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$\textbf{a)}$
$A=\dfrac{\left(\dfrac23\right)^3\cdot\left(-\dfrac34\right)^2\cdot(-1)^{2019}}{36\cdot\dfrac15\cdot\left(\dfrac25\right)^2\cdot\left(-\dfrac5{12}\right)^3}$
$=\dfrac{\dfrac8{27}\cdot\dfrac9{16}\cdot(-1)}{36\cdot\dfrac15\cdot\dfrac4{25}\cdot\left(-\dfrac{125}{1728}\right)}$
$=\dfrac{-\dfrac16}{-\dfrac5{12}}$
$=\dfrac16\cdot\dfrac{12}5$
$=\dfrac25.$
$\textbf{b)}$
$B=\dfrac1{19}+\dfrac9{19\cdot29}+\dfrac9{29\cdot39}+\cdots+\dfrac9{2009\cdot2019}$
$=\dfrac1{19}+\left(\dfrac1{19}-\dfrac1{29}\right)+\left(\dfrac1{29}-\dfrac1{39}\right)+\cdots+\left(\dfrac1{2009}-\dfrac1{2019}\right)$
$=\dfrac1{19}+\dfrac1{19}-\dfrac1{2019}$
$=\dfrac2{19}-\dfrac1{2019}$
$=\dfrac{2\cdot2019-19}{19\cdot2019}$
$=\dfrac{4019}{38361}.$
$\textbf{a)}$
$\left(-\dfrac34+\dfrac27\right):\dfrac27+\left(-\dfrac14+\dfrac57\right):\dfrac23$
$=\left(-\dfrac{13}{28}\right)\cdot\dfrac72+\dfrac{13}{28}\cdot\dfrac32$
$=-\dfrac{13}{8}+\dfrac{39}{56}$
$=-\dfrac{13}{14}.$
$\textbf{b)}$
$\left(-\dfrac13\right)^2\cdot\dfrac4{11}+\dfrac7{11}\cdot\left(-\dfrac13\right)^2$
$=\dfrac19\left(\dfrac4{11}+\dfrac7{11}\right)$
$=\dfrac19.$
a) 12. \(\frac{4}{9}\)+\(\frac{4}{3}\)=\(\frac{16}{3}\)+\(\frac{4}{3}\)=\(\frac{20}{3}\)
b) (\(\frac{-5}{7}\)) . (12,5+1,5)= (\(\frac{-5}{7}\)).14=-10
a) \(12.\left(-\frac{2}{3}\right)^2+\frac{4}{3}=12.\frac{4}{9}+\frac{4}{3}=\frac{16}{3}+\frac{4}{3}=\frac{20}{3}\)
b) \(12,5.\left(-\frac{5}{7}\right)+1,5.\left(-\frac{5}{7}\right)=-\frac{5}{7}.\left(12,5+1,5\right)=-\frac{5}{7}.14=-10\)
c) \(1:\left(\frac{2}{3}-\frac{3}{4}\right)^2=1:\left(-\frac{1}{12}\right)^2=1:\frac{1}{144}=1.144=144\)
d) \(15.\left(-\frac{2}{3}\right)^2-\frac{7}{3}=15.\frac{4}{9}-\frac{7}{3}=\frac{20}{3}-\frac{7}{3}=\frac{13}{3}\)
e) \(\frac{1}{2}\sqrt{64}-\sqrt{\frac{4}{25}}+\left(-1\right)^{2007}=\frac{1}{2}.8-\frac{2}{5}+\left(-1\right)=4-\frac{2}{5}-1=\frac{13}{5}\)
\(A=\frac{15}{34}+\frac{7}{21}+\frac{9}{34}-1\frac{15}{17}+\frac{2}{3}=\frac{15}{34}+\frac{7}{21}+\frac{9}{34}-\frac{64}{34}+\frac{14}{21}=\left(\frac{15}{34}+\frac{9}{34}-\frac{64}{34}\right)+\left(\frac{7}{21}+\frac{14}{21}\right)=\frac{30}{34}+\frac{21}{21}=\frac{15}{17}+1=\frac{32}{17}\)
Bài 1 :\(a,=\frac{4}{1.3}.\frac{9}{2.4}.\frac{16}{3.5}...\frac{100^2}{99.101}\)
\(=\frac{2.3.4...100}{1.2.3...99}.\frac{2.3.4...100}{3.4...101}\)
\(=100.\frac{2}{101}=\frac{200}{101}\)
chúc bạn học tốt !
chúc bạn học tốt !
chúc bạn học tốt !
chúc bạn học tốt !
\(A = {1\over2}-{3\over4}+{5\over6}-{7\over12}={6\over12}-{9\over12}+{10\over12}-{7\over12}\)\(={0\over12}=0\)
\(A=\left(-\frac{2}{3}+\frac{5}{9}\right)\cdot \frac{3}{4}+\left(\frac{11}{9}-\frac{1}{3}\right)\cdot \frac{3}{4}\)Câu 2:
\(B=23\frac{1}{4}\cdot \left(-\frac{3}{7}\right)-13\frac{1}{4}\cdot \left(-\frac{3}{7}\right)\)Câu 3:
\(C=\frac{1}{2}\cdot \sqrt{64}-\sqrt{\frac{4}{25}}+(-1)^{2026}\)
Huh
Huh
1: \(A=\left(-\frac23+\frac59\right)\cdot\frac34+\left(\frac{11}{9}-\frac13\right)\cdot\frac34\)
\(=\frac34\left(-\frac23+\frac59+\frac{11}{9}-\frac13\right)\)
\(=\frac34\left(\frac{16}{9}-1\right)=\frac34\cdot\frac79=\frac{21}{36}=\frac{7}{12}\)
2: \(B=23\frac14\cdot\left(-\frac37\right)-13\frac14\cdot\left(-\frac37\right)\)
\(=-\frac37\left(23+\frac14-13-\frac14\right)\)
\(=-\frac37\cdot10=-\frac{30}{7}\)
3: \(C=\frac12\cdot\sqrt{64}-\sqrt{\frac{4}{25}}+\left(-1\right)^{2026}\)
\(=\frac12\cdot8-\frac25+1\)
\(=5-\frac25=\frac{23}{5}\)