Thực hiện phép tính bằng cách tính hợp lí

a)\(\dfrac{15}{34}+\dfrac{7}{21}+\dfrac{19}{34}-1\dfrac{15}{17}+\dfrac{2}{3}=\)

=\(\dfrac{15}{34}+\dfrac{1}{3}+\dfrac{19}{34}-1\dfrac{15}{17}+\dfrac{2}{3}\)

=\(\left(\dfrac{15}{34}+\dfrac{19}{34}\right)+\left(\dfrac{1}{3}+\dfrac{2}{3}\right)-1\dfrac{15}{17}\)

=\(1+1-\dfrac{32}{17}\)

=\(\dfrac{34}{17}-\dfrac{32}{17}\)

=\(\dfrac{2}{17}\)

b)\(\left(-2\right)^3\cdot\left(\dfrac{3}{4}-0,25\right):\left(2\dfrac{1}{4}-1\dfrac{1}{6}\right)\)

=\(-8\cdot\left(\dfrac{3}{4}-\dfrac{1}{4}\right):\left(\dfrac{9}{4}-\dfrac{7}{6}\right)\)

=\(-8\cdot\dfrac{1}{2}:\left(\dfrac{54}{24}-\dfrac{28}{24}\right)\)

=\(-4:\dfrac{13}{12}\)

=\(-4\cdot\dfrac{12}{13}\)

=\(-\dfrac{48}{13}\)

a, \(\dfrac{15}{34}+\dfrac{7}{21}+\dfrac{19}{34}-\dfrac{20}{15}+\dfrac{3}{7}\)

= \(\left(\dfrac{15}{34}+\dfrac{19}{34}\right)+\left(\dfrac{7}{21}+\dfrac{3}{7}\right)-\dfrac{20}{15}\)

= 1 + \(\dfrac{16}{21}-\dfrac{20}{15}\)

= \(\dfrac{3}{7}\)

b, \(\dfrac{27}{25}+\dfrac{4}{21}-\dfrac{2}{25}+\dfrac{17}{21}-\dfrac{1}{2}\)

= \(\left[\dfrac{27}{25}+\left(-\dfrac{2}{25}\right)\right]+\left(\dfrac{4}{21}-\dfrac{7}{21}\right)-\dfrac{1}{2}\)

= 1 + \(\left(\dfrac{-1}{7}\right)-\dfrac{1}{2}\) = \(\dfrac{5}{14}\)

Câu 1:

\(=\dfrac{15}{34}+\dfrac{19}{34}-1-\dfrac{15}{17}+\dfrac{1}{3}+\dfrac{3}{5}\)

\(=-\dfrac{15}{17}+\dfrac{14}{15}=\dfrac{13}{255}\)

Câu 2: 

\(=\dfrac{5^4\cdot5^4\cdot2^8}{4^4\cdot6^4\cdot3^2\cdot5}=\dfrac{5^7}{6^4\cdot3^2}\)

\(\dfrac{15}{34}-\dfrac{7}{21}+\dfrac{19}{34}-\dfrac{15}{17}-\dfrac{2}{3}\)

\(=\left(\dfrac{15}{34}+\dfrac{19}{34}\right)-\left(\dfrac{7}{21}+\dfrac{2}{3}\right)-\dfrac{15}{17}\)

\(=1-\left(\dfrac{7}{21}+\dfrac{14}{21}\right)-\dfrac{15}{17}\)

\(=1-1-\dfrac{15}{17}\)

\(=-\dfrac{15}{17}\)

\(=4,2308\)

a)P=\(\dfrac{-2}{7}+\dfrac{14}{29}+\dfrac{12}{33}+\dfrac{15}{29}+\dfrac{21}{33}+\dfrac{2}{7}\)

      =\(\left(\dfrac{-2}{7}+\dfrac{2}{7}\right)+\left(\dfrac{14}{29}+\dfrac{15}{29}\right)+\left(\dfrac{12}{33}+\dfrac{21}{33}\right)\)

      =0+1+1=2

b)\(\dfrac{2}{7}.\dfrac{5}{19}+\dfrac{2}{7}.\dfrac{14}{19}+\dfrac{21}{19}-\dfrac{2}{7}.\dfrac{1}{5}\)

=\(\dfrac{2}{7}.\left(\dfrac{5}{19}+\dfrac{14}{19}-\dfrac{1}{5}\right)+\dfrac{21}{19}\)

=\(\dfrac{2}{7}.\dfrac{4}{5}+\dfrac{21}{19}=\dfrac{887}{665}\)

\(A=\dfrac{15}{34}+\dfrac{27}{21}+\dfrac{9}{34}-1\dfrac{15}{17}+\dfrac{2}{3}\)

\(A=\left(\dfrac{15}{34}+\dfrac{9}{34}-1\dfrac{15}{17}\right)+\left(\dfrac{27}{21}+\dfrac{2}{3}\right)\)

\(A=\left(\dfrac{15}{34}+\dfrac{9}{34}-\dfrac{32}{17}\right)+\left(\dfrac{27}{21}+\dfrac{2}{3}\right)\)

\(A=\left(\dfrac{15}{34}+\dfrac{9}{34}-\dfrac{64}{34}\right)+\left(\dfrac{27}{21}+\dfrac{14}{21}\right)\)

\(A=\dfrac{-20}{17}+\dfrac{41}{21}\)

\(A=\dfrac{-420}{357}+\dfrac{697}{357}=\dfrac{277}{357}\)

\(B=16\dfrac{2}{7}:\left(-\dfrac{3}{5}\right)-28\dfrac{2}{7}:\left(-\dfrac{3}{5}\right)\)

\(B=16\dfrac{2}{7}.\left(-\dfrac{5}{3}\right)-28\dfrac{2}{7}.\left(-\dfrac{5}{3}\right)\)

\(B=\left(-\dfrac{5}{3}\right)\left(16\dfrac{2}{7}-28\dfrac{2}{7}\right)\)

\(B=\left(-\dfrac{5}{3}\right)\left(-12\right)\)

\(B=20\)

\(A=\dfrac{15}{34}+\dfrac{1}{3}+\dfrac{9}{34}-\dfrac{32}{17}+\dfrac{2}{3}\)

\(A=\dfrac{15}{34}+\dfrac{1}{3}+\dfrac{9}{34}-\dfrac{64}{34}+\dfrac{2}{3}\)

\(A=\left(\dfrac{15}{34}+\dfrac{9}{34}-\dfrac{64}{34}\right)+\left(\dfrac{1}{3}+\dfrac{2}{3}\right)\)

\(A=\dfrac{40}{34}+1=2\dfrac{6}{34}\)

\(A=\dfrac{15}{34}+\dfrac{7}{21}+\dfrac{9}{34}-1\dfrac{15}{17}+\dfrac{2}{3}\)

\(=\dfrac{15}{34}+\dfrac{1}{3}+\dfrac{9}{34}-1\dfrac{15}{17}+\dfrac{2}{3}\)

\(=\left(\dfrac{15}{34}+\dfrac{9}{34}\right)+\left(\dfrac{1}{3}+\dfrac{2}{3}\right)-1\dfrac{15}{17}\)

\(=1+1-1\dfrac{15}{17}\)

\(=2-1\dfrac{15}{17}\)

\(=\dfrac{2}{17}\)