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a ) \(\frac{2}{5}+\frac{-1}{6}-\frac{3}{4}-\frac{-2}{3}\)
= \(\frac{2}{5}+\frac{-1}{6}+\frac{-3}{4}+\frac{2}{3}\)
= \(\left(\frac{2}{5}+\frac{-3}{4}\right)+\left(\frac{-1}{6}+\frac{2}{3}\right)\)
= \(\left(\frac{8}{20}+\frac{-15}{20}\right)+\left(\frac{-1}{6}+\frac{4}{6}\right)\)
= \(\left(\frac{8+\left(-15\right)}{20}\right)+\left(\frac{\left(-1\right)+4}{6}\right)\)
= \(\frac{-7}{20}+\frac{1}{2}\)
= \(\frac{-7}{20}+\frac{10}{20}=\frac{\left(7\right)+10}{20}=\frac{3}{20}\)
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\(a)\frac{5}{6}+\left(\frac{-1}{2}\right)+\frac{3}{4}\)
\(=\frac{1}{3}+\frac{3}{4}\)
\(=\frac{13}{12}\)
\(b)\left(0,75-\frac{1}{3}\right):\frac{7}{15}\)
\(=\left(\frac{3}{4}-\frac{1}{3}\right).\frac{15}{7}\)
\(=\frac{5}{12}.\frac{15}{7}\)
\(=\frac{25}{28}\)
\(c)\frac{7}{12}-\frac{3}{4}.\frac{5}{6}\)
\(=\frac{7}{12}-\frac{5}{8}\)
\(=\frac{-1}{24}\)
\(d)\left(2\frac{1}{3}+1\frac{3}{4}\right).\frac{12}{13}\)
\(=\left(\frac{7}{3}+\frac{7}{4}\right).\frac{12}{13}\)
\(=\frac{49}{12}.\frac{12}{13}\)
\(=\frac{49}{13}\)
a)\(\frac{5}{6}+\frac{-1}{2}+\frac{3}{4}=\frac{10}{12}-\frac{6}{12}+\frac{9}{12}=\frac{10-6+9}{12}=\frac{13}{12}\)
b)\(\left\{0,75-\frac{1}{3}\right\}:\frac{7}{15}=\left\{\frac{3}{4}-\frac{1}{3}\right\}.\frac{15}{7}=\left\{\frac{9}{12}-\frac{4}{12}\right\}.\frac{15}{7}=\frac{5}{12}.\frac{15}{7}=\frac{75}{84}\)
c)\(\frac{7}{12}-\frac{3}{4}.\frac{5}{6}=\frac{7}{12}-\frac{5}{8}=\frac{14}{24}-\frac{15}{24}=\frac{-1}{24}\)
d)\(\left\{2\frac{1}{3}+1\frac{3}{4}\right\}.\frac{12}{13}=\left\{\frac{7}{3}+\frac{7}{4}\right\}.\frac{12}{13}=\left\{\frac{28}{12}+\frac{21}{12}\right\}.\frac{12}{13}=\frac{39}{12}.\frac{12}{13}=3\)
\(a,=\frac{24}{60}+\left(-\frac{10}{60}\right)-\frac{45}{60}+\frac{40}{60}\)
\(=\frac{24+\left(-60\right)-45+40}{60}\)
\(=-\frac{41}{60}\)
a, \(A=\frac{2}{5}+\frac{-1}{6}-\frac{3}{4}-\frac{-2}{3}\)
\(A=\left(\frac{2}{5}-\frac{3}{4}\right)+\left(\frac{-1}{6}-\frac{-2}{3}\right)\)
\(A=\left(\frac{8}{20}-\frac{15}{20}\right)+\left(\frac{-3}{18}-\frac{-12}{18}\right)\)
\(A=\frac{-7}{20}+\frac{1}{2}\)
\(\Rightarrow A=\frac{-7}{20}+\frac{10}{20}=\frac{3}{20}\)
b, \(B=\frac{7}{10}-\frac{-3}{4}+\frac{-5}{6}-\frac{1}{5}+\frac{-2}{3}\)
\(B=\left(\frac{7}{10}-\frac{1}{5}\right)+\left(\frac{-5}{6}+\frac{-2}{3}\right)-\frac{-3}{4}\)
\(B=\left(\frac{7}{10}-\frac{2}{10}\right)+\left(\frac{-5}{6}+\frac{-4}{6}\right)-\frac{-3}{4}\)
\(B=\frac{1}{2}+\frac{-3}{2}-\frac{-3}{4}\)
\(B=\frac{2}{4}+\frac{-6}{4}-\frac{-3}{4}\)
\(\Rightarrow B=\frac{2+-6+3}{4}=\frac{-1}{4}\)
c, \(C=\frac{\left(\frac{1}{2}-0,75\right)\times\left(0,2-\frac{2}{5}\right)}{\frac{5}{9}-1\frac{1}{12}}\)
\(C=\frac{\left(\frac{1}{2}-\frac{3}{4}\right)\times\left(\frac{1}{5}-\frac{2}{5}\right)}{\frac{5}{9}-\frac{1\times12+1}{12}}\)
\(C=\frac{\left(\frac{2}{4}-\frac{3}{4}\right)\times\left(\frac{-1}{5}\right)}{\frac{5}{9}-\frac{13}{12}}\)
\(C=\frac{\left(\frac{-1}{4}\right)\times\left(\frac{-1}{5}\right)}{\frac{60}{108}-\frac{117}{108}}\)
\(C=\frac{\frac{1}{20}}{\frac{-19}{36}}=\frac{1}{20}\div\frac{-19}{36}=\frac{1}{20}\times\frac{36}{-19}\)
\(\Rightarrow C=\frac{36}{-380}=\frac{-9}{95}\)
d, \(D=\frac{\frac{2}{3}+\frac{2}{7}-\frac{1}{4}}{-1-\frac{3}{7}+\frac{3}{28}}\)
\(D=\frac{\frac{56}{84}+\frac{24}{84}-\frac{21}{84}}{\frac{-10}{7}+\frac{3}{28}}\)
\(D=\frac{\frac{59}{84}}{\frac{-40}{28}+\frac{2}{28}}=\frac{59}{84}\div\frac{-37}{28}=\frac{59}{84}\times\frac{28}{-37}\)
\(\Rightarrow D=\frac{1652}{-3108}=\frac{-59}{111}\)