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a) \(1\dfrac{7}{20}:2,7+2,7:1,35\)
\(=1,35:2,7+2,7:1,35\)
\(=0,5+2\)
\(=2,5\)
b) \(3\dfrac{1}{2}-\left(0,4:2\dfrac{1}{2}\right).\left(4,2-1\dfrac{3}{4}\right)\)
\(=\dfrac{7}{2}-\left(0,4:\dfrac{5}{2}\right).\left(4,2-\dfrac{7}{4}\right)\)
\(=\dfrac{7}{2}-\dfrac{4}{25}.\dfrac{49}{20}\)
\(=\dfrac{7}{2}-\dfrac{49}{125}\)
\(=\dfrac{777}{250}\)
a) \(1\dfrac{7}{20}:2,7+2,7:1,35+\left(0,4:2\dfrac{1}{2}\right).\left(4,2-1\dfrac{3}{40}\right)\)
\(=\dfrac{27}{20}:\dfrac{27}{10}+\dfrac{27}{10}:\dfrac{27}{10}+\left(\dfrac{2}{5}:\dfrac{5}{2}\right).\left(\dfrac{21}{5}-\dfrac{43}{40}\right)\)
\(=1+1+\dfrac{4}{25}.\dfrac{25}{8}\)
\(=2+\dfrac{1}{2}\)
\(=2\dfrac{1}{2}\)
b) \(\left(6\dfrac{3}{5}-3\dfrac{3}{14}\right).5\dfrac{5}{6}:\left(21-1.25\right):2,5\)
\(=\left(\dfrac{33}{5}-\dfrac{45}{14}\right).\dfrac{35}{6}:\left(-4\right):2,5\)
\(=\left(\dfrac{462}{60}-\dfrac{225}{60}\right).\dfrac{35}{6}.\dfrac{1}{-4}:\dfrac{5}{2}\)
\(=\dfrac{237}{60}.\dfrac{35}{6}.\dfrac{1}{-4}.\dfrac{2}{5}\)
\(=\dfrac{3.79.7.5.2}{5.14.3.2.\left(-4\right).5}\)
\(=\dfrac{79.7}{14.\left(-4\right).5}=\dfrac{553}{-280}\) (số xấu :v)
\(B=1x\frac{7}{20}:2,7+2,7:1,35+\left(0,4+2\frac{1}{2}\right)x\left(4,2-1\frac{3}{10}\right)\)
\(B=\frac{7}{20}:2,7+2+2,9x2,9\)
\(B=\frac{7}{54}+2+8,41\)
\(B=10,53962963\)
a,(3/5+0,415-3/200).\(2\dfrac{2}{3}\).0,25
=(0,6+0.415-3/200)8/3.1/4
=(1,015-3/200).8/3.1/4
=(1015/1000-3/200).2/3
=(203/200-3/200).2/3
=1.2/3=2/3
b,0,25:(10,3-9,8)-3/4
=0,25:910,3-9,8)-0.75
=0,25:0,5-0,75
=-0,25
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a) 20 : 22 + 59 : 58
= 20 : 4 + 59-8
= 5 + 51
= 5 + 5
= 10
b) 100 : 52 + 7 . 32
= 102 : 52 + 7 . 9
= ( 10 : 5 )2 + 63
= 22 + 63
= 4 + 63
= 67
a, \(\dfrac{x-2}{5}=\dfrac{x}{3}\)
\(\Leftrightarrow3\left(x-2\right)=5x\)
\(\Leftrightarrow3x-6=5x\)
\(\Leftrightarrow5x-3x=6\)
\(\Leftrightarrow2x=6\)
\(\Leftrightarrow x=3\)
b, \(\dfrac{x+23}{x+40}=\dfrac{3}{4}\)
\(\Leftrightarrow4\left(x+23\right)=3\left(x+40\right)\)
\(\Leftrightarrow4x+92=2x+80\)
\(\Leftrightarrow4x-2x=80-92\)
\(\Leftrightarrow2x=-12\)
\(\Leftrightarrow x=-6\)
c, \(A=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...........+\dfrac{1}{2^{2017}}\)
\(\Leftrightarrow2A=1+\dfrac{1}{2}+\dfrac{1}{2^2}+...........+\dfrac{1}{2^{2016}}\)
\(\Leftrightarrow2A-A=\left(1+\dfrac{1}{2}+\dfrac{1}{2^2}+........+\dfrac{1}{2^{2016}}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+........+\dfrac{1}{2^{2017}}\right)\)
\(\Leftrightarrow A=1-\dfrac{1}{2^{2017}}\)
d, \(B=1+2+2^2+........+2^{2017}\)
\(\Leftrightarrow2B=2+2^2+2^3+......+2^{2018}\)
\(\Leftrightarrow2B-B=\left(2+2^2+.....+2^{2018}\right)-\left(1+2+....+2^{2017}\right)\)
\(\Leftrightarrow B=2^{2018}-1\)
\(\dfrac{x-2}{5}=\dfrac{x}{3}=>3\left(x-2\right)=5x\)
\(< =>3x-6=5x=>x=-3\)
\(\dfrac{x+23}{x+40}=\dfrac{3}{4}=>4\left(x+23\right)=3\left(x+40\right)\)
\(4x+92=3x+120=>x=28\)
a: \(=\dfrac{11}{4}\cdot\dfrac{-2}{5}+\dfrac{36}{5}\cdot\dfrac{11}{9}=\dfrac{11}{9}\cdot\dfrac{34}{5}=\dfrac{374}{45}\)
b: \(=3\cdot\left(\dfrac{5}{6}-\dfrac{25}{12}\right):\dfrac{30}{7}-\dfrac{1}{4}\cdot\dfrac{-2}{3}\)
\(=3\cdot\dfrac{7}{30}\cdot\dfrac{-15}{12}+\dfrac{1}{6}\)
\(=\dfrac{7}{10}\cdot\dfrac{-5}{4}+\dfrac{1}{6}\)
\(=\dfrac{-7}{8}+\dfrac{1}{6}=\dfrac{-21+4}{24}=\dfrac{-17}{24}\)
1207:2,7+2,7:1,35+(0,4:212221).(4,2-13401403)=
\(1\dfrac{7}{20}\div2,7+2,7\div1,35+\left(0,4\div2\dfrac{1}{2}\right)\times\left(4,2-1\dfrac{3}{40}\right)\)
\(=\dfrac{27}{20}\div\dfrac{27}{10}+\dfrac{27}{10}\div\dfrac{27}{20}+\left(\dfrac{2}{5}\div\dfrac{5}{2}\right)\times\left(\dfrac{21}{5}-\dfrac{43}{40}\right)\)
\(=\dfrac{27}{20}\times\dfrac{10}{27}+\dfrac{27}{10}\times\dfrac{20}{27}+\left(\dfrac{2}{5}\times\dfrac{2}{5}\right)\times\dfrac{25}{8}\)
\(=\dfrac{1}{2}+2+\dfrac{4}{25}\times\dfrac{25}{8}\)
\(=\dfrac{5}{2}+\dfrac{1}{2}\)
\(=3\)