\(\eqalign{
& a)\;3,8:(2{\rm{x}}) = {1 \over 4}:2{2 \over 3} \cr
& \Rightarrow \left( {2{\rm{x}}} \right).{1 \over 4} = 3,8.2{2 \over 3} \cr
& \Rightarrow\dfrac{1}{2}x = {{19} \over 5}.{8 \over 3} \cr
& \Rightarrow x = {{152} \over {15}}:{1 \over 2} \cr& \Rightarrow x = {{152} \over {15}}.{2 \over 1} \cr
& \Rightarrow x = \dfrac{{304}}{{15}}=20{4 \over {15}} \cr} \)
b) \(\displaystyle \left( {0,25{\rm{x}}} \right):3 = {5 \over 6}:0,125\)
\( \displaystyle \Rightarrow \left( {0,25{\rm{x}}} \right).0,125 = 3.{5 \over 6}\)
\( \Rightarrow \left( {0,25{\rm{x}}} \right).0,125 = 2,5\)
\( \Rightarrow 0,25{\rm{x}} = 2,5:0,125\)
\( \Rightarrow 0,25{\rm{x}} = 20\)
\( \Rightarrow x = 20:0,25 = 80\)
c) \(0,01:2,5 = \left( {0,75x} \right):0,75\)
\(\Rightarrow \left( {0,75{\rm{x}}} \right).2,5 = 0,01.0,75\)
\(\Rightarrow {0,75{\rm{x}}} = 0,01.0,75:2,5\)
\( \Rightarrow 0,75{\rm{x}} = 0,003\)
\(\Rightarrow x = 0,003:0,75\)
\( \Rightarrow x = 0,004\)
d) \(\displaystyle {\rm{}}1{1 \over 3}:0,8 = {2 \over 3}:(0,1{\rm{x}})\)
\( \Rightarrow 1\dfrac{1}{3}.\left( {0,1x} \right) = 0,8.\dfrac{2}{3}\)
\( \displaystyle \Rightarrow {4 \over 3}.\left( {0,1{\rm{x}}} \right) = {4 \over 5}.{2 \over 3}\)
\(\displaystyle \Rightarrow \left( {0,1{\rm{x}}} \right) = {4 \over 5}.{2 \over 3}:{4 \over 3}\)
\( \displaystyle \Rightarrow 0,1{\rm{x}} = {8 \over {15}}.{3 \over 4}\)
\(\displaystyle \Rightarrow {1 \over {10}}x = {2 \over 5}\)
\(\displaystyle \Rightarrow x = {2 \over 5}:{1 \over {10}} = {2 \over 5}.{{10} \over 1} = 4\)
