Isbeddellada aqoonsiga ee tibaaxaha

Daabacaaddan, waxaanu tixgelin doonaa noocyada ugu muhiimsan ee isbeddellada isku midka ah ee tibaaxaha aljabrada, anagoo la soconna qaacido iyo tusaalooyin si loo muujiyo codsigooda ficil ahaan. Ujeedada isbeddellada noocaas ah waa in lagu beddelo tibaaxaha asalka ah mid la siman yahay.

Dib u habaynta shuruudaha iyo qodobbada

Isku soo wada duuboo, waxaad dib u habeyn kartaa shuruudaha.

a + b = b + a

Badeeco kasta, waxaad dib u habeyn kartaa arrimaha.

a ⋅ b = b ⋅ a

tusaalooyin:

• 1 + 2 = 2 + 1
• 128 ⋅ 32 = 32 ⋅ 128

Erayada kooxaynta (ku-dhufashada)

Haddii ay jiraan wax ka badan 2 erey oo wadarta ah, waxaa lagu ururin karaa jaantusyo. Haddii loo baahdo, marka hore waad beddeli kartaa.

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

Alaabada, waxaad sidoo kale kooxeyn kartaa qodobada.

a ⋅ b⋅ c ⋅ d = (a ⋅ d) ⋅ (b⋅ c)

tusaalooyin:

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

Isu-geynta, kala-goynta, isku-dhufashada ama isu-qaybinta isla tirada

Haddii tiro isku mid ah lagu daro ama laga jaro labada qaybood ee aqoonsiga, markaas waa run.

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

Sidoo kale, sinnaanta lama jabin doono haddii labada qayboodba la badiyo ama la qaybsado tiro isku mid ah.

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

tusaalooyin:

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

Ku Bedelka Farqiga Wadarta (badanaa Alaab)

Kala duwanaansho kasta waxa loo matalli karaa wadar ereyo.

a - b = a + (-b)

Isla khiyaamo la mid ah ayaa lagu dabaqi karaa qaybinta, ie beddelka joogtada ah ee badeecada.

a: b = a ⋅ b^-1

tusaalooyin:

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

Samaynta hawlaha xisaabta

Waxaad fududayn kartaa tibaaxaha xisaabeed (mararka qaarkood si weyn) adoo samaynaya hawlo xisaabeed (isugeyn, kala-goyn, isku dhufasho iyo qaybin), iyadoo la tixgalinayo guud ahaan la aqbalay amarka fulinta:

• marka hore waxaan kor u qaadnaa awood, soo saarno xididdada, xisaabin logarithms, trigonometric iyo hawlo kale;
• ka dib waxaan ku fulinaa ficilada ku jira xirmooyinka;
• Ugu dambeyntii - bidix ilaa midig, samee ficilada soo haray. Isku dhufashada iyo qaybinta ayaa ka horraysa isku-darka iyo kala-goynta. Tani waxay sidoo kale khuseysaa tibaaxaha qaaska ah.

tusaalooyin:

• 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

Balaadhinta birta

Waalidiinta ku jira tibaaxda xisaabta waa laga saari karaa. Ficilkan waxaa loo sameeyaa si waafaqsan qaar gaar ah - iyadoo ku xiran calaamadaha (" lagu daray ", "laga jaray", "ku dhufo" ama "qaybi") ka hor ama ka dib xirmooyinka.

tusaalooyin:

• 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

Xakamaynta Qodobka Guud

Haddii dhammaan ereyada ku jira tibaaxuhu ay leeyihiin arrin guud, waxaa laga saari karaa geesaha, taas oo erayada loo qaybiyay qodobkan ay sii ahaanayaan. Farsamadan waxay sidoo kale khusaysaa doorsoomayaasha suugaanta.

tusaalooyin:

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

Codsiga hababka isku dhufashada ee la soo gaabiyey

Waxa kale oo aad isticmaali kartaa si aad u sameyso isbeddel isku mid ah ee tibaaxaha aljabrada.

tusaalooyin:

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