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a ) ( 1978 x 1979 + 1980 x 21 + 1958 ) / ( 1980 x 1979 - 1978 x 1979 ) = 1978 x 1979 + 1980 / 1979 . ( 1980 - 1978 )
= 0/1979
(1978.1979+1980.21+1958)/(1980.1979+1978...
= (1978.1979+1979.21 + 21 + 1958 )/(1980.1979+1978.1979)
= (1978.1979+1979.21 + 1979 )/[(1980+1978).1979)]
= [(1978 + 21+1).1979]/[(1980+1978).1979)] = (2000.1979)/(2.1979.1979)
= 2000/(2.1979)=1000/1979
a)\(\frac{1978x1979+1980x21+1958}{1980x1979-1978x1979+100}\)
\(=\frac{1978x1979+\left(1+1979\right)x21+1958}{\left(1980-1978\right)x1979+100}\)
\(=\frac{1978x1979+1979x21+21+1958}{2x1979+2x50}\)
\(=\frac{1979x\left(1978+21\right)+\left(21+1958\right)}{2x\left(1979+50\right)}\)
\(=\frac{1979x1999+1979x1}{2x2029}\)
\(=\frac{1979x2000}{2x2029}\)
\(=\frac{1979000}{2029}\)
a,\(\frac{2015.2016+2015-1}{2014+2015.2016}=\frac{2015.2016+2014}{2014+2015.2016}=1\)\(1\)
b,\(=1-\frac{1}{5}+\frac{1}{5}...-\frac{1}{2011}+\frac{1}{2011}-\frac{1}{2015}=1-\frac{1}{2015}=\frac{2014}{2015}\)
c,\(=\frac{12}{35}+\frac{12}{35}+\frac{12}{35}+\frac{12}{35}=\frac{12}{35}.4=\frac{48}{35}\)
a ) \(\frac{2016\cdot12+2003+2000\cdot2015+2015}{2015+2015\cdot502+504\cdot2015}\)
\(=\frac{\left(2015+1\right)\cdot12+2003+2000\cdot2015+2015}{2015\cdot\left(1+502+504\right)}\)
\(=\frac{2015\cdot12+12\cdot1+2003+2000\cdot2015+2015}{2015\cdot1007}\)
\(=\frac{2015\cdot12+\left(12\cdot1+2003\right)+2000\cdot2015+2015}{2015\cdot1007}\)
\(=\frac{2015\cdot12+2015+2000\cdot2015+2015}{2015\cdot1007}\)
\(=\frac{2015\cdot\left(12+1+2000+1\right)}{2015\cdot1007}\)
\(=\frac{2015\cdot2014}{2015\cdot1007}\)
\(=2\)
b ) \(\frac{1978\cdot1979+1980\cdot21+1958}{1980\cdot1979-1978\cdot1979}\)
\(=\frac{1978\cdot1979+\left(1979+1\right)\cdot21+1958}{\left(1980-1978\right)\cdot1979}\)
\(=\frac{1979\cdot1978+1979\cdot21+21\cdot1+1958}{2\cdot1979}\)
\(=\frac{1978\cdot1979+1979\cdot21+1979}{2\cdot1979}\)
\(=\frac{\left(1978+21+1\right)\cdot1979}{2\cdot1979}\)
\(=\frac{2000\cdot1979}{2\cdot1979}\)
\(=1000\)