\(\dfrac{-9}{46}\)-4\(\dfrac{1}{23}\):(3\(\dfrac{1}{4}\)-x:\(\dfrac{3}{5}\))+2\(\dfrac{8}{23}\)=1
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\(a,\dfrac{3}{5}+\dfrac{-5}{9}=\dfrac{27-25}{45}=\dfrac{2}{49}.\)
\(c,\dfrac{-27}{23}+\dfrac{5}{21}+\dfrac{4}{23}+\dfrac{16}{21}+\dfrac{1}{2}=\dfrac{-23}{23}+\dfrac{21}{21}+\dfrac{1}{2}=-1+1+\dfrac{1}{2}=\dfrac{1}{2}.\)
\(d,\dfrac{-8}{9}+\dfrac{1}{9}.\dfrac{2}{9}+\dfrac{1}{9}.\dfrac{7}{9}=\dfrac{-8}{9}+\dfrac{1}{9}.\left(\dfrac{2}{9}+\dfrac{7}{9}\right)=\dfrac{-8}{9}+\dfrac{1}{9}.1=\dfrac{-8+1}{9}=\dfrac{-7}{9}.\)
a) \(4.\left(-\dfrac{1}{2}\right)^3-2.\left(-\dfrac{1}{2}\right)^2+3.\left(-\dfrac{1}{2}\right)+1\)
\(=4.\left(-\dfrac{1}{8}\right)-2.\dfrac{1}{4}+3.\left(-\dfrac{1}{2}\right)+1\)
\(=-\dfrac{1}{2}-\dfrac{1}{2}-\dfrac{3}{2}+1\)
\(=-\dfrac{3}{2}\)
b) \(8.\sqrt{9}-\sqrt{64}\)
\(=8.3-8\)
\(=24-8\)
\(=16\)
c) \(\sqrt{\dfrac{9}{16}}+\dfrac{25}{46}:\dfrac{5}{23}-\dfrac{7}{4}\)
\(=\dfrac{3}{4}+\dfrac{5}{2}-\dfrac{7}{4}\)
\(=-1+\dfrac{5}{2}\)
\(=\dfrac{3}{2}\)
a, \(\dfrac{7}{8}\) \(\times\) \(\dfrac{3}{13}\) + \(\dfrac{4}{9}\) \(\times\) \(\dfrac{4}{13}\)
= \(\dfrac{1}{13}\) \(\times\)( \(\dfrac{21}{8}\) + \(\dfrac{16}{9}\))
= \(\dfrac{1}{13}\) \(\times\)( \(\dfrac{189}{72}\) + \(\dfrac{128}{72}\))
= \(\dfrac{1}{13}\) \(\times\) \(\dfrac{317}{73}\)
= \(\dfrac{317}{949}\)
b, \(\dfrac{6}{5}\) + \(\dfrac{7}{3}\) + \(\dfrac{8}{9}\)
= \(\dfrac{54}{45}\) + \(\dfrac{105}{45}\) + \(\dfrac{40}{45}\)
= \(\dfrac{199}{45}\)
c, 23 : \(\dfrac{5}{14}\) + \(\dfrac{6}{7}\) + \(\dfrac{4}{9}\)
= \(\dfrac{322}{5}\) + \(\dfrac{6}{7}\) + \(\dfrac{4}{9}\)
= \(\dfrac{20286}{315}\) + \(\dfrac{270}{315}\) + \(\dfrac{140}{315}\)
= \(\dfrac{20696}{315}\)
d, 4\(\dfrac{1}{4}\) + 7\(\dfrac{3}{7}\) - 2\(\dfrac{4}{17}\)
= 4 + \(\dfrac{1}{4}\) + 7 + \(\dfrac{3}{7}\) - 2 - \(\dfrac{4}{17}\)
= (4+7-2) + (\(\dfrac{1}{4}\) + \(\dfrac{3}{7}\) - \(\dfrac{4}{17}\))
= 9 + \(\dfrac{119}{476}\) + \(\dfrac{204}{476}\) - \(\dfrac{112}{476}\)
= 9\(\dfrac{211}{476}\) = \(\dfrac{4495}{476}\)
e, 8 - (9\(\dfrac{2}{11}\) + \(\dfrac{8}{33}\))
= 8 - 9 - \(\dfrac{2}{11}\) - \(\dfrac{8}{33}\)
= -1 - \(\dfrac{2}{11}\) - \(\dfrac{8}{33}\)
= \(\dfrac{-33}{33}\) - \(\dfrac{-6}{33}\) - \(\dfrac{8}{33}\)
= - \(\dfrac{47}{33}\)
a: \(\left(\frac{9}{25}-2,18\right):\left(3\frac45+0,2\right)\)
=(0,36-2,18):(3,8+0,2)
=-1,82:4
=-0,455
b: \(\frac38\cdot19\frac13-\frac38\cdot33\frac13\)
\(=\frac38\cdot\left(19+\frac13-33-\frac13\right)\)
\(=\frac38\cdot\left(-14\right)=-\frac{42}{8}=-\frac{21}{4}\)
c: \(1\frac{4}{23}+\frac{5}{21}-\frac{4}{23}+0,5+\frac{16}{21}\)
\(=\left(1+\frac{4}{23}-\frac{4}{23}\right)+\left(\frac{5}{21}+\frac{16}{21}\right)+0,5\)
=1+1+0,5
=2,5
d: Sửa đề: \(\frac{2^{12}\cdot3^5-4^6\cdot81}{2^{12}\cdot3^6+8^4\cdot3^5}\)
\(=\frac{2^{12}\cdot3^5-2^{12}\cdot3^4}{2^{12}\cdot3^6+2^{12}\cdot3^5}=\frac{2^{12}\cdot3^4\cdot\left(3-1\right)}{2^{12}\cdot3^5\cdot\left(3+1\right)}=\frac13\cdot\frac24=\frac13\cdot\frac12=\frac16\)
e: \(4\cdot\left(-\frac12\right)^2-2\cdot\left(-\frac12\right)^2+3\cdot\left(-\frac12\right)+1\)
\(=2\cdot\frac14-\frac32+1\)
=1/2-3/2+1
=-2/2+1
=-1+1
=0
g: \(\sqrt{\frac{4}{81}}:\sqrt{\frac{25}{81}}-1\frac25\)
\(=\frac29:\frac59-\frac75=\frac25-\frac75\)
=-5/5
=-1
\(\Leftrightarrow-\dfrac{93}{23}:\left(\dfrac{13}{4}-x\cdot\dfrac{5}{3}\right)=1-\dfrac{99}{46}=-\dfrac{53}{46}\)
\(\Leftrightarrow\dfrac{13}{4}-\dfrac{5}{3}x=-\dfrac{99}{23}:-\dfrac{53}{46}=\dfrac{198}{53}\)
=>5/3x=-103/212
hay x=-309/1060
a: \(-\frac47+\frac{15}{4}-\left(\frac{11}{4}+\frac37+\frac12-\frac13\right)\)
\(=-\frac47+\frac{15}{4}-\frac{11}{4}-\frac37-\left(\frac12-\frac13\right)\)
\(=\left(-\frac47-\frac37\right)+\left(\frac{15}{4}-\frac{11}{4}\right)-\frac16=\left(-1\right)+1-\frac16=-\frac16\)
b: \(\frac15\left(\frac12-\frac13\right):\left(-\frac{9}{10}\right)+\frac{-7}{3}\)
\(=\frac15\cdot\frac16\cdot\frac{10}{-9}+\frac{-7}{3}=\frac{1}{3\cdot\left(-9\right)}+\frac{-7}{3}\)
\(=-\frac{1}{27}-\frac73=-\frac{1}{27}-\frac{63}{27}=-\frac{64}{27}\)
c: \(-\frac{20}{23}+\frac23-\frac{3}{23}+\frac25+\frac{7}{15}\)
\(=\left(-\frac{20}{23}-\frac{3}{23}\right)+\left(\frac23+\frac25+\frac{7}{15}\right)\)
\(=-1+\frac{10+6+7}{15}=-1+\frac{23}{15}=\frac{8}{15}\)
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