatus lej. Yog tias, ntawm qhov tsis sib xws, tus denominator tsawg dua tus lej, nws yuav yog ib feem tsis tsim nyog. Yog hais tias muaj ib tug integer nyob rau hauv pem hauv ntej ntawm qhov tseeb, lawv hais txog cov zauv sib xyaw. Yog li, feem 1/2 yog qhov tseeb, tab sis 7/2 tsis yog. Thiab yog koj sau rau hauv daim foos no: 3 1/2, ces nws yuav sib tov.
Txhawm rau kom nkag siab yooj yim dua qhov sib ntxiv ntawm cov feem yog, thiab ua kom yooj yim, nws tseem ceeb heev kom nco ntsoov cov khoom tseem ceeb ntawm ib feem. Nws essence yog raws li nram no. Yog tias tus lej thiab tus lej tau muab faib los ntawm tib tus lej, ces qhov feem yuav tsis hloov. Nws yog cov cuab yeej no uas tso cai rau koj ua cov haujlwm yooj yim tshaj plaws nrog cov khoom siv zoo tib yam thiab lwm cov feem. Qhov tseeb, qhov no txhais tau tias 1/15 thiab 3/45 yog, qhov tseeb, tib tus lej.
Ntxiv cov feem nrog tib tus lej
Qhov kev ua no feem ntau yooj yim ua. Qhov sib ntxiv ntawm cov feem nyob rau hauv cov ntaub ntawv no yog heev zoo li ib tug zoo xws li kev txiav txim nrog integers. Tus denominator tseem tsis hloov pauv, thiab cov lej tsuas yog ntxiv ua ke. Piv txwv li, yog tias koj xav tau ntxiv cov feem 2/7 thiab 3/7, ces kev daws teeb meem hauv tsev kawm ntawv hauv phau ntawv yuav zoo li no:
2/7 + 3/7=(2+3)/7=5/7.
Tsis tas li ntawd, qhov sib ntxiv ntawm cov feem ntau tuaj yeem piav qhia nrog piv txwv yooj yim. Siv ib lub txiv apple zoo tib yam thiab txiav, piv txwv li, ua 8 qhov chaw. Npog tawm ua ntej 3 ntu, thiab tom qab ntawd ntxiv 2 ntxiv rau lawv, thiab yog li ntawd, 5/8 ntawm tag nrho cov kua yuav pw hauv lub khob. Qhov teeb meem arithmetic nws tus kheej yog sau raws li qhia hauv qab no:
3/8 + 2/8=(3+2)/8=5/8.
Ntxivfeem ntau nrog tus lej sib txawv
Tab sis feem ntau muaj teeb meem nyuaj dua, qhov uas koj yuav tsum tau ntxiv ua ke, piv txwv li, 5/9 thiab 3/5. Qhov no yog qhov uas thawj qhov teeb meem tshwm sim hauv kev ua nrog cov feem. Tom qab tag nrho, ntxiv cov lej no yuav xav tau kev paub ntxiv. Tam sim no koj yuav tsum nco ntsoov tag nrho lawv cov khoom tseem ceeb. Txhawm rau ntxiv cov feem ntawm qhov piv txwv, ua ntej lawv yuav tsum raug txo kom tsawg rau ib tus lej. Txhawm rau ua qhov no, tsuas yog muab 9 thiab 5 ntawm lawv tus kheej, muab tus lej "5" los ntawm 5, thiab "3", feem, los ntawm 9. Yog li, cov feem ntau twb tau ntxiv: 25/45 thiab 27/45. Tam sim no nws tsuas yog tseem ntxiv cov lej thiab tau txais cov lus teb 52/45. Ntawm ib daim ntawv, ib qho piv txwv yuav zoo li no:
5/9 + 3/5=(5 x 5) / (9 x 5) + (3 x 9) / (5 x 9)=25/45 + 27/45=(25 + 27) /45=52/45=17/45.
Tab sis ntxiv cov feem nrog cov lej zoo li no tsis tas yuav tsum muaj qhov sib npaug ntawm cov lej hauv kab. Ua ntej saib rau tus lej qis tshaj plaws. Piv txwv li, rau feem 2/3 thiab 5/6. Rau lawv, qhov no yuav yog tus lej 6. Tab sis cov lus teb tsis yog ib txwm pom tseeb. Hauv qhov no, nws tsim nyog nco ntsoov txoj cai txhawm rau nrhiav qhov tsawg tshaj plaws ntau yam (LCM luv luv) ntawm ob tus lej.
Nws nkag siab tias qhov tsawg tshaj plaws ntawm ob tus lej. Txhawm rau nrhiav nws, decompose txhua yam rau hauv qhov tseem ceeb. Tam sim no sau tawm cov ntawm lawv uas tshwm sim tsawg kawg ib zaug hauv txhua tus lej. Muab lawv ua ke thiab tau txais tib lub denominator. Qhov tseeb, txhua yam zoo li yooj yim me ntsis.
Piv txwv li, koj xav tauntxiv cov seem 4/15 thiab 1/6. Yog li, 15 yog tau los ntawm kev muab cov lej yooj yim 3 thiab 5, thiab rau - ob thiab peb. Qhov no txhais tau hais tias LCM rau lawv yuav yog 5 x 3 x 2=30. Tam sim no, faib 30 los ntawm tus lej ntawm thawj feem, peb tau txais ib qho tseem ceeb rau nws tus lej - 2. Thiab rau feem thib ob nws yuav yog tus lej 5. Yog li, nws tseem yuav ntxiv cov feem zoo tib yam 8/30 thiab 5/30 thiab tau txais cov lus teb rau 13/30. Txhua yam yog yooj yim heev. Hauv phau ntawv sau, txoj haujlwm no yuav tsum tau sau raws li hauv qab no:
4/15 + 1/6=(4 x 2)/(15 x 2) + (1 x 5)/(6 x 5)=8/30 + 5/30=13/30.
NOK (15, 6)=30.
Ntxiv cov lej sib xyaw
Tam sim no, paub tag nrho cov lus qhia yooj yim hauv kev ntxiv cov feem yooj yim, koj tuaj yeem sim koj txhais tes ntawm cov piv txwv nyuaj. Thiab cov no yuav yog cov lej sib xyaw, uas txhais tau tias ib feem ntawm hom no: 22/3. Ntawm no, tus lej feem yog sau ua ntej qhov feem zoo. Thiab ntau tus tau tsis meej pem thaum ua yeeb yam nrog cov lej zoo li no. Qhov tseeb, tib txoj cai siv ntawm no.
Txhawm rau ntxiv cov lej sib xyaw ua ke, ntxiv tag nrho cov seem thiab cov feem kom raug cais. Thiab ces 2 cov txiaj ntsig no twb tau sau tseg lawm. Hauv kev xyaum, txhua yam yooj yim dua, koj tsuas yog yuav tsum tau xyaum me ntsis. Piv txwv li, hauv ib qho teeb meem koj yuav tsum ntxiv cov lej sib xyaw hauv qab no: 11/3 thiab 42 /5. Ua li no, ua ntej ntxiv 1 thiab 4 kom tau 5. Tom qab ntawd ntxiv 1/3 thiab 2/5 siv cov txheej txheem tsawg tshaj plaws denominator. Qhov kev txiav txim yuav yog 11/15. Thiab cov lus teb kawg yog 511/15. Nyob rau hauv ib lub tsev kawm ntawv phau ntawv nws yuav zoo heevluv luv:
11/3+ 42/5=(1 + 4) + (1/3 + 2/5)=5 + 5/15 + 6/15=5 + 11/15=511/ 15.
Ntxiv cov lej
Ntxiv rau cov feem zoo tib yam, kuj muaj cov lej. Los ntawm txoj kev, lawv muaj ntau ntau nyob rau hauv lub neej. Piv txwv li, tus nqi hauv khw feem ntau zoo li no: 20.3 rubles. Qhov no yog tib feem. Ntawm chav kawm, cov no yooj yim dua rau quav dua li cov qub. Hauv txoj cai, koj tsuas yog yuav tsum tau ntxiv 2 tus lej zoo tib yam, qhov tseem ceeb tshaj plaws, muab lub cim rau hauv qhov chaw. Qhov no yog qhov nyuaj tuaj.
Piv txwv li, koj yuav tsum tau ntxiv cov zauv feem 2, 5 thiab 0, 56. Txhawm rau ua qhov no kom raug, koj yuav tsum ntxiv xoom rau thawj qhov kawg, thiab txhua yam yuav zoo.
2, 50 + 0, 56=3, 06.
Nws yog ib qho tseem ceeb kom paub tias txhua feem ntawm tus lej tuaj yeem hloov mus rau ib feem yooj yim, tab sis tsis yog txhua feem yooj yim tuaj yeem sau ua tus lej. Yog li, los ntawm peb qhov piv txwv 2, 5=21/2 thiab 0, 56=14/25. Tab sis xws li ib feem li 1/6 tsuas yog kwv yees li sib npaug rau 0, 16667. Cov xwm txheej zoo ib yam yuav nrog lwm tus lej zoo sib xws - 2/7, 1/9 thiab lwm yam.
Zoo kawg
Ntau cov menyuam kawm ntawv, tsis nkag siab txog qhov ua tau zoo ntawm kev ua nrog feem, kho cov ncauj lus no tsis tu ncua. Txawm li cas los xij, hauv cov qib qub, qhov kev paub yooj yim no yuav tso cai rau koj nyem zoo li cov txiv ntoo ntawm cov piv txwv nyuaj nrog logarithms thiab nrhiav cov derivatives. Thiab yog li ntawd, nws tsim nyog ib zaug kom nkag siab zoo cov kev ua nrog feem, yog li tom qab ntawd koj tsis tom koj lub luj tshib tawm ntawm kev ntxhov siab. Tom qab tag nrho, tsis yog ib tug xib fwb nyob rau hauv high schoolyuav rov qab mus rau qhov no, twb dhau lawm, lub ncauj lus. Txhua tus menyuam kawm ntawv theem siab yuav tsum muaj peev xwm ua tau cov kev qhia no.
