b)
[tex] b)0,1(3)= \frac{13-1}{90}= \frac{12}{90}= \frac{2}{15} \\ 0,1(6)= \frac{16-1}{90}= \frac{1}{6}\\ \\0,2(27)= \frac{227-2}{990}= \frac{45}{98}\\ \\ \frac{ \frac{2}{15} +\frac{1}{6} }{ \frac{6}{10} }+ \frac{45}{98}= \\ \\ \frac{12+15}{90}* \frac{10}{6}+ \frac{45}{98}= \frac{27}{9} \frac{3}{6}= \frac{49+45}{98}= \frac{94}{98}= \frac{47}{49} \\ \\ [/tex]
[tex]c) [3,(8)-1,5]:4,3 \\ 1,5= \frac{15}{10}= \frac{3}{2} \\ \\ 3,(8)= \frac{38-3}{9}= \frac{35}{9}\\ \\4,3= \frac{43}{10} [/tex]
[tex] (\frac{35}{9}- \frac{3}{2}): \frac{43}{10}= \frac{35*2-3*9}{18}* \frac{10}{43}= \\ \\ =\frac{70-27}{18}* \frac{10}{43} \\ \\ = \frac{43}{18}*\frac{10}{43} \\ \\ = \frac{10}{18}=\frac{5}{9} [/tex]
[tex]e) \frac{5}{6}+\frac{5}{6}:3 \frac{1}{3}-\frac{3}{20}= \\ \\\frac{5}{6}+\frac{5}{6}:\frac{3*3+1}{3}-\frac{3}{20}= \\ \\ \frac{5}{6}+\frac{5}{6}: \frac{10}{3}-\frac{3}{20}= \\ \\ \frac{5}{6}+\frac{5}{6}* \frac{3}{10}-\frac{3}{20}= \\ \\ \frac{5}{6}+\frac{1}{4}-\frac{3}{20}= \\ \\ \frac{5*10+15*1-3*3}{60}= \frac{50+15-9}{60} = \frac{56}{60}= \frac{14}{15} [/tex]
[tex]f) [5,(6)+4,5]:0,61+3,(3)= \\ \\ 5,(6)= \frac{56-5}{9}= \frac{51}{9} \\ \\ 3,(3)= \frac{33-3}{9}= \frac{10}{3} \\ \\ 4,5= \frac{45}{10}= \frac{9}{2} \\ \\[/tex]
[tex] [5,(6)+4,5]:0,61+3,(3)= [ \frac{51}{9}+ \frac{9}{2}] : \frac{61}{100}+ \frac{10}{3}= \\ \\ (\frac{51*2+9*9}{18})* \frac{100}{61}+ \frac{10}{3}= \frac{102+81}{18}* \frac{100}{61}+ \frac{10}{3} \\ \\ [/tex]
