Iqhezu. Uphindaphindo amaqhezu eziqhelekileyo, idesimali, ugalelwe

aba komxholo othi "Amaqhezu" Ekuhambeni yabafundi ophakathi kunye nesikolo samabanga aphakamileyo. Noko ke, le ngcamango ibanzi kakhulu kunoko anikwe kwinkqubo yokufunda. Namhlanje ingqikelelo amaqhekeza asinto ingaqhelekanga, kwaye wonke umntu enze yokubala ibinzana, umzekelo, ukuphinda-zamaqhezu.

Yintoni maqhezu?

Ngokwembali, ukuba amanani iqhezu baba ngenxa imfuneko yokulinganisa. Njengoko yokusebenza ibonisa, wayesoloko imizekelo kwenkcazo ubude ceke, ivolyum engunxantathu parallelepiped, indawo elide.

Ekuqaleni, abafundi baqhelane ingqikelelo ukwabelana ngayo. Umzekelo, ukuba uwahlule melon lezabelo 8, ngoko ke elowo uya kufumana olunye-wesibhozo ivatala. Nantsi enye inxalenye ekuthiwa isithinzi ezisibhozo.

Share, lingana ½ se ixabiso ekuthiwa enesiqingatha; ⅓ - wesithathu; ¼ - ngekota. Amangenelo ifomu ^{_{5/8, 4/5, 2/4}} ngokuba amaqhezu aqhelekileyo. amaqhezu aqhelekileyo bahlulwe njengenani eliphezulu nenani eliphantsi. Phakathi kubo umgca lwamaqhezu, okanye slashes. Slashes kufuneka sibhalwe kwifomu zombini iilayini ezithe tye kunye elibhalwe ngokumileyo. Kulo mzekelo, libonisa umqondiso hlula.

Nedinomineyitha imele Izabelo ezininzi kangakanani enye into ixabiso ekwabelwana; kwaye inani elingezantsi - inani elifanayo kwizabelo ithinjiwe. Elingezantsi ibhalwe ngaphezulu kwesithuba, idinomineyitha - ngaphantsi.

Eyona ndlela elula yokubonisa amaqhezu aqhelekileyo ukulungelelanisa akhanya. Ukuba iyunithi kwicandelo yahlulwe 4 alinganayo, bonisa isabelo unobumba ngamnye Latin, umphumo ube ukuze ufumane uncedo olubonakalayo elungileyo. Ngenxa yoko, indawo A ibonisa umyinge alinganayo ^_1/4 yobude zizonke yunithi, yaye uphawula indawo B i ^_2/8 ye ingxenye elinikiweyo.

zegazi imihlobo

Amaqhezu eziqhelekileyo, idesimali, kwaye amanani axubeneyo. Ukongeza, iqhezu lungohlulwa lube okulungileyo nokubi. Le yokuhlela sifaneleke ngakumbi malunga namaqhezu aqhelekileyo.

Phantsi iqhekeza efanelekileyo ukuqonda amanani abo kwinani ingaphantsi elingezantsi. Ngako oko, le iqhezu engafanelekanga - inani elo liye ngaphezu elingezantsi kwinani. Uhlobo lwesibini ibhalwe njenge ngeendlela ezahlukeneyo. Loo ibinzana yenziwe udibaniso kunye namalungu fraction. Ngokomzekelo, 1½. 1 - isahlulo yonke, ½ - iqhezu. Noko ke, xa ufuna ukwenza nayiphi manipulation ibinzana (ukwahlulwa okanye ukuphinda-amaqhezu kunye zokunciphisa okanye ukuguqulwa), inani mixed iguqulelwe amaqhezu ezingafanelekanga.

njalo ibinzana olululo iqhezu ingaphantsi kwe mnye, nokubi - mkhulu kune okanye ilingana ne-1.

Njengoko ngokuba ngenani leshumi, ngoko eli binzana ukuqonda ingxelo ebonisa naliphi na inani, idinomineyitha ibinzana iqhezu apho ingavezwa iyunithi kunye amaqanda ezimbalwa. Ukuba roll luchanekile, ngoko inxalenye yonke ubhalo lokugqibela ilingana zero.

Ukuze ubhale iqhezu lokugqibela, kufuneka kuqala ubhale yonke inxalenye, ukuba bazahlule ukusuka kwi iqhezu kunye ikoma, uze emva koko ubhale amazwi iqhezu. Kufuneka kukhunjulwe ukuba emva kwinani ngongoma kufuneka siqulathe inani elifanayo loonobumba digital njengoko amaqanda kwinani elingaphezulu.

Umzekelo. adubula inkcaza ^₇ 21/1000 ngokwe wokugqibela.

Translation Algorithm amaqhezu ngokungafanelekanga ukuba amanani axubeneyo and vice versa

Ibhalwe ukuphendula amaqhezu ngokungafanelekanga ngokungachanekanga ingxaki, ngoko kufuneka kube mayitshintshelwe kumanqaku apho itotali yenani exubeneyo:

• yahlula inani yi idinomineyitha ekhoyo;
• kulo mzekelo ethile le QUOTIENT buso - unit;
• namasalela - elingezantsi wenxalenye iqhezu, elingezantsi kuhlala ingatshintshanga.

Umzekelo. Guqula amaqhezu ngokungafanelekanga ukuba amanani axubeneyo: ^_47/5.

Isigqibo. 47: 5. Le QUOTIENT buso ilingana no 9, intsalela = 2. Ngenxa yoko, ^_47/5 = 9 ^_2/5.

Maxa wambi kuyimfuneko ukwazisa inani ugalelwe njengento iqhezu engafanelekanga. Ngoko kufuneka usebenzise algorithm zilandelayo:

• inxalenye elipheleleyo iyanda yi elingezantsi eli binzana fraction;
• imveliso kubangele idityaniswe kwinani;
• isiphumo ibhalwe elingezantsi, nenani kuhlala ingatshintshanga.

Umzekelo. Bonisa inani ngohlobo mixed njengengxenye ngokungafanelekanga 9 ^_8/10.

Isigqibo. 9 x 10 + 8 = 90 + 8 = 98 - kwinani.

Impendulo: ^_98/10.

Uphindaphindo amaqhezu

On amaqhezu aqhelekileyo unako ukwenza imisebenzi eyahlukeneyo algebra. Ukuze phinda amanani amabini, kufuneka phinda inani elingezantsi kunye inani elingezantsi kunye nenani kunye nedinomineyitha. Ngaphezu koko, ukuphindaphindwa amaqhezu anedinomineyitha ezahlukeneyo Akunamsebenzi kwahluke njani imveliso yamanani iqhezu kunye idominetha efanayo.

Kuyenzeka ukuba emva ukufumana iziphumo kufuneka ukunciphisa iqhezu. Kunyanzelekile ukuba kufuneka lula ibinzana ngenxa. Kakade ke, asinakukwazi sithi ukuba iqhezu engafanele impendulo - kuba yimpazamo, kodwa ngokuba impendulo ekunene kube nzima kakhulu.

Umzekelo. Fumana imveliso amaqhezu amabini aqhelekileyo: ½, no ^_20/18.

Njengoko sibonile kumzekelo, emva kokufumanisa nemveliso fraction wajika yokurekhoda cancellative. Kwaye ke inani elingezantsi kunye nenani kulo mzekelo liyohluleka ngo-4, kunye umphumo ikhonza impendulo ^_5/9.

Uphindaphindo amaqhezu wokugqibela

needesimali wobuciko leyo yahluke imisebenzi zesiqhelo ngumgaqo yayo. Ngenxa yoko, ukuphinda-amaqhezu na ngolu hlobo lulandelayo:

• needesimali ezimbini ukuze zibhalwe phantsi omnye komnye, ukuze ukuba umvo abaninzi bomtya baba enye ngezantsi enye ngasentla;
• kufuneka phinda inani abhalwe nangona iikoma, oko nje zendalo;
• ukubala inani lamasuntswana emva kokuba uphawu kwesishumi kwi nganye amanani;
• ukuze emva phinda isiphumo kufuneka babale ilungelo njengabalinganiswa ezininzi amanani njengoko equlethwe isixa multipliers zombini emva indawo enedesimali, uze ubeke uphawu eyohlula;
• ukuba amanani kule mveliso ixesha ngaphantsi phambi kwabo ukuba babhale abayi- ezininzi zokuxhasa ngemali le mali, wabeka kwekoma kwaye kuthiwa inxenye ngu zero.

Umzekelo. Ungabala udibaniso idesimali ezimbini: 2.25 no 3.6.

Isigqibo.

Uphindaphindo amaqhezu exutyiweyo

Ukuze Ungabala udibaniso amaqhezu ezimbini engumxube, kufuneka usebenzise ulawulo phindo amaqhezu:

• ukudlulisela inani ngendlela mixed kwi iqhezu ephosakeleyo;
• Fumana imveliso ye amanani;
• ufumane imveliso ye idominetha;
• ukurekhoda isiphumo wafumana;
• ukuba lula binzana.

Umzekelo. Fumana imveliso ka-4½-6 ^_2/5.

Phinda inani ngu iqhezu (iqhekeza inani)

Ukongezelela ekufumaneni imveliso amaqhezu amabini, amanani axubeneyo wadibana imisebenzi apho kuyimfuneko liphindaphindwe inani yendalo ngesekhondi.

Ngoko ke, ukufumana umsebenzi kunye iqhezu iidecimal inani yendalo, kufuneka:

• abhale inombolo phantsi obethe ngawo, ukuze ukuba umvo abaninzi bomtya baba enye ngezantsi enye ngasentla;
• ukufumana umsebenzi, nangona kwekoma;
• isiphumo ifunyenwe ukwahlukanisa inxalenye elipheleleyo ukusuka lokugqibela ngu ikoma, ukubala inani ekunene amanani emva kokuba kwesishumi ise iqhezu.

Ukuze iphindaphindwe ngenani iqhezu eziqhelekileyo, elingezantsi kufuneka ukufumana umsebenzi kunye factor yendalo. Ukuba impendulo ngu iqhezu cancellative, kufuneka kuguqulwa.

Umzekelo. Ungabala udibaniso ^_5/8 no-12.

Isigqibo. _{^{* 12 = 5/8 (5}} * 12) / 8 = 60/8 = 30/4 = 15/2 = 7 1/2 _.

A: Julayi ^_1/2.

Njengoko sibonile kumzekelo ongaphambili, kuyimfuneko oko ukunciphisa isiphumo yesiphumo kwaye ukuguqula ibinzana ngokungafanelekanga iqhezu kwenani mixed.

Kwakhona, phinda isiphumo siphathelele amaqhezu kwemveliso ngendlela ephikisanayo kunye factor zendalo. Ukuze phinda lamanani mabini kufuneka inxenye yexabiso into ezahlukeneyo liphindaphindwe ngenani, elingezantsi iphinda ixabiso enye, kunye nenani zishiywe zingatshintshanga. Ukuba kuyimfuneko, kuyimfuneko ukuba lula isiphumo.

Umzekelo. Fumana imveliso-9 ^_5/6 no-9.

Isigqibo. 9 ^_5/6 x 9 = 9 + 9 x ^{(5 x _{9) / 6 = 81 + 45}} /6 = 81 + 7 3/6 = 88 1/2 _.

Impendulo: 88 ^_1/2.

Multiplication yi multipliers-10, 100, 1000 okanye 0.1; 0,01; 0,001

Lo mhlathi elandulelayo kukhokelela umthetho ilandelayo. Kuba phinda ngenani leshumi ngo-10, 100, 1000, 10000, njalo njalo. D. Kufuneka ukususa isiphumlisi ekunene ngu iisimboli amanani amaninzi njengoko amaqanda angu ku kwiyunithi wokuphindaphinda emva.

Umzekelo 1. Fumana imveliso ye 0.065 no 1000.

Isigqibo. 0.065 x 1000 = 0065 = 65.

Impendulo: 65.

Umzekelo 2. Fumana imveliso ka-3.9 no-1000.

Isigqibo. 3.9 x 1000 = 3,900 x 1000 = 3900.

Impendulo: 3900.

Ukuba kuyimfuneko ukuba phinda kweqanda, no 0.1; 0,01; 0.001; 0,0001 njalo. E., Ukuba bafudukela ekhohlo isiphumlisi kwimveliso ngenxa ibe iisimboli amanani ezininzi zicinga ukuba umanyano. Ukuba kuyimfuneko, phambi kokuba inani zendalo abhalwe amaqanda amaninzi ngokwaneleyo.

Umzekelo 1. Fumana imveliso-56 no 0,01.

Isigqibo. 56 x 0,01 = 0056 = 0,56.

Impendulo: 0,56.

Umzekelo 2. Fumana imveliso ka-4 no 0,001.

Isigqibo. 4 x 0,001 = 0004 = 0,004.

Impendulo: 0.004.

Ngoko ke, ukufumana imveliso iincindi eziliqela kufuneka kuqonde, ngaphandle kokuba iziphumo ubalo; kulo mzekelo ngaphandle sokubala akayi kuyenza.