Ingxenyenamba. Ukubuyabuyelela kwamafrakshini abavamile, idesimali, exubile

babe isihloko "Izibalo" Ngokuhamba abafundi maphakathi kanye esikoleni esiphakeme. Nokho, lo mbono ubanzi kakhulu kunalokho ezinikezwe enqubweni yokufunda yonke. Namuhla umqondo kwamafrakshini akuyona into engavamile, futhi akubona bonke angafeza ekubalweni isisho, isibonelo, ukubuyabuyelela kwamafrakshini.

Kuyini ingxenyenamba?

Ngokomlando, ukuthi izinombolo wamaqhuzu bekulindeleke ukuthi isidingo ukukala. Njengoba umkhuba ubonisa, ngokuvamile atholakala nezibonelo kwencazelo ubude ingxenye, ivolumu a elingunxande parallelepiped, endaweni we isikwele.

Ekuqaleni, abafundi bajwayelane umqondo ukuthi ukwabelana. Ngokwesibonelo, uma ukwehlukana ikhabe ibe izingxenye 8 ke yilowo nalowo uyothola zuza one-eighth of ibhece. Nansi enye ingxenye iyizingxenye eyisishiyagalombili okuthiwa.

Abelana, ilingana ½ lwenani ngokuthi nengxenye; ⅓ - lwesithathu; ¼ - ikota. Okufakiwe yakha ^{_{5/8, 4/5, 2/4}} ngokuthi letetayelekile. amafraktjhini Common yahlukaniswa numerator kanye Iningi. Phakathi kwabo umugqa ingxenyenamba, noma amasileshi. Amasileshi kungenziwa shi ngesimo yomibili imigqa evundla etshekile. Kulokhu, kubonisa uphawu division.

Imbangela limelela ukwabelana eziningi kanjani okufanayo igugu esabelana ngalo into; kanye numerator - inani elifanayo ukwabelana esithathwayo. I numerator kulotshiwe phezu slash, le zifana - ngaphansi.

Indlela elula kunazo ukukhombisa letetayelekile kuhlelembisa uvumelanise. Uma iyunithi ingxenye ihlukaniswe yaba izingxenye 4 alinganayo, ukhombise isabelo incwadi ngayinye Latin, umphumela kungaba ukuthola usizo ezinhle ezibukwayo. Ngakho, iphuzu A kubonisa inani elilingana ^_1/4 of the Ubude iyunithi, futhi iphuzu B uphawula ^_2/8 ingxenye inikezwe.

izinhlobonhlobo amafraktjhini

Izingxenyana zivamile, amadesimali, nezinombolo okuxubile. Ngaphezu kwalokho, ingxenyenamba zingahlukaniswa zibe okulungile nokungalungile. Lokhu kuhlukaniswa kuyinto ekahle amafraktjhini abavamile.

Ngaphansi ingxenyenamba efanele uqonde izinombolo kabani numerator ingaphansi zifana. Ngenxa yalokho, ingxenyenamba okungafanele - inombolo njalo seliphindeke izikhathi ezingaphezu le zihilela numerator. Uhlobo lwesibili Ivame kubhalwa njengoba amafomu okuxubile. inkulumo enjengokuthi yakhiwa inamba nezingxenye wamaqhuzu. Ngokwesibonelo, 1½. 1 - yonke ingxenye, ½ - wamaqhuzu. Nokho, uma kudingeka ukuba afeze noma iyiphi manipulation isisho (division nofana ukubuyabuyelela kwamafrakshini nokwehlisa zabo noma ukuguqulwa), inombolo okuxubile ihunyushwa amafraktjhini okungafanele.

Proper Inkulumo wamaqhuzu uhlale engaphansi, nokungalungile - mkhulu noma elilingana 1.

Ngokuqondene amadesimali, ke yilo inkulumo baqonde Umbhalo ogciniwe ubonisa ukuthi noma iyiphi inombolo, zifana okuvela kuyo le nkulumo wamaqhuzu zazo ungaboniswa iyunithi nge amaqanda ambalwa. Uma roll ilungile, khona-ke wonke iqhaza inotheshini yedesimali ilingana no-zero.

Ukubhala ingxenyenamba yedesimali, kuzomele uqale ukubhala yonke ingxenye, ukuhlukanisa ke kusukela ingxenyenamba ngekhefana, bese ubhala inkulumo wamaqhuzu. Kumele kukhunjulwe ukuthi ngemva numerator iphuzu kumele siqukathe inani elifanayo izinhlamvu digital njengoba amaqanda ku zifana.

Isibonelo. 7 Nanamuhla shot ^_21/1000 e inotheshini yedesimali.

Ukuhumusha Algorithm amafraktjhini okungafanele ukuba izinombolo exubile kanye noHezekeli

Ibhalwe ekuphenduleni amafraktjhini okungafanele ngokungalungile inkinga, ngakho-ke kumelwe liguqulelwe inombolo okuxubile:

• ukwehlukana numerator yi Iningi etholakalayo;
• kulesibonelo okukhethekile quotient esinqunyiwe - iyunithi;
• insali - the numerator we wamaqhuzu Ngokwengxenye, zifana uhlala ingashintshiwe.

Isibonelo. Guqula amafraktjhini okungafanele ukuba izinombolo okuxubile: ^_47/5.

Isinqumo. 47: 5. quotient ngokwengxenye ilingana 9, lezi zinsalela ziyavezwa = 2. Ngakho, ^_47/5 = 9 ^_2/5.

Ngesinye isikhathi kuyadingeka ukwethula inombolo okuxubile njengenhlangano ingxenyenamba okungafanele. Khona-ke udinga ukusebenzisa algorithm ezilandelayo:

• integer ingxenye iyanda yi zihilela okuvela kuyo le nkulumo wamaqhuzu;
• umkhiqizo okuholela yengezwe numerator;
• umphumela okulotshwe numerator, zifana uhlala ingashintshiwe.

Isibonelo. Amele inani ngefomu okuxubile njengoba amafraktjhini okungafanele 9 ^_8/10.

Isinqumo. 9 x 10 + 8 = 90 + 8 = 98 - numerator.

Impendulo: ^_98/10.

Ukubuyabuyelela kwamafrakshini

On letetayelekile ongenza imisebenzi ehlukahlukene Aljibhra. Ukuze uphindaphinde izinombolo ezimbili, udinga uphindaphinde numerator kanye numerator kanye Iningi ne zifana. Ngaphezu kwalokho, ukubuyabuyelela kwamafrakshini nge denominators ezahlukene It akahlukile umkhiqizo izinombolo wamaqhuzu ne denominators efanayo.

Kwenzeka ukuthi ngemva kokuthola imiphumela udinga ukwehlisa ingxenyenamba. Kuphoqelekile ukuba lula Inkulumo okuholela. Yiqiniso, ngeke sikwazi ukusho ukuthi ingxenyenamba engafanele impendulo - kuyiphutha, kodwa futhi ngokuthi impendulo enembile kube nzima kakhulu.

Isibonelo. Thola umkhiqizo kwamafrakshini ezimbili ezivamile: ½, futhi ^_20/18.

Njengoba singabona kusukela Ngokwesibonelo, ngemva kokuthola umkhiqizo wamaqhuzu waphenduka ukuqoshwa cancellative. Futhi numerator kanye Iningi kuleli cala uyahlukaniswa ngu 4, futhi umphumela ukhonza impendulo ^_5/9.

Ukubuyabuyelela of amafrakshini wedesimali

Umsebenzi wobuciko aya kuhlukile kunokunikeza imisebenzi ejwayelekile yizimiso zawo. Ngakho, ukubuyabuyelela kwamafrakshini simiswe ngalendlela lelandzelako:

• aya ezimbili letawubhalwa ngaphansi komunye nomunye, ukuze amadijithi ezingakwesokudla eyodwa ngaphezu kwamanye;
• udinga ukuba azale ande inani eqoshiwe naphezu amakhoma, okungukuthi njengoba yemvelo;
• ukubala inani kwamadijithi emva idesimali iphuzu uphawu in ngamunye izinombolo;
• ukuze uthole emva siphindaphindeka umphumela udinga ukubala ilungelo njengoba abalingiswa abaningi yezinombolo njengoba kuqukethwe inani kokubili multipliers emva iphuzu zamadesimali, futhi ubeke uphawu ehlukanisa;
• uma izinombolo umkhiqizo kwaba isikhathi esincane phambi kwabo ukubhala amaqanda amaningi ukuze bahlanganise le mali, ukubeka ukhefana futhi chasiselwe inamba ingxenye zero.

Isibonelo. Bala umkhiqizo aya ezimbili: 2.25 futhi 3.6.

Isinqumo.

Ukubuyabuyelela kwamafrakshini okuxubile

Ukuze abale umkhiqizo kwamafrakshini ezimbili okuxubile, udinga ukusebenzisa umthetho zokuphindaphinda kwamafrakshini:

• ukudlulisa inombolo ifomu okuxubile ku ingxenyenamba okungalungile;
• Thola umkhiqizo numerators;
• thola umkhiqizo denominators;
• ukurekhoda umphumela etholwe;
• ukwenza lula le nkulumo.

Isibonelo. Thola umkhiqizo 4½ futhi 6 ^_2/5.

Ukuphindaphinda inombolo ngumuntu ingxenyenamba (ingxenyenamba inombolo)

Ngaphezu kokuthola umkhiqizo kwamafrakshini ezimbili, izinombolo okuxubile ihlangabezane imisebenzi lapho kudingeka iphindwe inombolo yemvelo ngendlela ingxenyenamba.

Ngakho, ukuze sithole umsebenzi ingxenyenamba yedesimali yenombolo zemvelo, udinga:

• alobe inani ngaphansi shot, ukuze amadijithi ezingakwesokudla eyodwa ngaphezu kwamanye;
• ukuthola umsebenzi, naphezu kwezinkinga elalibhekene ukhefana;
• umphumela etholwe ukuhlukanisa inamba ingxenye kusukela idesimali ngekhoma, ukubala izinombolo ezifanele emva iphuzu zamadesimali Itholakala ingxenyenamba.

Ukuze siphindwe ngesibalo kokulingana abavamile, le numerator kufanele sithole umsebenzi isici zemvelo. Uma impendulo ingxenyenamba cancellative, kufanele iguqulwe.

Isibonelo. Bala umkhiqizo ^_5/8 no-12.

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

A: Julayi ^_1/2.

Njengoba singabona esibonelweni langaphambilini, kwakudingekile ukunciphisa umphumela okuholela futhi uguqule okungafanele Inkulumo fraction inombolo okuxubile.

Futhi, ukubuyabuyelela kanye nokuthola siphathelene kukhishwa nezingxenyana ezithile umkhiqizo ngendlela okuxubile futhi isici zemvelo. Ukuze uphindaphinde lezi zinombolo ezimbili kufanele kube inombolo ephelele ingxenye isici okuxubile siphindwe ngesibalo, le numerator iphindwe kwenani elifanayo, futhi zifana kwesokunxele zinjalo. Uma kudingeka, kubalulekile ukuba lula yi.

Isibonelo. Thola umkhiqizo 9 ^_5/6 futhi 9.

Isinqumo. 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.

Ukubuyabuyelela nge multipliers 10, 100, 1000 noma 0.1; 0.01; 0.001

Of esigabeni esandulele kuholela mithetho elandelayo. Ukuze siphindaphindeka aya-10, 100, 1000, 10000, nokunye. D. Udinga ukuhambisa ukhefana kuya kwesokudla eziningi amadijithi njengezifanekiselo amaqanda e multiplier iyunithi emva.

Isibonelo 1. Thola umkhiqizo 0.065 futhi 1,000.

Isinqumo. 0.065 x 1000 = 0065 = 65.

Impendulo: 65.

Isibonelo 2. Thola umkhiqizo 3.9 no-1000.

Isinqumo. 3.9 x 1000 = 3.900 x 1000 = 3900.

Impendulo: 3900.

Uma kubalulekile ukuba azale ande nenombolo evumayo ephelele, futhi 0.1; 0.01; 0,001; 0,0001 nokunye. E., Kufanele wathuthela kwesokunxele ukhefana e umkhiqizo okuholela ku eziningi amadijithi njengezifanekiselo amaqanda kuyinto indlela eya ebunyeni. Uma kudingekile, ngaphambi inombolo zemvelo eqoshiwe amaqanda eliningi eyanele.

Isibonelo 1. Thola umkhiqizo 56 futhi 0.01.

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

Impendulo: 0.56.

Isibonelo 2. Thola umkhiqizo 4 futhi 0.001.

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

Impendulo: 0.004.

Ngakho, ekutholeni umkhiqizo wezingxenyana ezihlukahlukene kufanele kube kuqondile, ngaphandle ukuthi umphumela ukubala; kuleli cala ngaphandle wokubala nje ngeke akwenze.