\(1.\dfrac{3}{4}-\dfrac{5}{6}+\dfrac{2}{3}\\ =\dfrac{9}{12}-\dfrac{10}{12}+\dfrac{8}{12}\\ =\dfrac{7}{12}\\ 2.-\left(\dfrac{2}{7}-\dfrac{13}{8}\right)+\left(\dfrac{3}{8}+\dfrac{2}{7}\right)\\ =\left(-\dfrac{2}{7}+\dfrac{2}{7}\right)+\left(\dfrac{13}{8}+\dfrac{3}{8}\right)\\ =0+\dfrac{16}{8}\\ =2\\ 3.\dfrac{11}{24}-\dfrac{25}{31}+\dfrac{13}{24}+0,5-\dfrac{37}{31}\\ =\left(\dfrac{11}{24}+\dfrac{13}{24}\right)+\left(-\dfrac{25}{31}-\dfrac{37}{31}\right)+\dfrac{1}{2}\\ =\dfrac{24}{24}+\left(\dfrac{-62}{31}\right)+\dfrac{1}{2}\\ =1-2+\dfrac{1}{2}\\ =\dfrac{1}{2}-1\\ =-\dfrac{1}{2}\)
1: \(\dfrac{3}{4}-\dfrac{5}{6}+\dfrac{2}{3}=\dfrac{9}{12}-\dfrac{10}{12}+\dfrac{8}{12}=\dfrac{7}{12}\)
2: \(-\left(\dfrac{2}{7}-\dfrac{13}{8}\right)+\left(\dfrac{3}{8}+\dfrac{2}{7}\right)\)
\(=-\dfrac{2}{7}+\dfrac{13}{8}+\dfrac{3}{8}+\dfrac{2}{7}\)
\(=\dfrac{13}{8}+\dfrac{3}{8}=\dfrac{16}{8}=2\)
3: \(\dfrac{11}{24}-\dfrac{25}{31}+\dfrac{13}{24}+0,5-\dfrac{37}{31}\)
\(=\left(\dfrac{11}{24}+\dfrac{13}{24}\right)+\left(-\dfrac{25}{31}-\dfrac{37}{31}\right)+0,5\)
=1-2+0,5
=-0,5
4: \(\dfrac{11}{24}-\dfrac{5}{41}+\dfrac{13}{24}+0,5-\dfrac{36}{41}\)
\(=\left(\dfrac{11}{24}+\dfrac{13}{24}\right)+\left(-\dfrac{5}{41}-\dfrac{36}{41}\right)+0,5\)
=1-1+0,5=0,5
5: \(-\dfrac{15}{11}+\dfrac{10}{12}+\dfrac{15}{33}+\dfrac{4}{11}+\dfrac{18}{33}\)
\(=\left(-\dfrac{15}{11}+\dfrac{4}{11}\right)+\left(\dfrac{15}{33}+\dfrac{18}{33}\right)+\dfrac{5}{6}\)
=-1+1+5/6=5/6
6: \(\dfrac{15}{34}+\dfrac{-7}{27}+\dfrac{19}{34}-\dfrac{20}{27}+\dfrac{21}{7}\)
\(=\left(\dfrac{15}{34}+\dfrac{19}{34}\right)+\left(-\dfrac{7}{27}-\dfrac{20}{27}\right)+3\)
=1-1+3=3
