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a) Ta có: \(\frac{\frac{4}{17}-\frac{4}{177}-\frac{4}{1779}}{\frac{5}{17}-\frac{5}{177}-\frac{5}{1779}}=\frac{4.\left(\frac{1}{7}-\frac{1}{177}-\frac{1}{1779}\right)}{5.\left(\frac{1}{7}-\frac{1}{177}-\frac{1}{1779}\right)}=\frac{4}{5}\)
b) \(\frac{1330}{1331}-\frac{7}{1.8}-\frac{19}{8.27}-.....-\frac{331}{1000.1331}\)
\(=\frac{1330}{1331}-\left(\frac{8-7}{1.8}+\frac{27-8}{8.27}+.....+\frac{1331-1000}{1000.1331}\right)\)
\(=\frac{1330}{1331}-\left(1-\frac{1}{8}+\frac{1}{8}-\frac{1}{27}+....+\frac{1}{1000}-\frac{1}{1331}\right)\)
\(=\frac{1330}{1331}-\left(1-\frac{1}{1331}\right)\)
\(=\frac{1330}{1331}-\frac{1330}{1331}=0\)
Vậy \(\frac{1330}{1331}-\frac{7}{1.8}-\frac{19}{8.27}-....\frac{331}{1000.1331}=0\)
CHÚC BẠN HỌC TỐT
a) \(\frac{\frac{4}{17}-\frac{4}{177}-\frac{4}{1779}}{\frac{5}{17}-\frac{5}{177}-\frac{5}{1779}}\)
\(=\frac{4\left(\frac{1}{17}-\frac{1}{177}-\frac{1}{1779}\right)}{5\left(\frac{1}{17}-\frac{1}{177}-\frac{1}{1779}\right)}\)
\(=\frac{4}{5}\)
\(\left(-\frac{5}{12}\right):\frac{7}{3}-\left(-\frac{5}{12}\right):\frac{7}{4}=\left(-\frac{5}{12}\right):\left(\frac{7}{3}-\frac{7}{4}\right)=\left(-\frac{5}{12}\right):\frac{7}{12}=-\frac{5}{7}\)
\(\left[\left(\frac{2}{5}\right)^0\right].\frac{19}{13}-\left(\frac{7}{3}\right)^{2019}.\frac{3}{7}^{2019}\)
\(=\left(\frac{2}{5}\right)^0.\frac{19}{13}-\left(\frac{7}{3}.\frac{3}{7}\right)^{2019}\)
\(=1.\frac{19}{13}-1^{2019}\)
\(=1.\frac{19}{13}-1\)
\(=\frac{19}{13}-1\)
\(=\frac{6}{13}\)
Bài giải
a, \(\left(-\frac{5}{12}\right)\text{ : }\frac{7}{3}-\left(-\frac{5}{12}\right)\text{ : }\frac{7}{4}\)
\(=\left(-\frac{5}{12}\right)\text{ : }\frac{7}{3}-\left(-\frac{5}{12}\right)\text{ : }\frac{7}{4}\)
\(=\left(-\frac{5}{12}\right)\cdot\frac{3}{7}-\left(-\frac{5}{12}\right)\cdot\frac{4}{7}\)
\(=\frac{-15}{84}+\frac{20}{84}=\frac{5}{84}\)
b, \(\left[\left(\frac{2}{5}\right)^0\right]^{2020}\cdot\frac{19}{37}-\left(\frac{7}{3}\right)^{2019}\cdot\frac{3^{2019}}{7}\)
\(=1^{2020}\cdot\frac{19}{37}-\frac{7^{2019}}{3^{2019}}\cdot\frac{3^{2019}}{7}\)
\(=\frac{19}{37}-7^{2018}\)
\(A=\frac{3\left(\frac{1}{7}-\frac{1}{17}+\frac{1}{37}\right)}{5\left(\frac{1}{7}-\frac{1}{17}+\frac{1}{37}\right)}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}}{7\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}\right)}=\frac{3}{5}+\frac{1}{7}=\frac{26}{35}\)
\(A=\frac{\frac{3}{7}-\frac{3}{17}+\frac{3}{37}}{\frac{5}{7}-\frac{5}{17}+\frac{5}{37}}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}}{\frac{7}{5}-\frac{7}{4}+\frac{7}{3}-\frac{7}{2}}=\frac{3.\left(\frac{1}{7}-\frac{1}{17}+\frac{1}{37}\right)}{5.\left(\frac{1}{7}-\frac{1}{17}+\frac{1}{37}\right)}+\frac{\frac{-1}{5}+\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{\frac{-7}{2}+\frac{7}{5}-\frac{7}{4}+\frac{7}{3}}\)
\(A=\frac{3}{5}+\frac{\frac{1}{2}-\frac{1}{5}-\frac{1}{3}+\frac{1}{4}}{\frac{7}{5}-\frac{7}{2}-\frac{7}{4}+\frac{7}{3}}=\frac{3}{5}+\frac{\frac{1}{20}}{7.\frac{-13}{60}}=\frac{3}{5}+\frac{-3}{91}=\frac{258}{455}\)
\(\frac{42}{-37}va\frac{-56}{43}\)
\(\frac{42}{-37}=\frac{-42}{37}=\frac{-1806}{1591}\)
\(\frac{-56}{37}=\frac{-2408}{1591}\)
Vì\(\frac{-1806}{1591}>\frac{-2408}{1591}\)
=>\(\frac{42}{-37}>\frac{-56}{43}\)
\(\frac{217}{18}va\frac{217}{19}\)
Vì\(\frac{217}{18}>\frac{217}{19}\)
=>\(\frac{217}{18}>\frac{217}{19}\)
\(\frac{-9}{14}va\frac{19}{-25}\)
\(\frac{-9}{14}=\frac{-225}{350};\frac{19}{-25}=\frac{-19}{25}=\frac{-266}{350}\)
Vì\(\frac{-225}{350}>\frac{-266}{350}\)
=>\(\frac{-9}{14}>\frac{19}{-25}\)
Chúc bạn học tốt!
\(P=\frac{\frac{3}{7}-\frac{3}{13}+\frac{3}{37}}{\frac{5}{7}-\frac{5}{17}+\frac{5}{37}}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}}{\frac{7}{5}-\frac{7}{4}+\frac{7}{3}-\frac{7}{2}}\)
\(=\frac{3\left(\frac{1}{7}-\frac{1}{13}+\frac{1}{37}\right)}{5\left(\frac{1}{7}-\frac{1}{17}+\frac{1}{37}\right)}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}}{-7\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}\right)}\)
\(=\frac{3}{5}+\frac{1}{-7}\)
\(=\frac{16}{35}\)