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a) \(\frac{-1}{2}+\frac{-1}{9}-\frac{-3}{5}+\frac{1}{2006}-\frac{-2}{7}-\frac{7}{18}+\frac{4}{35}\)
\(=\left(\frac{-1}{2}-\frac{1}{9}-\frac{7}{18}\right)+\left(\frac{3}{5}+\frac{4}{35}\right)+\frac{1}{2006}\)
\(=\left(\frac{-9}{18}-\frac{2}{18}-\frac{7}{18}\right)+\left(\frac{21}{35}+\frac{4}{35}\right)+\frac{1}{2006}\)
\(=\left(\frac{-9-2-7}{18}\right)+\left(\frac{21+4}{35}\right)+\frac{1}{2006}\)
\(=\left(\frac{-18}{18}\right)+\left(\frac{25}{35}\right)+\frac{1}{2006}\)
\(=\left(-1\right)+\frac{5}{7}+\frac{1}{2006}\)\(=\frac{-4005}{14042}\)
b) \(\frac{1}{3}-\frac{3}{4}+\frac{3}{5}+\frac{1}{2007}-\frac{1}{36}+\frac{1}{15}-\frac{2}{9}\)
\(=\left(\frac{1}{3}+\frac{1}{2007}-\frac{2}{9}\right)-\left(\frac{3}{4}+\frac{1}{36}\right)+\left(\frac{3}{5}+\frac{1}{15}\right)\)
\(=\left(\frac{669}{2007}+\frac{1}{2007}-\frac{446}{2007}\right)-\left(\frac{27}{36}+\frac{1}{36}\right)+\left(\frac{9}{15}+\frac{1}{15}\right)\)
\(=\frac{224}{2007}-\frac{28}{36}+\frac{10}{15}\)
\(=\frac{224}{2007}-\frac{1561}{2007}+\frac{1338}{2007}\)\(=\frac{1}{2007}\)
1 - (49/9 + x -133/18) : 63/4 = 0
1 - (49/9 + x -133/18) = 0 x 63/4
1 - (49/9 + x -133/18) = 0
49/9 + x -133/18 = 1 - 0
49/9 + x -133/18 = 1
49/9 + x = 1 + 133/18
49/9 + x = 151/18
x = 49/9 +151/18
x = 53/18
a) \(\left(\frac{-3}{4}+\frac{2}{5}\right):\frac{3}{7}+\left(\frac{3}{5}+\frac{-1}{4}\right):\frac{3}{7}\)
= \(\left(-\frac{3}{4}+\frac{2}{5}+\frac{3}{5}+\frac{-1}{4}\right):\frac{3}{7}\)
= \(0:\frac{3}{7}\)
= \(0\)
b) \(\frac{2}{8}:\left(\frac{2}{9}-\frac{1}{18}\right)+\frac{7}{8}:\left(\frac{1}{36}-\frac{5}{12}\right)\)
= \(\frac{1}{4}:\frac{1}{6}+\frac{7}{8}:\frac{-7}{18}\)
=\(\frac{1}{4}.6+\frac{7}{8}.\frac{-18}{7}\)
= \(\frac{3}{2}-\frac{3}{4}\)
= \(\frac{3}{4}\)
\(1-\left(5\frac{5}{36}+y-7\frac{7}{18}\right):15\frac{3}{4}=0\)
=>\(1-\left(\frac{185}{36}+y-\frac{133}{18}\right):\frac{63}{4}=0\)
=>\(1-\left(-\frac{9}{4}+y\right).\frac{4}{63}=0\)
=>\(1-\left(-\frac{1}{7}+\frac{4}{63}y\right)=0\)
=>\(1+\frac{1}{7}-\frac{4}{63}y=0\)
=>\(\frac{8}{7}-\frac{4}{63}y=0\)
=>\(63.\frac{8}{7}-63.\frac{4}{63}y=63.0\)
=>\(72-4y=0\)
=>\(4y=72-0\)
=>\(4y=72\)
=>\(y=72:4\)
=>\(y=18\)
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