Ukuguqulwa kobunikazi bezinkulumo

Kulolu shicilelo, sizocubungula izinhlobo eziyinhloko zokuguqulwa okufanayo kwezinkulumo ze-algebraic, ezihambisana namafomula nezibonelo zokukhombisa ukusetshenziswa kwazo ekusebenzeni. Injongo yokuguqulwa okunjalo iwukuba esikhundleni senkulumo yokuqala ufake elingana ngokufanayo.

Ukuhlela kabusha imigomo nezinto

Kunoma iyiphi isamba, ungakwazi ukuhlela kabusha imigomo.

a + b = b + a

Kunoma yimuphi umkhiqizo, ungahlela kabusha izici.

a ⋅ b = b ⋅ a

izibonelo:

• 1 + 2 = 2 + 1
• 128 ⋅ 32 = 32 ⋅ 128

Imigomo yokuqoqa (iziphindaphindi)

Uma kunamatemu angaphezu kwama-2 esambeni, angahlanganiswa ngabakaki. Uma kudingeka, ungawashintsha kuqala.

a + b + c + d = (a + c) + (b + d)

Emkhiqizweni, ungaphinda uqoqe izici.

a ⋅ b ⋅ c ⋅ d = (a ⋅ d) ⋅ (b ⋅ c)

izibonelo:

• 15 + 6 + 5 + 4 = (15 + 5) + (6 + 4)
• 6 ⋅ 8 ⋅ 11 ⋅ 4 = (6 ⋅ 4 ⋅ 8) ⋅ 11

Ukwengeza, ukususa, ukuphindaphinda noma ukuhlukanisa ngenombolo efanayo

Uma inombolo efanayo yengezwa noma ikhishwa kuzo zombili izingxenye zobunikazi, kusho ukuthi ihlala iyiqiniso.

If a + b = c + dke (a + b) ± e = (c + d) ± e.

Futhi, ukulingana ngeke kuphulwe uma zombili izingxenye zakhona ziphindaphindeka noma zihlukaniswa ngenombolo efanayo.

If a + b = c + dke (a + b) ⋅/: e = (c + d) ⋅/: e.

izibonelo:

• 35 + 10 = 9 + 16 + 20 ⇒ (35 + 10) + 4 = (9 + 16 + 20) + 4
• 42 + 14 = 7 ⋅ 8 ⇒ (42 + 14) ⋅ 12 = (7 ⋅ 8) ⋅ 12

Ukushintsha Umehluko Ngesamba (ngokuvamile Umkhiqizo)

Noma yimuphi umehluko ungamelwa njengesamba samagama.

a – b = a + (-b)

Iqhinga elifanayo lingasetshenziswa ekuhlukaniseni, okungukuthi buyisela kaningi ngomkhiqizo.

a : b = a ⋅ b^-1

izibonelo:

• 76 – 15 – 29 = 76 + (-15) + (-29)
• 42 : 3 = 42 ⋅ 3^-1

Ukwenza imisebenzi ye-arithmetic

Ungenza isisho sezibalo sibe lula (kwesinye isikhathi ngokuphawulekayo) ngokwenza imisebenzi yezibalo (ukwengeza, ukususa, ukuphindaphinda nokuhlukanisa), ucabangela ukwamukelwa okuvamile. umyalelo wokubulawa:

• okokuqala siphakamisa amandla, sikhiphe izimpande, sibale ama-logarithms, i-trigonometric neminye imisebenzi;
• bese senza izenzo kubakaki;
• okokugcina - ukusuka kwesobunxele kuya kwesokudla, yenza izenzo ezisele. Ukuphindaphinda nokuhlukanisa kuza kuqala kunokwengeza nokususa. Lokhu kusebenza nakumazwi akubakaki.

izibonelo:

• 14 + 6 ⋅ (35 – 16 ⋅ 2) + 11 ⋅ 3 = 14 + 18 + 33 = 65
• 20 : 4 + 2 ⋅ (25 ⋅ 3 – 15) – 9 + 2 ⋅ 8 = 5 + 120 - 9 + 16 = 132

Ukunwetshwa kukabakaki

Abakaki kusisho se-arithmetic bangakhishwa. Lesi senzo senziwa ngokusho kwezithize - kuye ngokuthi yiziphi izimpawu (“hlanganisa”, “khipha”, “phindaphinda” noma “hlukanisa”) ezingaphambi noma ngemva kwabakaki.

izibonelo:

• 117 + (90 – 74 – 38) = 117 + 90 – 74 – 38
• 1040 - (-218 - 409 + 192) = 1040 + 218 + 409 – 192
• 22⋅(8+14) = 22 ⋅ 8 + 22 ⋅ 14
• 18 : (4 - 6) = 18: 4–18: 6

Ukufaka i-Common Factor

Uma wonke amagama enkulumo enesici esifanayo, ingakhishwa kubakaki, lapho imigomo ehlukaniswe yile nto izohlala khona. Le nqubo iyasebenza nasezinguqukweni zangempela.

izibonelo:

• 3 ⋅ 5 + 5 ⋅ 6 = 5⋅(3+6)
• 28 + 56 – 77 = 7 ⋅ (4 + 8 – 11)
• 31x + 50x = x ⋅ (31 + 50)

Ukusetshenziswa kwamafomula okuphindaphinda afushanisiwe

Ungasebenzisa futhi ukwenza izinguquko ezifanayo zezinkulumo ze-algebra.

izibonelo:

• (31 + 4)² = 31² + 2 ⋅ 31 ⋅ 4 + 4² = 1225
• 26² - 7² = (26 – 7) ⋅ (26 + 7) = 627