- \(\frac{5}{17}-\frac{11}{13}+\frac{12}{17}+\frac{27}{13}+\left(-2020\right)^2\)
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A = 5/7.(1+9/13) − 5/7.9/13
A= 5/7.(1+9/13 - 9/13)
A = 5/7.1
A = 5/7
B = 11/24 − 5/41 + 13/24 + 0.5 − 36/41
B = (11/24 + 13/24) - (5/41 + 36/41) + 0.5
B = 1 - 1 + 0.5
B = 0.5
C = −4/13.5/17 + (−12/13).4/17 + 4/13
C = 4/13.(-5/17) + (−12/13).4/17 + 4/13
C = 4/13.(-5/17 + 1) + (−12/13).4/17
C = 4/13.(−12/17) + (−12/13).4/17
C = (4.-12)/(13.17) + (−12/13).4/17
C = 4/17.(−12/13) + (−12/13).4/17
C = 4/17.(−12/13).2
C = 96/221
D = (4/3 − 3/2)2 − 2.∣−1/9∣ + (−5/18)
D = (4/3 − 3/2)2 − 2.1/9+ (−5/18)
D = -1/62 - 2/9+ (−5/18)
D = -1/12 - ( 2/9+ (−5/18) )
D = -1/12 - ( 4/18+ (−5/18) )
D = -1/12 - (-1/18)
D = -1/12 + 1/18
D = -3/36 + 2/36
D = -1/36
E = (−3/4 + 2/3):5/11 + (−1/4 + 1/3):5/11
E = (−3/4 + 2/3 + (−1/4) + 1/3):5/11
E = ((−3/4 + (−1/4)) + (2/3 + + 1/3)):5/11
E = ( - 1 + 1):5/11
E = 0:5/11
E = 0
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a)\(\frac{-10}{13}+\frac{8}{17}-\frac{3}{13}+\frac{12}{17}-\frac{11}{20}\)
= \(\frac{-10}{13}+\frac{8}{17}+\frac{-3}{13}+\frac{12}{17}+\frac{-11}{20}\)
=\(\left(\frac{-10}{13}+\frac{-3}{13}\right)+\left(\frac{8}{17}+\frac{12}{17}\right)+\frac{-11}{20}\)
=\(\frac{-13}{13}+\frac{20}{17}+\frac{-11}{20}\)
= \(\frac{-127}{340}\)
b) \(\frac{3}{4}+\frac{-5}{6}-\frac{11}{-12}\)
= \(\frac{3}{4}+\frac{-5}{6}+\frac{11}{12}\)
= \(\frac{9}{12}+\frac{-10}{12}+\frac{11}{12}\)
=\(\frac{10}{12}=\frac{5}{6}\)
c) \(\left[13.\frac{4}{9}+2.\frac{1}{9}\right]-3.\frac{4}{9}\)
= \(13+2.\left(\frac{4}{9}+\frac{1}{9}\right)-3.\frac{4}{9}\)
=\(15.\frac{5}{9}-3.\frac{4}{9}\)
=\(\left[15-3.\left(\frac{5}{9}-\frac{4}{9}\right)\right]\)
=\(12.\frac{1}{9}\)
=\(\frac{4}{3}\)
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\(\left(-1\frac{1}{6}\right)\left(\frac{1-\frac{3}{5}+\frac{3}{11}-\frac{3}{13}}{\frac{1}{3}-\frac{1}{5}+\frac{1}{11}-\frac{1}{13}}\right)\left(\frac{4-\frac{4}{17}+\frac{4}{19}-\frac{4}{2013}}{5-\frac{5}{7}+\frac{5}{19}-\frac{5}{2013}}\right)\)
\(=-\frac{7}{6}.\left(\frac{3\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{11}-\frac{1}{13}\right)}{\frac{1}{3}-\frac{1}{5}+\frac{1}{11}-\frac{1}{13}}\right):\left(\frac{4.\left(1-\frac{1}{7}+\frac{1}{19}-\frac{1}{2013}\right)}{5.\left(1-\frac{1}{7}+\frac{1}{19}-\frac{1}{2013}\right)}\right)\)
\(=-\frac{7}{6}.3:\frac{4}{5}=-\frac{7}{2}.\frac{5}{4}=-\frac{35}{8}\)
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\(E=\frac{1}{13}+\left(\frac{-5}{18}-\frac{1}{13}+\frac{12}{17}\right)-\left(\frac{12}{17}-\frac{5}{18}+\frac{7}{5}\right)\)
\(=\frac{1}{13}+\frac{-5}{18}-\frac{1}{13}+\frac{12}{17}-\frac{12}{17}+\frac{5}{18}-\frac{7}{5}\)
\(=\left(\frac{1}{13}-\frac{1}{13}\right)+\left(\frac{-5}{18}+\frac{5}{18}\right)+\left(\frac{12}{17}-\frac{12}{17}\right)-\frac{7}{5}\)
\(=0+0+0-\frac{7}{5}\)
\(=-\frac{7}{5}\)
\(E=\frac{1}{13}+\left(\frac{-5}{18}-\frac{1}{13}+\frac{12}{17}\right)-\left(\frac{12}{17}-\frac{5}{18}+\frac{7}{5}\right)\)
\(=\frac{1}{13}+\frac{-5}{18}-\frac{1}{13}+\frac{12}{17}-\frac{-12}{17}+\frac{5}{18}-\frac{7}{5}\)
\(=\left(\frac{1}{13}-\frac{1}{13}\right)+\left(\frac{-5}{18}+\frac{5}{18}\right)+\left(\frac{12}{17}-\frac{-12}{17}\right)-\frac{7}{5}\)
\(=0+0+\frac{24}{17}-\frac{7}{5}\)
\(=\frac{24}{17}-\frac{7}{5}\)
\(=\frac{120}{85}-\frac{119}{85}=\frac{1}{85}\)
\(\frac{5}{17}-\frac{11}{13}+\frac{12}{17}+\frac{27}{13}+\left(-2020\right)^2\)
\(=\left(\frac{5}{17}+\frac{12}{17}\right)+\left(\frac{-11}{13}+\frac{27}{13}\right)+\left(-2020\right)^2\)
\(=1+\frac{16}{13}+\left(-2020\right)^2\)\(=1+\frac{16}{13}+4080400\)
\(=4080402\frac{3}{13}\)