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a: =-2/49-5/3+2/49=-5/3
b: \(=\dfrac{5\cdot4^{15}\cdot9^9-4\cdot3^{20}\cdot8^9}{5\cdot2^9\cdot6^{19}-7\cdot2^{29}\cdot27^6}\)
\(=\dfrac{5\cdot2^{30}\cdot3^{18}-3^{20}\cdot2^{27}\cdot2^2}{5\cdot2^9\cdot2^{19}\cdot3^{19}-7\cdot2^{29}\cdot3^{18}}\)
\(=\dfrac{5\cdot2^{30}\cdot3^{18}-3^{20}\cdot2^{29}}{5\cdot2^{28}\cdot3^{19}-7\cdot2^{29}\cdot3^{18}}\)
\(=\dfrac{2^{29}\cdot3^{18}\left(2\cdot3-3^2\right)}{2^{28}\cdot3^{18}\left(5\cdot3-7\cdot2\right)}=2\cdot\dfrac{6-9}{15-14}=2\cdot\left(-3\right)=-6\)
a: \(x-\dfrac{10}{3}=\dfrac{7}{15}\cdot\dfrac{3}{5}\)
=>\(x-\dfrac{10}{3}=\dfrac{21}{75}=\dfrac{7}{25}\)
=>\(x=\dfrac{7}{25}+\dfrac{10}{3}=\dfrac{21+250}{75}=\dfrac{271}{75}\)
b: \(x+\dfrac{3}{22}=\dfrac{27}{121}\cdot\dfrac{9}{11}\)
=>\(x+\dfrac{3}{22}=\dfrac{243}{1331}\)
=>\(x=\dfrac{243}{1331}-\dfrac{3}{22}=\dfrac{123}{2662}\)
c: \(\dfrac{8}{23}\cdot\dfrac{46}{24}-x=\dfrac{1}{3}\)
=>\(\dfrac{8}{24}\cdot\dfrac{46}{23}-x=\dfrac{1}{3}\)
=>\(\dfrac{2}{3}-x=\dfrac{1}{3}\)
=>\(x=\dfrac{2}{3}-\dfrac{1}{3}=\dfrac{1}{3}\)
d: \(1-x=\dfrac{49}{65}\cdot\dfrac{5}{7}\)
=>\(1-x=\dfrac{49}{7}\cdot\dfrac{5}{65}=\dfrac{7}{13}\)
=>\(x=1-\dfrac{7}{13}=\dfrac{6}{13}\)
45-58+(-45)+(+58)-3=45-58-45+58-3=(45-45)+(58-58)-3=-3
(-57)-(-12)+3-(-57)=-57+12+3+57=(-57+57)+12+3=15
-(-24)-(-30)+(-24)-30+8=24+30-24-30+8=(24-24)+(30-30)+8=8
-(-12)+(+19)-(+12)+8-19=12+19-12+8-19=(12-12)+(19-19)+8=8
47-(-53)+(-47)-(+53)=47+53-47-53=(47-47)+(53-53)=0
-(+28)+32-(-28)+(-34)=-28+32+28-34=(-28+28)-(34-32)=-2
15-(+72)+(-15)+(+72)=15-72-15+72=(15-15)+(72-72)=0
20-(+46)+(-25)-(-46)=20-46-25+46=(20-25)+(46-46)=-5
28-(-32)+(-28)-32+5=28+32-28-32+5=(28-28)+(32-32)+5=5
-75+(-49)+(+75)+49-12=-75-49+75+49-12=(-75+75)+(49-49)-12=-12
\(...=45-58-45+58-3=-3\)
\(...=-57+12+3+57=15\)
\(...=24+30-24-30+8=8\)
\(...=12+19-12+8-19=8\)
\(...=47+53-47-53=0\)
\(...=-28+32+28-34=-2\)
\(...=15-72-15+72=0\)
\(...=20-46-25+46=-5\)
\(=...28+32-28-32+5=5\)
\(...=-75-49+75+49-12=-12\)
\(\frac{2}{3}.x=\frac{1}{3}\)1) x-\(\frac{10}{3}\)=\(\frac{7}{15}.\frac{3}{5}\)
x-10/3=7/25
x=7/25+10/3
x=\(\frac{271}{75}\)
2)\(\frac{8}{23}.\frac{46}{24}.x=\frac{1}{3}\)
2/3.x=1/3
x=1/3:2/3
x=1/2
a) 49.(-34)+(-65).49-49 = 49. (-34-65-1)= 49. (-100)= -4900
b) -268-(-47-168)-147 = (-268 + 168) - (147 - 47)= -100 -100=-200
c) (-2)2.(-3)-[(-1)2024+8]:(-3)2 = 4. (-3) - [1 +8]:9 = -12 - 9:9 = -12 - 1 = -13
d) 67-[8+7.32 -24:6+(9-7)3]:15 = 67 - [8 + 7.9 - 4 + 23 ] : 15
= 67 - [8+63-4+8]:15 = 67 - 75:15 = 67 - 5 = 62