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\(\left(\frac{3}{4}+\frac{2}{11}-\frac{8}{13}\right)+\left(\frac{1}{4}-\frac{5}{13}\right)\)
\(=\frac{3}{4}+\frac{2}{11}-\frac{8}{13}+\frac{1}{4}-\frac{5}{13}\)
\(=\left(\frac{3}{4}+\frac{1}{4}\right)+\frac{2}{11}-\left(\frac{8}{13}+\frac{5}{13}\right)\)
\(=1+\frac{2}{11}-1\)
\(=\frac{2}{11}\)
\(\left(\frac{9}{53}+\frac{21}{31}\right)+\left(\frac{44}{53}-\frac{16}{7}\right)+\frac{10}{31}\)
\(=\frac{9}{53}+\frac{21}{31}+\frac{44}{53}-\frac{16}{7}+\frac{10}{31}\)
\(=\left(\frac{9}{53}+\frac{44}{53}\right)+\left(\frac{21}{31}+\frac{10}{31}\right)-\frac{16}{7}\)
\(=1+1-\frac{16}{7}\)
\(=2-\frac{16}{7}\)
\(=\frac{14}{7}-\frac{16}{7}\)
\(=\frac{-2}{7}\)
\(A=\frac{21}{31}+\frac{-16}{7}+\frac{44}{53}+\frac{10}{21}+\frac{9}{53} \)
\(A=\left(\frac{16}{7}+\frac{10}{21}\right)+\left(\frac{44}{53}+\frac{9}{53}\right)+\frac{21}{31}\)
\(A=\frac{58}{21}+1+\frac{21}{31}\)
\(A=\frac{100}{21}\)
\(B=6\left(\frac{1}{15.18}+\frac{1}{18.21}+...+\frac{1}{87.90}\right)\)
\(B=6\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+...+\frac{1}{87}-\frac{1}{90}\right)\)
\(B=6\left(\frac{1}{15}-\frac{1}{90}\right)\)
\(B=6.\frac{1}{18}\)
\(B=\frac{1}{3}\)
\(\left(\frac{21}{31}+\frac{2013}{6039}\right)-\left(\frac{44}{53}-\frac{10}{31}\right)-\frac{9}{53}\)
\(=\frac{21}{31}+\frac{1}{3}-\frac{44}{53}+\frac{10}{31}-\frac{9}{53}\)
\(=\left(\frac{21}{31}+\frac{10}{31}\right)+\left(\frac{-44}{53}-\frac{9}{53}\right)+\frac{1}{3}\)
\(=1+\left(-1\right)+\frac{1}{3}\)
\(=\frac{1}{3}\)
\(\left(\dfrac{21}{31}+\dfrac{-16}{7}\right)+\left(\dfrac{44}{53}+\dfrac{10}{31}\right)+\dfrac{9}{53}.\)
\(\dfrac{21}{31}-\dfrac{16}{7}+\dfrac{44}{53}+\dfrac{10}{31}+\dfrac{9}{53}=\left(\dfrac{21}{31}+\dfrac{10}{31}\right)+\left(\dfrac{44}{53}+\dfrac{9}{53}\right)-\dfrac{16}{7}=1+1-\dfrac{16}{7}=\dfrac{-2}{7}.\)
\(a)\frac{-3}{4}+\frac{3}{7}+-\frac{1}{4}+\frac{4}{9}+\frac{4}{7}\)
\(=\left(\frac{-3}{4}+-\frac{1}{4}\right)+\left(\frac{3}{7}+\frac{4}{7}\right)+\frac{4}{9}\)
\(=-1+1+\frac{4}{9}\)
\(=\frac{4}{9}\)
\(\frac{-3}{4}+\frac{3}{7}+\frac{-1}{4}+\frac{4}{9}+\frac{4}{7}\)
\(=\left(\frac{-3}{4}+\frac{-1}{4}\right)+\left(\frac{3}{7}+\frac{4}{7}\right)+\frac{4}{9}\)
\(=\left(-1\right)+1+\frac{4}{9}\)
\(=0+\frac{4}{9}\)
\(=\frac{4}{9}\)
21 31 + − 16 7 + 44 53 + 10 31 + 9 53 = ( 21 31 + 10 31 ) + ( 44 53 + 9 53 ) + − 16 7 = 1 + 1 + − 16 7 = − 2 7