Katika uchapishaji huu, tutazingatia sheria za msingi za kufungua mabano, tukiambatana na mifano kwa ufahamu bora wa nyenzo za kinadharia.
Upanuzi wa mabano - uingizwaji wa usemi ulio na mabano na usemi sawa nayo, lakini bila mabano.
Sheria za upanuzi wa mabano
Utawala 1
Ikiwa kuna "plus" kabla ya mabano, basi ishara za nambari zote ndani ya mabano hubakia bila kubadilika.
maelezo: Wale. Plus mara plus hufanya plus, na plus mara minus hufanya minus.
mifano:
6 + (21 – 18 – 37) =6 + 21 – 18 – 37 20 + (-8 + 42 – 86 – 97) =20 – 8 + 42 – 86 – 97
Utawala 2
Ikiwa kuna minus mbele ya mabano, basi ishara za nambari zote ndani ya mabano zinabadilishwa.
maelezo: Wale. Minus mara plus ni minus, na minus mara minus ni plus.
mifano:
65 - (-20 + 16 - 3) =65 + 20 - 16 + 3 116 - (49 + 37 - 18 - 21) =116 - 49 - 37 + 18 + 21
Utawala 3
Ikiwa kuna ishara ya "kuzidisha" kabla au baada ya mabano, yote inategemea ni vitendo gani hufanywa ndani yao:
Kuongeza na/au kutoa
a ⋅ (b – c + d) =a ⋅ b – a ⋅ c + a ⋅ d (b + c – d) ⋅ a =a ⋅ b + a ⋅ c – a ⋅ d
Kuzidisha
a ⋅ (b ⋅ c ⋅ d) =a ⋅ b ⋅ c ⋅ d (b ⋅ c ⋅ d) ⋅ a =b ⋅ с ⋅ d ⋅ a
Idara
a ⋅ (b : c) =(a ⋅ b) : uk =(a : c) ⋅ b (a : b) ⋅ c =(a ⋅ c) : b =(c : b) ⋅ a
mifano:
18 ⋅ (11 + 5 - 3) =18 ⋅ 11 + 18 ⋅ 5 - 18 ⋅ 3 4 ⋅ (9 ⋅ 13 ⋅ 27) =4 ⋅ 9 ⋅ 13 ⋅ 27 100 ⋅ (36 : 12) =(100 ⋅ 36) : 12
Utawala 4
Ikiwa kuna ishara ya mgawanyiko kabla au baada ya mabano, basi, kama ilivyo katika sheria hapo juu, yote inategemea ni hatua gani zinazofanywa ndani yao:
Kuongeza na/au kutoa
Kwanza, hatua katika mabano inafanywa, yaani matokeo ya jumla au tofauti ya namba hupatikana, kisha mgawanyiko unafanywa.
a : (b – c + d)
b – с + d = e
a: e = f
(b + c – d) : a
b + с – d = e
e: a = f
Kuzidisha
a: (b ⋅ c) =a: b: c =a: c: b (b ⋅ c) : a =(b : a) ⋅ uk =(pamoja na : a) ⋅ b
Idara
a: (b: c) =(a : b) ⋅ uk =(c : b) ⋅ a (b: c): a =b :c:a =b: (a ⋅ c)
mifano:
72 : (9 - 8) =72:1 160 : (40 ⋅ 4) =160: 40:4 600 : (300 : 2) =(600 : 300) ⋅ 2