j: \(\dfrac{7}{23}+\dfrac{-10}{18}+\dfrac{-4}{9}+\dfrac{16}{23}+\dfrac{-5}{8}\)
\(=\left(\dfrac{7}{23}+\dfrac{16}{23}\right)+\left(-\dfrac{10}{18}-\dfrac{4}{9}\right)-\dfrac{5}{8}\)
\(=1-1-\dfrac{5}{8}=-\dfrac{5}{8}\)
k: \(\dfrac{1}{3}+\dfrac{-3}{4}+\dfrac{3}{5}+\dfrac{-1}{36}+\dfrac{1}{15}+\dfrac{-2}{9}\)
\(=\left(\dfrac{1}{3}+\dfrac{3}{5}+\dfrac{1}{15}\right)+\left(-\dfrac{3}{4}-\dfrac{1}{36}-\dfrac{2}{9}\right)\)
\(=\dfrac{5+9+1}{15}+\dfrac{-27-1-8}{36}\)
\(=\dfrac{15}{15}-\dfrac{36}{36}=1-1=0\)
l: \(-\dfrac{2}{15}+\dfrac{12}{13}+\dfrac{-13}{15}+\dfrac{-1}{13}\)
\(=\left(-\dfrac{2}{15}-\dfrac{13}{15}\right)+\left(\dfrac{12}{13}+\dfrac{-1}{13}\right)\)
\(=\dfrac{-15}{15}+\dfrac{11}{13}=-1+\dfrac{11}{13}=-\dfrac{2}{13}\)
m: \(-\dfrac{5}{7}+\dfrac{3}{4}+\dfrac{-1}{5}+\dfrac{-2}{7}+\dfrac{1}{4}\)
\(=\left(-\dfrac{5}{7}-\dfrac{2}{7}\right)+\left(\dfrac{3}{4}+\dfrac{1}{4}\right)+\dfrac{-1}{5}\)
\(=\dfrac{-7}{7}+\dfrac{4}{4}+\dfrac{-1}{5}=-1+1+\dfrac{-1}{5}=-\dfrac{1}{5}\)
n: \(\dfrac{4}{7}+\dfrac{-1}{9}+\dfrac{3}{7}+\dfrac{7}{10}+\dfrac{-8}{9}\)
\(=\left(\dfrac{4}{7}+\dfrac{3}{7}\right)+\left(-\dfrac{1}{9}-\dfrac{8}{9}\right)+\dfrac{7}{10}\)
\(=\dfrac{7}{7}-\dfrac{9}{9}+\dfrac{7}{10}=1-1+\dfrac{7}{10}=\dfrac{7}{10}\)
o: \(\dfrac{4}{7}+\dfrac{3}{4}+\dfrac{2}{7}+\dfrac{5}{4}+\dfrac{1}{7}\)
\(=\left(\dfrac{4}{7}+\dfrac{2}{7}+\dfrac{1}{7}\right)+\left(\dfrac{3}{4}+\dfrac{5}{4}\right)\)
\(=\dfrac{7}{7}+\dfrac{8}{4}\)
=1+2
=3
p: \(\dfrac{5}{2}+\dfrac{6}{11}+\dfrac{3}{8}+\dfrac{7}{2}+\dfrac{6}{8}+\dfrac{5}{11}\)
\(=\left(\dfrac{5}{2}+\dfrac{7}{2}\right)+\left(\dfrac{6}{11}+\dfrac{5}{11}\right)+\left(\dfrac{3}{8}+\dfrac{6}{8}\right)\)
\(=\dfrac{12}{2}+\dfrac{11}{11}+\dfrac{9}{8}\)
\(=6+1+\dfrac{9}{8}=7+\dfrac{9}{8}=\dfrac{65}{8}\)
q: \(\dfrac{4}{3}+\dfrac{3}{5}+\dfrac{7}{3}+\dfrac{2}{5}+\dfrac{1}{3}\)
\(=\left(\dfrac{4}{3}+\dfrac{7}{3}+\dfrac{1}{3}\right)+\left(\dfrac{3}{5}+\dfrac{2}{5}\right)\)
\(=\dfrac{12}{3}+\dfrac{5}{5}=4+1=5\)
r: \(\dfrac{5}{17}+\dfrac{-9}{15}+\dfrac{-2}{17}+\dfrac{2}{-5}\)
\(=\left(\dfrac{5}{17}-\dfrac{2}{17}\right)+\left(-\dfrac{3}{5}-\dfrac{2}{5}\right)\)
\(=\dfrac{3}{17}-1=-\dfrac{14}{17}\)
j: =(723+1623)+(−1018−49)−58=(723+1623)+(−1018−49)−58
13+−34+35+−136+115+−2913+−34+35+−136+115+−29
=5+9+115+−27−1−836=5+9+115+−27−1−836
−215+1213+−1315+−113−215+1213+−1315+−113
=−1515+1113=−1+1113=−213=−1515+1113=−1+1113=−213
m: =(−57−27)+(34+14)+−15=(−57−27)+(34+14)+−15
47+−19+37+710+−8947+−19+37+710+−89
=77−99+710=1−1+710=710=77−99+710=1−1+710=710
o: =(47+27+17)+(34+54)=(47+27+17)+(34+54)
52+611+38+72+68+51152+611+38+72+68+511
=122+1111+98=122+1111+98
43+35+73+25+1343+35+73+25+13
=123+55=4+1=5=123+55=4+1=5
r: =(517−217)+(−35−25)=(517−217)+(−35−25)