Ushbu nashrda biz nazariy materialni yaxshiroq tushunish uchun qavslarni ochishning asosiy qoidalarini ko'rib chiqamiz, ularga misollar keltiramiz.
Braketni kengaytirish – qavsdan iborat ifodani unga teng, lekin qavssiz ifoda bilan almashtirish.
Qavsni kengaytirish qoidalari
1 qoida
Qavslar oldidan "ortiqcha" belgisi bo'lsa, qavs ichidagi barcha raqamlarning belgilari o'zgarishsiz qoladi.
Izoh: Bular. Plyus marta plyus ortiqcha qiladi va ortiqcha marta minus minus qiladi.
misollar:
6 + (21 – 18 – 37) =6 + 21 – 18 – 37 20 + (-8 + 42 – 86 – 97) =20 – 8 + 42 – 86 – 97
2 qoida
Qavslar oldida minus bo'lsa, qavs ichidagi barcha raqamlarning belgilari teskari bo'ladi.
Izoh: Bular. Minus marta ortiqcha - minus va minus marta minus - ortiqcha.
misollar:
65 – (-20 + 16 – 3) =65 + 20 - 16 + 3 116 – (49 + 37 – 18 – 21) =116 – 49 – 37 + 18 + 21
3 qoida
Qavslardan oldin yoki keyin "ko'paytirish" belgisi bo'lsa, barchasi ular ichida qanday harakatlar bajarilishiga bog'liq:
Qo'shish va/yoki ayirish
a ⋅ (b – c + d) =a ⋅ b – a ⋅ c + a ⋅ d (b + c – d) ⋅ a =a ⋅ b + a ⋅ c - a ⋅ d
Ko'paytirish
a ⋅ (b ⋅ c ⋅ d) =a ⋅ b ⋅ c ⋅ d (b ⋅ c ⋅ d) ⋅ a =b ⋅ s ⋅ d ⋅ a
taqsimlash
a ⋅ (b : c) =(a ⋅ b): p =(a : c) ⋅ b (a : b) ⋅ c =(a ⋅ c): b =(c : b) ⋅ a
misollar:
18 ⋅ (11 + 5 – 3) =18 ⋅ 11 + 18 ⋅ 5 – 18 ⋅ 3 4 ⋅ (9 ⋅ 13 ⋅ 27) =4 ⋅ 9 ⋅ 13 ⋅ 27 100 ⋅ (36 : 12) =(100 ⋅ 36) : 12
4 qoida
Qavslardan oldin yoki keyin bo'linish belgisi bo'lsa, yuqoridagi qoidada bo'lgani kabi, barchasi ular ichida qanday harakatlar bajarilishiga bog'liq:
Qo'shish va/yoki ayirish
Avval qavs ichidagi amal bajariladi, ya'ni sonlar yig'indisi yoki ayirmasi natijasi topiladi, so'ngra bo'linish bajariladi.
a : (b – c + d)
b – s + d = e
a : e = f
(b + c - d) : a
b + s – d = e
e : a = f
Ko'paytirish
a : (b ⋅ c) =a : b : c =a : c : b (b ⋅ c): a =(b : a) ⋅ p =(bilan: a) ⋅ b
taqsimlash
a : (b : c) =(a : b) ⋅ p =(c : b) ⋅ a (b : c): a =b : c : a =b : (a ⋅ c)
misollar:
72 : (9 – 8) =72:1 160 : (40 ⋅ 4) =160: 40: 4 600 : (300 : 2) =(600 : 300) ⋅ 2