a, \(\dfrac{4}{7}+\dfrac{3}{4}+\dfrac{2}{7}+\dfrac{5}{4}+\dfrac{1}{7}\)
\(=\left(\dfrac{4}{7}+\dfrac{2}{7}+\dfrac{1}{7}\right)+\left(\dfrac{3}{4}+\dfrac{5}{4}\right)\)
\(=1+2=3\)
b, \(\dfrac{5}{2}+\dfrac{6}{11}+\dfrac{3}{8}+\dfrac{7}{2}+\dfrac{6}{8}+\dfrac{5}{11}\)
\(=\left(\dfrac{5}{2}+\dfrac{7}{2}\right)+\left(\dfrac{6}{11}+\dfrac{5}{11}\right)+\left(\dfrac{3}{8}+\dfrac{6}{8}\right)\)
\(=6+1+\dfrac{9}{8}\)
\(=7+\dfrac{9}{8}=\dfrac{65}{8}\)
c, \(\dfrac{4}{3}-\dfrac{3}{5}+\dfrac{-20}{3}-\dfrac{2}{5}+\dfrac{2}{3}\)
\(=\left(\dfrac{4}{3}+\dfrac{-20}{3}+\dfrac{2}{3}\right)+\left(\dfrac{-3}{5}-\dfrac{2}{5}\right)\)
\(=\dfrac{-14}{3}+\left(-1\right)=\dfrac{-17}{3}\)
d, \(\dfrac{5}{12}+\dfrac{5}{3}-\dfrac{2}{12}-\dfrac{2}{3}\)
\(=\left(\dfrac{5}{12}-\dfrac{2}{12}\right)+\left(\dfrac{5}{3}-\dfrac{2}{3}\right)\)
\(=\dfrac{1}{4}+1=\dfrac{5}{4}\)
e, \(\dfrac{1}{28}+\dfrac{-1}{14}+\dfrac{3}{28}+\dfrac{1}{7}+\dfrac{-5}{28}+\dfrac{3}{14}+\dfrac{-1}{4}\)
\(=\left(\dfrac{1}{28}+\dfrac{3}{28}+\dfrac{-5}{28}\right)+\left(\dfrac{-1}{14}+\dfrac{3}{14}\right)+\dfrac{1}{7}+\dfrac{-1}{4}\)
\(=-\dfrac{1}{28}+\dfrac{1}{7}+\dfrac{1}{7}+-\dfrac{1}{4}\)
\(=\dfrac{-1}{28}+\left(\dfrac{1}{7}+\dfrac{1}{7}+\dfrac{-1}{4}\right)\)
\(=\dfrac{-1}{28}+\dfrac{1}{28}=0\)
a: \(\dfrac{4}{7}+\dfrac{3}{4}+\dfrac{2}{7}+\dfrac{5}{4}+\dfrac{1}{7}\)
\(=\left(\dfrac{4}{7}+\dfrac{2}{7}+\dfrac{1}{7}\right)+\left(\dfrac{3}{4}+\dfrac{5}{4}\right)\)
\(=1+2=3\)
b: \(\dfrac{5}{2}+\dfrac{6}{11}+\dfrac{3}{8}+\dfrac{7}{2}+\dfrac{6}{8}+\dfrac{5}{11}\)
\(=\left(\dfrac{5}{2}+\dfrac{7}{2}\right)+\left(\dfrac{3}{8}+\dfrac{6}{8}\right)+\left(\dfrac{6}{11}+\dfrac{5}{11}\right)\)
\(=\dfrac{12}{2}+\dfrac{9}{8}+\dfrac{11}{11}\)
\(=6+1+\dfrac{9}{8}=7+\dfrac{9}{8}=\dfrac{7\cdot8+9}{8}=\dfrac{65}{8}\)
c: \(\dfrac{4}{3}-\dfrac{3}{5}+\dfrac{-20}{3}-\dfrac{2}{5}+\dfrac{2}{3}\)
\(=\left(\dfrac{4}{3}-\dfrac{20}{3}+\dfrac{2}{3}\right)+\left(-\dfrac{3}{5}-\dfrac{2}{5}\right)\)
\(=\dfrac{-14}{3}+\dfrac{-5}{5}=\dfrac{-14}{3}-1=-\dfrac{17}{3}\)
d: \(\dfrac{5}{12}+\dfrac{5}{3}-\dfrac{2}{12}-\dfrac{2}{3}\)
\(=\left(\dfrac{5}{3}-\dfrac{2}{3}\right)+\left(\dfrac{5}{12}-\dfrac{2}{12}\right)\)
\(=\dfrac{3}{3}+\dfrac{3}{12}=1+\dfrac{3}{12}=\dfrac{15}{12}=\dfrac{5}{4}\)
e: \(\dfrac{1}{28}+\dfrac{-1}{14}+\dfrac{3}{28}+\dfrac{1}{7}+\dfrac{-5}{28}+\dfrac{3}{14}+\dfrac{-1}{4}\)
\(=\left(\dfrac{1}{28}+\dfrac{3}{28}-\dfrac{5}{28}\right)+\left(-\dfrac{1}{14}+\dfrac{3}{14}\right)+\left(\dfrac{1}{7}-\dfrac{1}{4}\right)\)
\(=\dfrac{-1}{28}+\dfrac{2}{14}+\dfrac{1}{7}-\dfrac{1}{4}\)
\(=\dfrac{-1+4+4-7}{28}=0\)
