Izinombolo Eziphelele Nezakhiwo Zazo
Ama-integer angomunye wemibono eyisisekelo kakhulu kwizibalo, kodwa adlala indima ebalulekile empilweni yansuku zonke. Uma sibala izinto, sinquma amazinga okushisa angaphansi kwezinga-zero, sibala inani lezitezi ezingaphansi, noma siqopha inzuzo nokulahlekelwa ebhizinisini, empeleni sibhekene nama-integer. Ukuqonda ama-integer kanye nezakhiwo zawo kuzokwenza kube lula ukufunda izibalo, i-algebra, ngisho nemibono yezibalo yezinga eliphezulu.
Incazelo yama-Integers
Izinombolo eziphelele ziyisethi yezinombolo equkethe izinombolo eziphelele ezingezinhle, u-zero, kanye nezinombolo eziphelele eziqondile. Uphawu oluvame ukusetshenziselwa ukumelela isethi yezinombolo eziphelele ngu-Z (olususelwa egameni lesiJalimane elithi Zahlen, elisho "izinombolo"). Ngokuvamile, izinombolo eziphelele zingabhalwa kanje:
…, -3, -2, -1, 0, 1, 2, 3, …
Ngokungafani nezinombolo eziphelele eziqukethe izinombolo ezingu-0 kanye nezingu-positive kuphela, izinombolo eziphelele zifaka izinombolo ezingemihle ngakho ziphelele kakhulu ekuchazeni izimo ezahlukahlukene.
Izibonelo Zezinombolo Eziphelele Ekuphileni Kwansuku Zonke
Izinombolo eziphelele zihlobene kakhulu nemisebenzi yabantu. Ezinye izibonelo zokusetshenziswa kwazo zifaka:
1. Izinga lokushisa lomoya: Izinga lokushisa elingu--5°C libonisa ukuthi izinga lokushisa lingaphansi kwezinga-zero ngama-degrees ama-5.
2. Ukuphakama: Ukuphakama kwamamitha angu--20 kungasho indawo engamamitha angu-20 ngaphansi kolwandle.
3. Ezezimali: Ibhalansi engu--50.000 ikhombisa isikweletu noma ukushoda okungu-50.000.
4. Iphansi lesakhiwo: Iphansi -1 noma -2 livame ukusetshenziselwa iphansi.
5. Isikolo somdlalo: Kweminye imidlalo, isikolo singanda noma sinciphe, ngaleyo ndlela kuhileleke izinombolo ezinhle nezimbi.
Kulezi zibonelo kungabonakala ukuthi izinombolo eziphelele zisisiza ukuveza izimo "ezingaphezu kwalokho", "ezingaphansi kwalokho", noma "ezilinganayo" ngo-zero njengephuzu lokubhekisela.
Umugqa Wezinombolo Ophelele
Ukuze siqonde izinombolo eziphelele, sivame ukusebenzisa umugqa wezinombolo. Umugqa wezinombolo umugqa oqondile obeka izinombolo ezindaweni ezithile:
– Izinombolo eziqondile zingakwesokudla kuka-zero.
– Izinombolo ezingezinhle zingakwesokunxele se-zero.
– Uma inani likude ngakwesokudla, liba likhulu.
– Uma ubheka phambili ngakwesobunxele, inani liyancipha.
Ngomugqa wezinombolo, singaqhathanisa kalula izinombolo eziphelele. Isibonelo, u--2 mkhulu kuno--5 ngoba u--2 ungaphezulu kwesokudla kuno--5.
Izakhiwo ze-Integers
Izinombolo eziphelele zinezimpawu ezibalulekile eziningana ekusebenzeni kwezibalo. Lezi zimpawu ziwusizo kakhulu lapho senza izibalo, senza lula izinkulumo ze-algebra, noma senza imiqondo ifakazeleke.
1. Imvelo Evaliwe (Ukuvalwa)
Isethi yezinombolo eziphelele ivaliwe ngaphansi kwemisebenzi ethile, okusho ukuthi uma senza leyo misebenzi kuzinombolo eziphelele, umphumela uzoba inombolo ephelele.
– Ukwengeza: Uma u-a no-b beyizinombolo eziphelele, khona-ke u-a + b naye uyinombolo ephelele.
Isibonelo: -3 + 7 = 4
– Ukususa: Uma u-a no-b beyizinombolo eziphelele, khona-ke u-a − b naye uyinombolo ephelele.
Isibonelo: 5 − 12 = -7
– Ukuphindaphinda: Uma u-a no-b beyizinombolo eziphelele, khona-ke u-a × b naye uyinombolo ephelele.
Isibonelo: (-4) × 6 = -24
Noma kunjalo, izinombolo eziphelele azivalwa njalo ngokumelene nokuhlukaniswa, ngoba umphumela wokuhlukaniswa ungaba yingxenyana.
Isibonelo: 1 ÷ 2 = 1/2 (hhayi inombolo ephelele).
2. Impahla Yokushintshana (Ukushintshana)
Impahla eguquguqukayo isho ukuthi ukuhleleka kwezinombolo kungashintshaniswa ngaphandle kokushintsha umphumela.
– Ukwengeza: a + b = b + a
Isibonelo: 2 + (-5) = (-5) + 2 = -3
– Ukuphindaphinda: a × b = b × a
Isibonelo: (-3) × 4 = 4 × (-3) = -12
Kubalulekile ukukhumbula ukuthi ukususa nokuhlukanisa akuzona izinto ezishintshashintshayo.
Isibonelo: 7 − 2 ≠ 2 − 7.
3. Izakhiwo Ezihlangene (Ukuhlanganisa)
Impahla ehambisanayo isho ukuthi indlela izinombolo ezihlelwe ngayo emsebenzini ayishintshi umphumela.
– Ukwengeza: (a + b) + c = a + (b + c)
Isibonelo: (1 + 2) + 3 = 1 + (2 + 3) = 6
– Ukuphindaphinda: (a × b) × c = a × (b × c)
Isibonelo: (2 × 3) × 4 = 2 × (3 × 4) = 24
Njenge-commutative, impahla ehambisanayo ayisebenzi ekususeni nasekuhlukaniseni.
4. Izakhiwo Zokusabalalisa (Ukusabalala)
Impahla yokusabalalisa ihlobanisa imisebenzi yokuphindaphinda nokwengeza noma ukususa:
– a × (b + c) = (a × b) + (a × c)
Isibonelo: 3 × (2 + 5) = (3 × 2) + (3 × 5) = 6 + 15 = 21
– a × (b − c) = (a × b) − (a × c)
Isibonelo: 4 × (10 − 3) = 40 − 12 = 28
Le mfanelo ibaluleke kakhulu ekwenzeni lula amafomu e-algebra kanye nokuxazulula izibalo.
5. Izinto Zobunikazi (Ubunikazi Bokwengeza Nokuphindaphinda)
Ubunikazi yinombolo engashintshi inani lenye inombolo uma isebenza.
– Ubunikazi bokwengeza bungu-0: a + 0 = a
Isibonelo: -9 + 0 = -9
– Ubunikazi bokuphindaphinda bungu-1: a × 1 = a
Isibonelo: 8 × 1 = 8
Ubunikazi busisiza siqonde umqondo ongathathi hlangothi ekusebenzeni kwezibalo.
6. Izinto Eziphambene (Izinombolo Eziphambene)
I-integer ngayinye ine-inverse eyengeziwe, okuphambene nenombolo okuthi uma ihlanganiswa ndawonye iphumele ku-0.
– Okuphambene no-a ngu--a, ngakho-ke: a + (-a) = 0
Isibonelo: 6 + (-6) = 0, kanye no -4 + 4 = 0
Nokho, akuzona zonke izinombolo eziphelele ezine-inverse ekuphindaphindeni. Isibonelo, i-inverse ephindaphindayo ka-2 ingu-1/2, okungeyona inombolo ephelele.
7. Izimpawu Ezinhle Nezimbi Ziyasebenza
Kumanani aphelele, izimpawu ezinhle nezimbi zinikeza imithetho ekhethekile yokuphindaphinda nokuhlukanisa:
– (+) × (+) = (+)
– (+) × (-) = (-)
– (-) × (+) = (-)
– (-) × (-) = (+)
Isibonelo:
– 3 × (-2) = -6
– (-5) × (-4) = 20
Ukuze sihlanganise futhi sisuse, sivame ukusebenzisa umqondo womugqa wezinombolo noma umthetho:
– Ukwengeza izinombolo ezingezinhle kufana “nokususa”.
– Ukususa inombolo engemihle kufana “nokwengeza”.
Isibonelo:
– 7 + (-3) = 4
– 5 − (-2) = 7
Isiphetho
Ama-Integer ayiqoqo lezinombolo eziqukethe izinombolo ezingezinhle, u-zero, kanye nezinombolo ezinhle. Lezi zinombolo zibaluleke kakhulu ngoba zingachaza izimo ezahlukahlukene empilweni, njengokushisa okungaphansi kwezinga le-zero, ukulahlekelwa kwezezimali, noma izindawo ezingaphansi kolwandle. Ama-Integer nawo anezakhiwo eziyisisekelo njengokuvalwa (kokuhlanganisa, ukususa, kanye nokuphindaphinda), ukushintshashintsha, ukuhlanganisa, ukusabalalisa, ubunikazi, kanye nokuphambene kokwengeza. Ngokuqonda izakhiwo zama-integer, sizokwenza izibalo kalula, senze imisebenzi ibe lula, futhi sifunde izihloko zezibalo ezilandelayo njenge-algebra, ama-equation, nezinye izinhlelo zezinombolo.
Uma uthanda, ngingenza inguqulo yalesi sihloko yezinga lesikole samabanga aphansi/esikoleni esiphakathi (elula) noma inguqulo ehlelekile njengephepha eliphelele elinemibuzo yokuzijwayeza kanye nezingxoxo.
