Ukukhupha kwamafrakshini nge denominators ezahlukene. Kuhlanganisa nekususa kwamafrakshini

Omunye isayensi ezibaluleke kakhulu, isicelo zazo kungabonakala eyala ezifana nechemistry, i-physics, ngisho biology, mathematics. Lolu cwaningo kwale sayensi kusivumela ukuthuthukisa ezinye izimfanelo ngokwengqondo, ukuthuthukisa ukucabanga abstract kanye nekhono ukugxilisa ingqondo. Omunye izihloko ezidinga ukunakekelwa okukhethekile ngokuhamba "Mathematics" - nekususa kwamafrakshini. Abafundi abaningi silitadishe kubangela ubunzima. Mhlawumbe i-athikili yethu kuzokusiza uqonde kangcono lesi sihloko.

Indlela amafraktjhini kabani denominators ziyafana Khupha

Shot - kungcono inombolo efanayo, okungase ukukhiqiza izenzo ezihlukahlukene. Ziyahlukahluka kuye kusukela integers kuyinto nokuba khona zifana. Yingakho uma enza imisebenzi enamafrakshini kudingeka uhlole ezinye izici kanye nemithetho. Icala elula kuyinto ukukhupha kwamafrakshini kabani denominators zivezwa inombolo efanayo. Yenza lesi senzo ngeke kube nzima uma wazi umthetho elula:

• Ukuze sidonsa ucezu ozolandela, kubalulekile kusukela numerator we ingxenyenamba ngaphandle ngincipha ukhupha numerator we ezikhokhiswayo ingxenyenamba. Le nombolo irekhodi Nakube kunomehluko ngamalimi numerator kanye Iningi lale ndaba akhuluma efanayo: k / m - b / m = (kb) / m.

Izibonelo nekususa amafraktjhini kabani denominators ziyafana

Ake sibone indlela okubukeka ngayo ku isibonelo:

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

Ngaphandle ukunciphisa numerator we ingxenyenamba "7" ukhupha numerator we ingxenyenamba ezikhokhiswayo "3", sithola "4". Le nombolo sibhala ku numerator impendulo, bese efakwa zihilela inombolo efanayo eyayikhona denominators we amafraktjhini lokuqala nelesibili - "19".

Isithombe esingezansi sibonisa izibonelo ezimbalwa kakhudlwana.

Ake ucabange ngalesi sibonelo eziyinkimbinkimbi, okuyinto ezikhiqizwa ukukhupha zimbili izingxenye zihilela efanayo:

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

Ngaphandle ukunciphisa numerator we ingxenyenamba "29" ngokukhipha le numerators bazabela zonke izingxenyana okwalandela - "3", "8", "2", "7". Ngenxa yalokho, sithola umphumela "9", okulotshiwe kule numerator impendulo, bese ubhala ku zihilela inombolo okusemzini zihilela yazo zonke lezi zingxenyana - "47".

Ukwengezwa amafraktjhini ne zihilela efanayo

Kuhlanganisa nekususa kwamafrakshini kwenziwa isimiso esifanayo.

• Phinda amafraktjhini kabani denominators ziyafana, udinga ukwengeza i numerators. inombolo Tholakele - isamba numerator kanye Iningi izohlala injalo: k / m + b / m = (k + b) / m.

Ake sibone indlela okubukeka ngayo ku isibonelo:

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

Ukuze numerator ekuchubekeni kwethemu lokuqala ingxenyenamba - "1" - kwengezwa numerator kwegama elithi amafraktjhini yesibili -. "2" Umphumela - "3" - isamba irekhodi numerator kanye Iningi ka esiqiwini kuyafana ukuthi ekhona amafraktjhini -. "4"

Izingxenyana nge denominators ezahlukene nokukhupha

Isenzo enamafrakshini ukuthi unayo zihilela efanayo, sixoxisane kakade. Njengoba ubona, ukwazi imithetho elula ukuxazulula lezi zibonelo ngempela kalula. Kodwa kuthiwani uma kudingeka ukwenza isenzo enamafrakshini ukuthi babe denominators ezahlukene? Abafundi abaningi secondary school ukuza ubunzima ukuze izibonelo ezinjalo. Kodwa nalapha futhi, uma wazi isimiso izixazululo, izibonelo ngeke zisaba khona ubunzima. Nalapha futhi kukhona umthetho, ngaphandle kwalokho ikhambi zingxenyana akunakwenzeka.

• Ukuze wenze ukukhupha zimbili izingxenye denominators ezahlukene, kufanele abalethe okufanayo aphansi zifana.

Ukuze ufunde indlela ukwenza lokho, sizobe ukukhuluma okwengeziwe.

amafraktjhini impahla

Emafraktjhinini eziningana eziholela zihilela efanayo, ukuze kusetshenziswe ukuxazulula impahla ebaluleke kakhulu kwamafrakshini: emva sokuhlukanisa noma siphindaphindeka le numerator kanye Iningi ngenani elifanayo ozosigingqela elilingana lokhu.

Ngokwesibonelo, ingxenyenamba 2/3 ungaba denominators ezifana "6", "9", "12" futhi t. D., isb kungathatha ifomu yanoma iyiphi inombolo okungukuthi iphindaphindeke "3". Ngemva numerator kanye Iningi we gaya ngu "2", uthola ingxenyenamba 4/6. Ngemva numerator kanye Iningi we ingxenyenamba we gaya yomthombo kuya "3", sithola 6/9, futhi uma nomphumela ofanayo ukukhiqiza nenani "4", sithola 8/12. ke singatlolwa bunjesi ezothando olulodwa kanje:

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

Indlela cite a amafraktjhini ambalwa kuya zihilela efanayo

Cabanga indlela ukuletha amafraktjhini eziningana zihilela efanayo. Ngokwesibonelo, ukuthatha amafraktjhini kuboniswe esithombeni esingezansi. Okokuqala, kudingeka sithole ukuthi bangaki kungaba zihilela kwazo. Ukuze iwenze ube lula ukwandisa denominators ekhona kahle.

Imbangela ye-ingxenyenamba 1/2, futhi 2/3 ayikwazi ukubola zibe izici. 7/9 Denominator has ezimbili isici 7/9 = 7 / (3 × 3), zifana we ingxenyenamba 5/6 = 5 / (2 x 3). Manje kudingeka ukuthi ziyini izici kuyoba phansi kwabo bonke kuziwa ezine. Kusukela ingxenyenamba wokuqala kule zihilela linenani "2" Khona-ke kumelwe abe khona kuwo wonke denominators ku ingxenyenamba 7/9 has kathathu ezimbili, khona-ke kumelwe bobabili abe khona kuwo zifana. Banikezwe ngenhla, sithola ukuthi zifana siqukethe izici ezintathu: 3, 2, no-3 3 x 2 x 3 = 18.

Cabanga Inhlamvu yokuqala - 1/2. Ngo Iningi layo has "2", kodwa akukho enamadijithi eyodwa "3", futhi kufanele kube ezimbili. Ukuze wenze lokhu, we gaya yi zihilela we kathathu ezimbili, kodwa, ngokuvumelana impahla ingxenyenamba, le numerator futhi sidinga ukuba azale ande ngu kathathu ezimbili:
= 1/2 (1 x 3 x 3) / (2 x 3 x 3) = 9/18.

Ngokufanayo ukukhiqiza isenzo ne amafraktjhini asele.

• 2/3 - ku zihilela sishoda omunye abathathu oyedwa ezimbili:
  = 2/3 (2 x 3 x 2) / (3 x 3 x 2) = 12/18.
• 7/9 noma 7 / (3 x 3) - ku zihilela sishoda ngababili:
  7/9 = (7 x 2) / (9 x 2) = 14/18.
• 5/6 noma 5 / (2 x 3) - ku zihilela sishoda kathathu:
  5/6 = (5 x 3) / (6 x 3) = 15/18.

Sekukonke kubukeka sengathi lokhu:

Kanjani ukuze iqede bese wengeza zimbili izingxenye denominators ezahlukene

Njengoba kushiwo ngenhla, ukuze enze ukuhlanganisa okubuyelelwe nofana ukukhupha zimbili izingxenye denominators ezahlukene, kufanele kuholele zifana, bese ukusizakala imithetho nekususa zimbili izingxenye zifana efanayo, okuyinto sesivele watshela.

Bheka isibonelo: 4/18 - 3/15.

Sithola eziningi-18 no-15:

• Inombolo 18 yakhiwa 3 x 2 x 3.
• Inombolo 15 sakhiwe 5 x 3.
• Nesibaya jikelele izokuba lezi zinto ezilandelayo 5 x 3 x 3 x 2 = 90.

Lapho zihilela kutholakala, kubalulekile ukubala Okuphindaphinda, okuzoba elahlukile ingxenyenamba ngamunye, okungukuthi inombolo ezodingeka ukuze wande hhayi kuphela zifana, kodwa numerator. Kule nombolo sithola (multiple ezivamile), zihlukaniswe zihilela we ingxenyenamba, okuyilona elidingekayo ukuze ukhombe izinto ezengeziwe.

• 90 ehlukaniswa 15. Inombolo okuholela "6" kuyisici ukuze 3/15.
• 90 ehlukaniswa 18. Inombolo okuholela "5" kuyisici ukuze 4/18.

Esigabeni esilandelayo izixazululo zethu - ngokuletha ingxenyenamba ngamunye zifana "90".

Indlela lokhu kwenziwa, siye kakade okukhulunywa. Cabanga, njengoba kulotshiwe Isibonelo:

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

Uma ingxenyenamba ngetinombolo letincane, kungenzeka ukunquma zifana njengoba kulesibonelo kuboniswe esithombeni esingezansi.

Ngokufanayo kukhiqizwa futhi ngaphezu kwamafrakshini kokuba denominators ezahlukene.

Kuhlanganisa nekususa kwamafrakshini nge izingxenye lonke

Ukukhupha kwamafrakshini futhi ngaphezu kwabo, siye kakade idingidwa. Kodwa kanjani ukususa, uma kukhona ingxenye encane lonke? Nalapha futhi, ukusebenzisa izimiso ezimbalwa:

• Zonke zimbili izingxenye inamba ingxenye, lihunyushelwe okungalungile. Ngamagama alula, susa inamba ingxenye. Ukuze wenze lokhu, wonke inombolo ingxenye iyanda yi zihilela we ingxenyenamba etholwe ngokungeza komkhiqizo numerator. Lelo nani, okuyinto etholakala emva lezi zenzo - the numerator amafraktjhini okungafanele. Imbangela uhlala ingashintshiwe.
• Uma kuziwa babe denominators ezahlukene, kufanele abalethe okufanayo.
• Yenza ukuhlanganisa okubuyelelwe nofana ukukhupha we denominators efanayo.
• Phezu kokuthola amafraktjhini okungafanele ukwaba yingxenye yalo lonke.

Kukhona enye indlela esingathola ngayo angafeza nekususa kwamafrakshini nge inamba izingxenye. Kuze kube yimanje, izenzo kwenziwe ngokuhlukile wonke izingxenye, nemisebenzi ehlukile enamafrakshini, futhi imiphumela alotshwe ndawonye.

Isibonelo ngenhla yakhiwa izingxenyana ube zihilela efanayo. Esimeni lapho denominators zihlukile, kufanele kuholele okufanayo, futhi ukwenza izenzo okwengeziwe, njengoba kukhonjisiwe kulesibonelo.

Ukukhupha kukhishwa nezingxenyana ezithile inenombolo

Omunye izinhlobonhlobo zemisebenzi enamafrakshini kunjalo uma udinga ukuthatha ucezu inombolo zemvelo. Uma uthi nhlá kubonakala sengathi isibonelo nzima ukuzixazulula. Nokho, kungcono pretty elula lapha. Ukuxazulula kumele elihunyushwe ibe ingxenyenamba inamba ne zihilela kokuba ukuthi kukhona sisuswe ku izingxenyana zaso. Eminye imikhiqizo ukukhupha, ukukhupha fanekiso ne denominators efanayo. Ngokwesibonelo kubukeka sengathi lokhu:

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

Sikhishwe kulesi sihloko ukukhupha kwamafrakshini (Libanga 6) isisekelo ikhambi ngaphezulu izibonelo eziyinkimbinkimbi, zazo kuxoxwa ngazo amakilasi alandelayo. Ulwazi lesi sihloko asetshenziswa kamuva ukuxazulula imisebenzi, nemikhiqizo nokunye. Ngakho-ke kubaluleke kakhulu ukuba baqonde futhi baqonde kwemisebenzi enamafrakshini, okuxoxwe ngawo ngenhla.