Cov cai rau kev nthuav dav brackets nrog piv txwv

Hauv kev tshaj tawm no, peb yuav txiav txim siab txog cov cai yooj yim rau kev qhib cov hlua, nrog rau lawv nrog cov piv txwv kom nkag siab zoo dua ntawm cov khoom siv theoretical.

Bracket expansion - Hloov cov kab lus uas muaj cov kab lus sib npaug nrog nws, tab sis tsis muaj kab.

Bracket expansion cov cai

kav 1

Yog tias muaj "ntxiv" ua ntej cov kab tuav, tom qab ntawd cov cim ntawm txhua tus lej hauv cov kab ke tsis hloov pauv.

a + (b – c – d + e) = a + b - c - d + e

Piav qhia: Cov. Ntxiv lub sij hawm ntxiv ua ib qho ntxiv, thiab ntxiv rau lub sij hawm rho tawm ua tus rho tawm.

piv txwv:

• 6 + (21–18–37) : kuv. = 6+21–18–37 : kuv
• 20 + (-8 + 42-86-97) = 20–8 + 42–86–97 : kuv

kav 2

Yog hais tias muaj ib tug rho tawm nyob rau hauv pem hauv ntej ntawm lub brackets, ces cov cim qhia ntawm tag nrho cov xov tooj nyob rau hauv lub brackets yog thim rov qab.

a – (b – c – d + e) = a - b + c + d - e

Piav qhia: Cov. Ib tug minus lub sij hawm ib tug ntxiv yog ib tug rho, thiab ib tug minus lub sij hawm ib tug rho tawm yog ib tug ntxiv.

piv txwv:

• 65 – (-20 + 16 – 3) = 65 + 20–16 + 3
• 116-(49+37-18-21) ib. = 116-49-37+ 18+ 21 ib

kav 3

Yog tias muaj ib qho "multiplication" kos npe ua ntej lossis tom qab cov brackets, txhua yam nyob ntawm seb yuav ua li cas hauv lawv:

Ntxiv thiab/los yog rho tawm

• a ⋅ (b – c + d) = a ⋅ b – a ⋅ c + a ⋅ d
• (b + c – d) ⋅ a = a ⋅ b + a ⋅ c – a ⋅ d

Txooj

• a ⋅ (b ⋅ c ⋅ d) = a ⋅ b ⋅ c ⋅ d
• (b ⋅ c ⋅ d) ⋅ a = b ⋅ с ⋅ d ⋅ a

Division

• ib ⋅ (b : c) = (a ⋅ b): p = (a : c) ⋅ b
• (a : b) ⋅ c = (a ⋅ c): b = (c: b) ⋅ a

piv txwv:

• 18 ⋅ (11 + 5 - 3) = 18 ⋅ 11 + 18 ⋅ 5 – 18 ⋅ 3
• 4 ⋅ (9 ⋅ 13 ⋅ 27) = 4 ⋅ 9 ⋅ 13 ⋅ 27
• 100 ⋅ (36:12) = (100 ⋅ 36): 12

kav 4

Yog tias muaj ib qho kev faib ua ntej lossis tom qab cov kab tuav, tom qab ntawd, raws li txoj cai saum toj no, txhua yam nyob ntawm seb yuav ua li cas hauv lawv:

Ntxiv thiab/los yog rho tawm

Ua ntej, qhov kev txiav txim hauv kab lus yog ua, piv txwv li qhov tshwm sim ntawm cov lej lossis qhov sib txawv ntawm cov lej raug pom, tom qab ntawd faib ua tiav.

a : (b – c + d)

b – s + d = e

ib: e = f

(b + c - d): a

b + s - d = e

e: ib = f

Txooj

• a : (b ⋅ c) = ib: b:c = ib: c:b
• (b ⋅ c): a = (b : a) ⋅ p = (nrog : a) ⋅ b

Division

• ib : (b : c) = (a : b) ⋅ p = (c: b) ⋅ a
• (b: c): a = b:c: ua = b : (a ⋅ c)

piv txwv:

• 72: (9–8) hnub. = 72:1
• 160: (40 ⋅ 4) = 160: 40: 4: ib
• 600 : 300 : 2 : kuv. = (600:300) ⋅ 2