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Bài 1
a) 15 + 4.12 - 3²
=15 + 48 - 9
= 63 - 9
= 54
b) {[(37 + 13) : 5].2 - 45 : 5}.7 - 2022⁰
= [(50 : 5).2 - 9].7 - 1
= (10.2 - 9).7 - 1
= (20 - 9).7 - 1
= 11.7 - 1
= 77 - 1
= 76
Bài 2
a) 13x + 3 = 16
13x = 16 - 3
13x = 13
x = 13 : 13
x = 1
b) 2x - 138 = 2⁴ : 2³
2x = 2 + 138
2x = 140
x = 140 : 2
x = 70
a) \(S4=\frac{3}{50}+\frac{3}{150}+\frac{3}{300}+...+\frac{3}{9500}\)
\(S4=\frac{3}{5.10}+\frac{3}{10.15}+\frac{3}{15.20}+...+\frac{3}{95.100}\)
\(S4=\frac{3}{5}\left(\frac{1}{5}-\frac{1}{10}+\frac{1}{10}-\frac{1}{15}+\frac{1}{15}-\frac{1}{20}+...+\frac{1}{95}-\frac{1}{100}\right)\)
\(S4=\frac{3}{5}\left(\frac{1}{5}-\frac{1}{100}\right)\)
\(S4=\frac{3}{5}.\frac{19}{100}\)
\(S4=\frac{57}{500}\Rightarrow S=\frac{57}{500}:4=\frac{57}{2000}\)
b) \(S5=\frac{55}{11.16}+\frac{55}{16.21}+...+\frac{55}{36.41}\)
\(S5=\frac{55}{5}.\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{36}-\frac{1}{41}\right)\)
\(S5=11.\left(\frac{1}{11}-\frac{1}{41}\right)\)
\(S5=11.\frac{30}{451}\)
\(S5=\frac{30}{41}\Rightarrow S=\frac{30}{41}:5=\frac{6}{41}\)
\(5^{2021}.5^2:5^{2020}-75:25+5.2^3-2022^0=5^{2021+2-2020}-3+5.8-1=5^3-3+40-1=125-3+40-1=161\)
1: \(\dfrac{-7}{4}\cdot\dfrac{2}{9}=\dfrac{-14}{36}=\dfrac{-7}{18}\)
2: \(=\dfrac{12}{13}\cdot\dfrac{26}{5}=\dfrac{24}{5}\)
3: \(=\dfrac{20}{11}\cdot\dfrac{55}{21}=\dfrac{100}{21}\)
4: \(=\dfrac{-40}{240}=\dfrac{-1}{6}\)
a: \(\left(-150\right):\left(-5\right)-2\cdot5^2\)
\(=\dfrac{150}{5}-2\cdot25\)
=30-50
=-20
b: \(2040-\left[10\cdot\left(4^3-46\right):18+2^3\right]\cdot2022^0\)
\(=2040-\left[10\cdot\left(64-46\right):18+8\right]\)
\(=2040-\left[10\cdot18:18+8\right]\)
\(=2040-10-8=2030-8=2022\)
\(a,\left(-113\right)+55+113-155=\left(-113+133\right)+\left(55-155\right)=0+\left(-100\right)=-100\\ b,-25.17+17.\left(-75\right)=17\left[\left(-25\right)+\left(-75\right)\right]=17.\left(-100\right)=-1700\)
\(c,6^8:6^6-3\left[\left(-53\right)-\left(-21-53\right)\right]+2022^0\\ =6^2-3\left(-53+21+53\right)+1\\ =36-3.21+1\\ =36-63+1\\ =-26\)
a(-113) + 55 + 113 - 155
=>(-113)+ 113+(55 - 155)
=>-100
b -25.17+17.(-75)
=>17(-25-75)
=>17. (-100)
=>-1700
c 68 : 66-3 [( -53) - ( -21 -53 )] + 20220
=>62- 3[ -53 +21 +53 )]+1
=>36−3.21+1
=>36−63+1
=>−26
\(3^2\cdot5\left[7:1^{2022}-\left(11-9\right)^2\right]+2022^0\)
\(=9\cdot5\cdot\left(7:1-2^2\right)+1\)
\(=9\cdot5\cdot\left(7-4\right)+1\)
\(=45\cdot3+1\)
\(=135+1\)
\(=136\)
\(15+4.12-3^2=15+48-9=63-9=54\\ ---\\ \left\{\left[\left(37+13\right):5\right]-45:5\right\}.7-2022^0=\left\{\left[50:5\right]-9\right\}.7-1\\ =\left\{10-9\right\}.7-1\\ =1.7-1=6\)
a) 15 + 4.12 - 3²
=15 + 48 - 9
= 63 - 9
= 54
b) {[(37 + 13) : 5].2 - 45 : 5}.7 - 2022⁰
= [(50 : 5).2 - 9].7 - 1
= (10.2 - 9).7 - 1
= (20 - 9).7 - 1
= 11.7 - 1
= 77 - 1
= 76
150:[55-(16-11)2]+20200
=150:[55-52]+1
=150:[55-25]+1
=150:30+1
=5+1=6
150 : [ 55 - (16 -11)2 ] + 20220
=150 : [ 55- 52 ] + 1
=150 : [ 55-25] +1
= 150 : 30 + 1
= 5 + 1
= 6