Rho cov lej uas txawv denominators. Ntxiv thiab rho tawm ntawm cov zauv feem

Ib tug ntawm cov tseem ceeb tshaj plaws science, daim ntawv thov ntawm cov uas muaj peev xwm yuav pom nyob rau hauv xws disciplines li chemistry, physics, thiab txawm biology, ua lej yog. Txoj kev tshawb no ntawm no science tso cai rau peb kom peb tsim ib co kev puas hlwb zoo, ua kom paub daws teeb xav thiab muaj peev xwm mus mloog zoo. Ib tug ntawm lub ntsiab lus uas yuav tsum tau txais tshwj xeeb xim nyob rau hauv lub chav kawm "Mathematics" - ntxiv thiab sib rho cov lej. Muaj ntau cov tub ntxhais kawm kawm nws ua rau muaj teeb meem. Tej zaum peb tsab xov xwm yuav pab tau koj to taub zoo dua no lub npe.

Yuav ua li cas Rho fractions uas nws denominators yog tib yam

Txhaj koob tshuaj tivthaiv - nws yog tib yam pes tsawg tus, uas yuav ua tau ntau yam ntawm kev ua. Lawv txawv los ntawm lub zauv yog lub xub ntiag ntawm lub denominator. Uas yog vim li cas thaum ua hauj lwm nrog cov zauv feem yuav tau tshawb ib co ntawm cov yam ntxwv thiab cov kev cai. Qhov yooj yim cov ntaub ntawv yog ib tug sib rho cov lej uas nws denominators yog muaj tuaj raws li cov tib tooj. Ua qhov kev txiav txim yuav tsis tau yooj yim yog tias koj paub tej yam yooj yim txoj cai:

• Nyob rau hauv thiaj li yuav rho tawm tau ib feem ntawm ib tug thib ob, nws yog tsim nyog los ntawm cov numerator ntawm lub feem tsis muaj zuj zus lawm rho cov numerator ntawm lub feem uas yus them yus. Qhov no cov ntaub ntawv xov tooj ntawm txawv nyob rau hauv lub numerator thiab denominator ntawm tib txoj kev kawm: k / m - b / m = (kb) / m.

Piv txwv subtracting fractions uas nws denominators yog tib yam

Cia peb kawm saib ua li cas nws zoo rau cov piv txwv:

7/19 - 3/19 = (7 - 3) / 19 = 4/19.

Tsis muaj zuj zus lawm lub numerator ntawm lub feem "7" rho cov numerator ntawm lub feem deductible "3", peb tau txais "4". Qhov no naj npawb peb sau nyob rau hauv lub numerator ntawm cov lus teb, thiab muab tso rau hauv lub denominator tib yam pes tsawg tus uas yog nyob rau hauv lub denominators ntawm tus thawj thiab thib ob fractions - "19".

Cov duab hauv qab no qhia tau hais tias ib tug ob peb ntau cov piv txwv.

Cia peb xav txog ib tug ntau Piv txwv li, uas ua kev rho tawm ntawm cov zauv feem nrog tib denominator:

29/47 - 3/47 - 8/47 - 2/47 - 7/47 = (29 - 3 - 8 - 2 - 7) / 47 = 9/47.

Tsis muaj zuj zus lawm lub numerator ntawm lub feem "29" by subtracting qhov numerators nyob rau hauv lem tag nrho tom ntej fractions - "3", "8", "2", "7". Raws li ib tug tshwm sim, peb tau txais lub txiaj ntsim ntawm "9", uas yog sau ntawv nyob rau hauv lub numerator ntawm cov lus teb, thiab sau nyob rau hauv lub denominator yog lub xov tooj uas yog nyob rau hauv lub denominator ntawm tag nrho cov zauv feem - "47".

Tsis tas li ntawd ntawm cov zauv feem nrog tib denominator

Ntxiv thiab rho tawm ntawm cov zauv feem yog nqa tawm nyob rau hauv tib lub hauv paus ntsiab lus.

• Yuav kom quav fractions uas nws denominators yog tib yam, koj yuav tau ntxiv txog lub numerators. Txais xov tooj - lub sum ntawm cov numerator thiab denominator lub yuav zoo ib yam: k / m + b / m = (k + b) / m.

Cia peb kawm saib ua li cas nws zoo rau cov piv txwv:

1/4 + 2/4 = 3/4.

Rau cov numerator ntawm cov thawj lub sij hawm ntawm lub feem - "1" - muab cov numerator ntawm lub thib ob lub sij hawm fractions -. "2" Cov - "3" - ib cov ntaub ntawv sum nyob rau hauv lub numerator thiab denominator ntawm lub zeem cia yog tib yam li hais tias tam sim no nyob rau hauv cov zauv feem -. "4"

Cov zauv uas sib txawv denominators thiab sib rho

Action nrog cov zauv feem uas muaj tib lub denominator, peb twb sib tham. Raws li koj tau pom, paub kev cai yooj yim los daws kom tau cov piv txwv yooj yim heev. Tab sis yog hais tias koj yuav tsum tau ua ib qho kev txiav txim nrog cov zauv feem uas muaj sib txawv denominators? Muaj ntau theem nrab tsev kawm ntawv cov tub ntxhais kawm tuaj rau cov teeb meem xws li cov piv txwv. Tiam sis ntawm no, dhau lawm, yog tias koj paub lub hauv paus ntsiab lus ntawm kev daws teeb meem, piv txwv yuav tsis tau tam sim no kom koj ua. Ntawm no ib yam nkaus thiab muaj ib tug txoj cai, tsis muaj uas cov tshuaj ntawm tej feem me me tsuas yog tsis yooj yim sua.

• Mus ua ib tug sib rho cov lej uas txawv denominators, koj yuav tsum coj lawv mus rau cov tib qis tshaj li ib qho denominator.

Yuav kom kawm tau li cas ua li ntawd, peb mam li tham ntxiv.

fractions vaj tse

Mus rau ob peb fractions ua rau tib denominator, yuav tsum tau siv nyob rau hauv kev daws cov tseem ceeb tshaj plaws vaj tse ntawm cov zauv feem: tom qab faib los txawj cov numerator thiab denominator los ntawm tib lub xov tooj yuav yob sib npaug zos rau qhov no.

Piv txwv li, lub feem 2/3 yuav muaj denominators xws li "6", "9", "12" thiab t. D., I.e. tej zaum nws yuav siv sij hawm rau hauv daim ntawv ntawm tej xov tooj uas yog ib tug ntau yam ntawm "3". Tom qab lub numerator thiab denominator, peb muab los ntawm "2", koj tau txais cov feem 4/6. Tom qab lub numerator thiab denominator ntawm lub feem peb muab lub qhov mus rau lub "3", peb tau txais 6/9, thiab yog hais tias ib tug zoo xws li cov nyhuv yuav tsim muaj pes tsawg "4", peb tau txais 8/12. nws yuav sau raws li ib tug tib kab zauv raws li nram no:

2/3 = 4/6 = 6/9 = 8/12 ...

Yuav ua li cas mus pabneeg ib tug ob peb fractions rau tib lub denominator

Xav txog yuav ua li cas nqa ob peb fractions rau tib lub denominator. Piv txwv li, muab lub fractions qhia nyob rau hauv daim duab hauv qab no. Ua ntej peb yuav los mus txiav txim yuav ua li cas muaj ntau yam yuav ua tau ib tug denominator rau tag nrho cov ntawm lawv. Yuav kom pab txhawb nthuav uas twb muaj lawm denominators factoring.

Lub denominator ntawm lub feem 1/2, thiab 2/3 tsis tau decomposed rau hauv yam. 7/9 denominator muaj ob tug tshaj 7/9 = 7 / (3 × 3), cov denominator ntawm lub feem 5/6 = 5 / (2 x 3). Tam sim no koj yuav tsum txiav txim seb cov yam tseem ceeb yuav tsum tau tus nqi qis tshaj ntawm tag nrho cov plaub fractions. Txij li thaum thawj feem nyob rau hauv lub denominator tus xov tooj "2", ces nws yuav tsum yog tam sim no nyob rau hauv tag nrho cov denominators nyob rau hauv lub feem 7/9 muaj ob tug triples, ces lawv kuj yuav tsum ob leeg yuav tam sim no nyob rau hauv lub denominator. Muab qhov saum toj no, peb txiav txim siab tias lub denominator muaj peb yam tseem ceeb: 3, 2, thiab 3 yog 3 x 2 x 3 = 18.

Xav txog cov thawj txhaj koob tshuaj tivthaiv - 1/2. Nyob rau hauv nws cov denominator muaj "2", tab sis tsis muaj ib tug tib tug lej "3", thiab yuav tsum muaj ob tug. Ua li no, peb muab los ntawm lub denominator ntawm ob triples, tab sis, raws li cov khoom teejtug uas yog cov feem, lub numerator thiab peb yuav tsum muab los ntawm ob triples:
= 1/2 (1 x 3 x 3) / (2 x 3 x 3) = 9/18.

Ib yam li ntawd tsim kev txiav txim nrog rau seem uas fractions.

• 2/3 - nyob rau hauv lub denominator yog uas ploj lawm ib tug ntawm peb thiab ib tug ntawm ob tug:
  2/3 = (2 x 3 x 2) / (3 x 3 x 2) = 12/18.
• 7/9 los yog 7 / (3 x 3) - nyob rau hauv lub denominator yog uas ploj lawm twos:
  7/9 = (7 x 2) / (9 x 2) = 14/18.
• 5/6 los yog 5 / (2 x 3) - nyob rau hauv lub denominator yog uas ploj lawm triples:
  5/6 = (5 x 3) / (6 x 3) = 15/18.

Tag nrho cov nyob rau hauv tag nrho nws zoo li no:

Yuav ua li cas mus rho thiab ntxiv mus fractions uas txawv denominators

Raws li hais saum toj no, nyob rau hauv thiaj li yuav ua rau qhov sib ntxiv los yog kev rho tawm ntawm cov zauv feem uas sib txawv denominators, lawv yuav tsum ua rau ib qho denominator, thiab ces coj kom zoo dua ntawm cov kev cai ntawm subtracting fractions nrog tib denominator, uas twb tau hais.

Saib ib qho piv txwv: 4/18 - 3/15.

Peb nrhiav tau ntau yam ntawm 18 thiab 15:

• Tus xov tooj 18 yog muaj li ntawm 3 x 2 x 3.
• Tus xov tooj 15 yog muaj ib tug 5 x 3.
• Cov kev quav yuav muaj xws li cov nram qab no yam 5 x 3 x 3 x 2 = 90.

Thaum lub denominator yog pom, nws yog tsim nyog los mus laij lub d, uas yuav sib txawv rau txhua feem, uas yog lub xov tooj uas yuav tsim nyog los muab tsis tau tsuas yog lub denominator, tab sis lub numerator. Yuav kom qhov no naj npawb peb nrhiav (cov ntau yam), muab faib los ntawm lub denominator ntawm lub feem, uas yog tsim nyog los qhia hais tias tus ntxiv yam.

• 90 muab faib los ntawm 15. Qhov tus xov tooj "6" yog ib qhov zoo tshaj rau 3/15.
• 90 muab faib los ntawm 18. Qhov tus xov tooj "5" yog ib qhov zoo tshaj rau 4/18.

Cov theem tom ntej ntawm peb lub ntsiab - nqa txhua feem rau cov denominator "90".

Yuav ua li cas qhov no yog ua, peb twb hais. Xav txog, raws li sau nyob rau hauv lub Piv txwv li:

(4 x 5) / (18 x 5) - (3 x 6) / (15 x 6) = 20/90 - 18/90 = 2/90 = 1/45.

Yog hais tias lub feem nrog me me xov tooj, nws yog ua tau los mus txiav txim cov denominator raws li nyob rau cov piv txwv qhia nyob hauv daim duab hauv qab no.

Ib yam li ntawd ua thiab tsis tas li ntawd ntawm cov zauv feem coj txawv denominators.

Ntxiv thiab rho tawm ntawm cov zauv feem nrog tag nrho qhov chaw

Rho ntawm cov zauv feem thiab lawv tas li ntawd, peb twb sib tham nyob rau hauv kom meej. Tab sis yuav ua li cas ua ib tug sib rho, yog hais tias muaj yog ib feem ntawm tag nrho cov? Ib zaug ntxiv, siv ib tug ob peb cov kev cai:

• Tag nrho cov zauv feem nrog integer ib feem, txhais mus rau hauv lub tsis ncaj ncees lawm. Nyob rau hauv cov lus yooj yim, tshem tawm cov integer ib feem. Ua li no, tag nrho cov xov tooj feem yog multiplied los ntawm cov denominator ntawm lub feem tau los ntawm kev ntxiv cov khoom rau cov numerator. Tus xov tooj, uas yog tau tom qab cov kev ua - qhov numerator kev fractions. Lub denominator tseem unchanged.
• Yog hais tias lub fractions muaj ntau denominators, koj yuav tsum coj lawv mus rau lub qub.
• Ua rau qhov sib ntxiv los yog kev rho tawm ntawm tib denominators.
• Thaum tau txais daim ntawv ntawm kev fractions faib ib feem ntawm tag nrho cov.

Muaj yog ib txoj kev los ntawm cov uas koj yuav nqa tawm ntxiv thiab rho cov lej nrog integer qhov chaw. Yuav kom qhov no kawg, ua yog nqa tawm nyias los ntawm tag nrho cov qhov chaw, thiab cais ua hauj lwm nrog cov zauv feem, thiab cov kev tshwm sim yog kaw ua ke.

Qhov saum toj no piv txwv yog muaj li ntawm cov zauv feem uas muaj tib lub denominator. Nyob rau hauv lub rooj plaub uas lub denominators yog sib txawv, lawv yuav tsum ua rau lub tib yam, thiab ua ntxiv tej yam yuav ua, raws li qhia nyob rau hauv tus piv txwv.

Rho ntawm cov zauv feem ntawm ib tug integer

Lwm yam uas ntawm ua hauj lwm nrog cov zauv feem yog cov ntaub ntawv thaum koj yuav tau muab ib feem ntawm ib tug tej yam ntuj tso xov tooj. Thaum xub thawj siab ib muag mas, zoo li ib qho piv txwv ntawm tsis yooj yim kho. Txawm li cas los, nws yog yooj yim zoo nkauj ntawm no. Yuav kom daws tau nws yuav tsum tau txhais rau hauv ib qho integer feem nrog lub denominator ua hais tias muaj yuav raug txiav nyob rau hauv cov zauv feem. Ntxiv khoom sib rho, sib rho analogous nrog tib denominators. Piv txwv li, nws zoo li no:

7 - 4/9 = (7 x 9) / 9 - 4/9 = 53/9 - 4/9 = 49/9.

Muab nyob rau hauv no tsab xov xwm kev rho tawm ntawm cov zauv feem (Qib 6) yog lub hauv paus rau kev daws ntawm ntau cov piv txwv, uas yuav sib tham txog hauv qab no cov chav kawm ntawv. Paub txog no lub npe yog siv tom qab daws kev khiav dej num, derivatives thiab thiaj li nyob. Yog li ntawd nws yog ib qho tseem ceeb heev kom to taub thiab to taub kev ua hauj lwm nrog cov zauv feem, sib tham saum toj no.