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\(\dfrac{15}{34}+\dfrac{7}{21}+\dfrac{19}{34}-1\dfrac{15}{17}+\dfrac{2}{3}\)
= \(\left(\dfrac{15}{34}+\dfrac{19}{34}\right)+\left(\dfrac{7}{21}+\dfrac{2}{3}\right)-1\dfrac{15}{17}\)
= \(1+\left(\dfrac{7}{21}+\dfrac{14}{21}\right)-1\dfrac{15}{17}\)
= \(1+1-1\dfrac{15}{17}\)
= \(2-1\dfrac{15}{17}\)
= \(\dfrac{2}{17}\)
\(\dfrac{15}{34}+\dfrac{7}{21}+\dfrac{19}{34}-\dfrac{32}{17}+\dfrac{2}{3}\)
\(=\left(\dfrac{15}{34}+\dfrac{19}{34}\right)+\dfrac{7}{21}+\dfrac{-32}{17}+\dfrac{2}{3}\)
\(=1+\dfrac{1}{3}+\dfrac{-32}{17}+\dfrac{2}{3}\)
\(=1+\left(\dfrac{1}{3}+\dfrac{2}{3}\right)+\dfrac{-32}{17}\)
\(=1+1+\dfrac{-32}{17}\)
\(2+\dfrac{-32}{17}=\dfrac{2}{17}\)
\(\dfrac{15}{34}-\dfrac{7}{21}+\dfrac{19}{34}-\dfrac{15}{17}-\dfrac{2}{3}\)
\(=\left(\dfrac{15}{34}+\dfrac{19}{34}\right)-\left(\dfrac{7}{21}+\dfrac{2}{3}\right)-\dfrac{15}{17}\)
\(=1-\left(\dfrac{7}{21}+\dfrac{14}{21}\right)-\dfrac{15}{17}\)
\(=1-1-\dfrac{15}{17}\)
\(=-\dfrac{15}{17}\)
\(\frac{15}{34}+\frac{7}{21}+\frac{19}{34}-\frac{20}{15}+\frac{3}{7}\)
\(\frac{15}{34}+\frac{1}{3}+\frac{19}{34}+\left(-\frac{4}{3}\right)+\frac{3}{7}\)
\(\left(\frac{15}{34}+\frac{19}{34}\right)+\left(\frac{1}{3}-\frac{4}{3}\right)+\frac{3}{7}\)
\(1+\left(-1\right)+\frac{3}{7}\)
\(=0+\frac{3}{7}=\frac{3}{7}\)
\(\frac{15}{34}+\frac{7}{21}+\frac{19}{34}-\frac{20}{15}+\frac{3}{7}\)
\(=\)\(\frac{15}{34}+\frac{1}{3}+\frac{19}{34}+\left(-\frac{4}{3}\right)+\frac{3}{7}\)
\(=\)\(\left(\frac{15}{34}+\frac{19}{34}\right)+\left(\frac{1}{3}-\frac{4}{3}\right)+\frac{3}{7}\)
\(=\)\(1+\left(-1\right)+\frac{3}{7}\)
\(=\)\(0+\frac{3}{7}\)
\(=\)\(\frac{3}{7}\)
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 + \(\left(\dfrac{-1}{7}\right)-\dfrac{1}{2}\) = \(\dfrac{5}{14}\)
\(\dfrac{15}{34}+\dfrac{7}{21}+\dfrac{19}{34}-\dfrac{3}{1}+\dfrac{7}{21}+2\)
\(=\left(\dfrac{15}{34}+\dfrac{19}{34}\right)+\left(\dfrac{7}{21}+\dfrac{7}{21}\right)-\left(3-2\right)\)
\(=1-1+\dfrac{14}{21}\)
\(=\dfrac{14}{21}\)
\(\dfrac{15}{34}+\dfrac{7}{21}+\dfrac{19}{34}-3+\dfrac{7}{21}+2\)
= \(\dfrac{15}{34}+\dfrac{19}{34}+\dfrac{7}{21}+\dfrac{7}{21}-3+2\)
= \(\left(\dfrac{15}{34}+\dfrac{19}{34}\right)+\left(\dfrac{7}{21}+\dfrac{7}{21}\right)-\left(3-2\right)\)
= \(1+\dfrac{2}{3}-1\)
= \(1-1+\dfrac{2}{3}\)
= \(\dfrac{2}{3}\)
GOOD LUCK!