Ngokuqinisekileyo uye wazibuza ukuba yintoni ukuhambisa ipropathi kunye nendlela enokusetyenziswa ngayo. Ukuba kunjalo, ke ufikelele kwinqaku elichanekileyo, kuba apha siza kuchaza ngendlela elula kakhulu yonke inkqubo yalo msebenzi ulonwabisayo wezibalo. Dibana nathi!

## Ukuhanjiswa kwepropathi

Kuqhelekile ukuthandabuzaYintoni ipropathi yokuhambisa? Sukuba nexhala kuba siza kukucacisela ngendlela elula kakhulu.

Kukusebenza kwezibalo apho ukulingana kweziphumo kufunwa, ngeendlela ezahlukeneyo: (ukongeza, ukuthabatha nokuphindaphinda izinto ezichaphazelekayo).

Yipropathi ye-algebraic esivumela ukuba sisebenzise ukongeza kunye nokukhupha amanani, athi ke xa ephindaphindwa, asinike iziphumo. Kwaye ukuba sitshintsha i-odolo apho ezi zinto zifunyenwe, imveliso yokugqibela iya kufana.

Sinokumisela oku kulandelayo: A x (B + C) = A x B + A x C. kunye no-A x (B - C) = A x B - A x C.

### Kubalulekile

Phambi kokuba ubeke imizekelo yepropathi ehambisa impahla, kubalulekile ukuba ukhankanye ukuba isimboli yokuphindaphinda inokubekwa ecaleni kwenani eliza kuphindaphindwa, kodwa singasebenzisa oonobumba kwaye, ngendlela efanayo, sizakubonisa ukuba kukho ukuphindaphinda ekufuneka kwenziwe .

Jonga oku: a) 3 (2) = 6. b) 3 x 2 = 6.

Kuyo yomibini le mizekelo sinokubona ukuba amanani makaphindaphindwe. Ke ngoko, siya kusebenzisa i-parentheses njengophawu lokuphinda-phinda kwipropathi yokuhambisa.

### Ukuhambisa ipropathi: imizekelo yokuphindaphinda ngokudibanisa

Siza kubeka imizekelo emininzi elula yepropathi yokuhambisa yokuphindaphinda kunye nemisebenzi yokongeza, ukuze uziqonde kakuhle:

a) 2 (3 + 5) = 2 (3) + 2 (5)

Siyaqhubeka nokuphindaphinda kuqala, ngoluhlobo:

2 (3+ 5) = 6 + 10

Emva koko siqala ukongeza:

2 (8) = 16

Kwaye sigqiba ngenkqubo:

16 = 16.

Kuyo yomibini le misebenzi sifumene ukulingana okuthe gca kulo msebenzi. Ogqwesileyo!

Masibeke eminye imizekelo:

b) 6 (5 + 6) = 6 (5) + 6 (6)

Siqala ngokuphindaphinda amanani ahambelanayo, njengoko senze kumzekelo wangaphambili:

6 (5 + 6) = 30 + 36

Siqhubeka ukongeza:

6 (11) = 66

Kwaye siyawugqiba umsebenzi:

66 = 66.

Ndiyakuvuyela!. Sifumene ukulingana kwipropathi yokuhambisa.

#### Olunye uqeqesho:

c) 7 (3 + 4) = 7 (3) + 7 (4) d) 8 (2 + 5) = 8 (2) + 8 (5) e) 2 (9 + 3) = 2 (9) + 2. 3)

7 (3 + 4) = 21 + 28 8 (2 + 5) = 16 + 40 2 (9 + 3) = 18 + 6

7 (7) = 49 8 (7) = 56 2 (12) = 24

49 = 49. 56 = 56. 24 = 24.

Nje ukuba uqhelane nenkqubo, ndiza kukufundisa indlela ukuze ufunde ukwenza lula nokwenza umsebenzi ngokukhawuleza okukhulu:

Imalunga nokwenza imisebenzi yezinto ezingaphakathi kubazali ngaxeshanye, ngaphandle kokuphinda ubeke yonke imithambo. Ndiza kukucacisela ngalo mzekelo ulandelayo:

f) 3 (6 + 7) = 3 (6) + 3 (7)

3 (13) = 18 + 21

39 = 39.

Njengoko ubona, siyenzile imisebenzi ebingaphakathi kubazali (ukongeza nokuphindaphinda izinto, ngokomqondiso ohambelanayo). Ukwenza yonke inkqubo ibe lula.

### Ipropathi yokuhambisa: Imizekelo yokuPhinda-phinda ngokuthabatha

Ngoku siza kufunda indlela yokwenza ulwabiwo lweepropathi usebenzisa ukuthabatha nokuphindaphinda njengeyona nto iphambili.

Yinkqubo efanayo esisenzileyo ngokudibanisa, kodwa kule meko siza kuthabatha. Ilula kakhulu, jonga le mizekelo ilandelayo:

a) 5 (6 - 3) = 5 (6) - 5 (3)

Siza kuqhuba imisebenzi engaphakathi kubazali, ngolu hlobo:

5 (3) = 30 - 15

Kwaye, siyaqhubeka ukugqibezela:

15 = 15.

Sikwazile ukufumana ukulingana kwipropathi ehambisa impahla.

Masisebenzise omnye umzekelo:

b) 7 (8-5) = 7 (8) - 7 (5)

Senza imithambo phakathi kwabazali:

7 (3) = 56 - 35

Kwaye okokugqibela:

21 = 21.

Singakufumana ukulingana okungangqinelaniyo. Ogqwesileyo!

#### Eminye imizekelo:

c) 9 (7 - 3) = 9 (7) - 9 (3) d) 10 (6 - 4) = 10 (6) - 10 (4) e) 8 (3 - 2) = 8 (3) - Isi-8 (2)

9 (4) = 63 - 27 10 (2) = 60 - 40 8 (1) = 24 - 16

36 = 36. 20 = 20. 8 = 8.

Kulula kakhulu kwaye kuyonwabisa ukwenza olu hlobo lomsebenzi. Ifuna ukuziqhelanisa rhoqo kwaye uya kuba nakho ukufumana ukulingana kwipropathi yokuhambisa kwimizuzwana embalwa. Tyhila!

### Enye indlela

Unokufunda noku-odola ngale ndlela ilandelayo, isebenza kwaye isebenza ngokufanayo:

Kuya kufuneka uyi-odole ngendlela eyahlukileyo, kule meko siza kusebenzisa ubalo:

a) (5 + 3) 4 = (5) 4 + (3) 4

Siqhubeka nokwenza imisebenzi efunyenwe ngaphakathi kubazali:

(8) 4 = 20 + 12

Kwaye sigqiba umthambo:

32 = 32.

Ucwangco lwezinto aluzange lutshintshe sisiphumo salo msebenzi. Ngoku ukuba uyabazi obu buchule, ungayisebenzisa nanini na xa ufuna, kufuneka uqiniseke ukuba imveliso yokugqibela igcina ukulingana okufunwayo kwipropathi yokuhambisa.

Ungayenza ngokuthabatha nayo, yabona:

b) (9 - 3) 5 = (9) 5 - (3) 5

Senza imisebenzi ngaphakathi kubazali:

(6) 5 = 45 - 15

Kwaye sigqiba umthambo:

30 = 30.

Yayilula kakhulu, akunjalo? Ukuba ufuna ukufunda malunga nenye ipropathi eyonwabisayo yokuphindaphinda, eli nqaku linomdla lelakho: Ipropathi yokutshintsha.

### Ubudlelwane nantlukwano nezinye iipropathi

Ukuhanjiswa kwepropathi kuyafana nezinye iipropathi (zokudibanisa kunye nezokuguquguquka), zokuphindaphinda. Kuphela zizinto ezithile eziguqukayo, ezinje: ngenani lamanani asetyenziswayo kunye nemisebenzi eyenziwayo.

Ubudlelwane obukhoyo phakathi kwazo zonke iipropathi; Kukuba babonakalise ngeendlela ezahlukeneyo, ukulingana okuchaphazeleka kwimisebenzi yemathematika, kugxininisa ukuba ukulandelelana kwezinto akuthethi kuguqula iziphumo zokugqibela.

Ukusebenza kwipropathi yokudibanisa kunye nokuguqula kubandakanya ukudibanisa nokuphinda-phinda, ngelixa kwipropathi yokuhambisa zonke zidibanisa kwaye zibandakanya ukuthabatha. Yiyo loo nto ibonisa ukuba isetyenziswa ngokuchanekileyo kule nkqubo.

## Ukuhanjiswa kwepropathi kunye nolwahlulo

Le propati inokusetyenziswa ngokwahlula-hlulo kuphela ukuba isahlulo eso sinesixa se-algebra kwaye imigaqo iyahlulwahlulwa ngumhluli. Oko kukuthi, ukuba sibeka ulwahlulo ngokuthe ngqo kwaye siyaqonda ukuba xa kubola isahlulelo silingana ngokulinganayo, sinokusetyenziswa.

Masibeke lo mzekelo ulandelayo, siqaqambisa ukuba asizukuphinda-phinda kodwa ukwahlula-hlula inani elingaphandle kwabazali kunye namaqela, ngolu hlobo lulandelayo:

Icandelo ngqo:

a) (20 + 10) kunye 10

30 = 10

3.

Siqhubeka nokwenza ipropathi yokuhambisa enje:

a) (20 + 10) kunye 10

20-10 + 10 ÷ 10

2 + 1 = 3.

Ukuhanjiswa kunokusetyenziswa ukuba nje kungqamana ngqo nokwahlulahlula ngokuthe ngqo. Oomatshini bahlukile, kodwa iziphumo kufuneka zibonise ukulingana.

### Umlando omncinci

Le propati yaziwa ukusukela nge-1800, xa iingcali zezibalo ezininzi zaqala ukuqaphela ubunzima obukhoyo kwimisebenzi yemathematika, kwaye basebenzise le ndlela ukwenza iinkqubo ezilula kakhulu, ngendlela yokuba, iinkqubo zenziwa lula xa kusetyenzwa ngamanani.

Banokubonakala kunzima ukwenza, kodwa nganye yeepropathi ze-algebraic zisivumela ukuba sifikelele ngokukhawuleza kwiziphumo ngeenkqubo ezilula zokudibanisa imisebenzi eyahlukeneyo, esithi, ukuba izinto zitshintshiwe, iziphumo ziyafana, ukuba iipropathi zisetyenziswe ngokuchanekileyo.

Izibalo zilula kwaye zinokonwabisa, zithatha ukuziqhelanisa kwaye uya kuba nakho ukwenza imisebenzi ngemizuzwana. Unga!.