Explicație pas cu pas:
1.
[tex]a)\frac{3}{2}\\\\b) -\frac{5}{7}\\\\c) \frac{17}{8}\\\\d)2\\\\e)-\frac{1}{3}\\\\f)-8\\\\g)\frac{25}{100}=\frac{1}{4} , invers = 4\\\\h) 0.(3) = \frac{3}{9}, invers = \frac{9}{3}=3\\\\i) \frac{1}{9}\\\\j) 1.2 = \frac{12}{10}=\frac{6}{5},invers=\frac{5}{6}\\\\k) -0.(6)=\frac{6}{9}, invers = -\frac{9}{6}=-\frac{3}{2}\\\\l) 0.5(7)=\frac{57-5}{90}=\frac{52}{90}=\frac{26}{45},invers =\frac{45}{26}\\\\[/tex][tex]m)-0.75=-\frac{75}{100}=-\frac{3}{4},invers=-\frac{4}{3}\\\\n) 0,08(3)=\frac{83-8}{900}=\frac{75}{900}=\frac{15}{180}=\frac{3}{36}=\frac{1}{12},invers = 12\\\\o)-0,3(8)=-\frac{38-3}{90}=-\frac{35}{90}=-\frac{7}{18}\\\\p) 1\frac{3}{5}=\frac{1*5+3}{5}=\frac{8}{5},invers = \frac{5}{8}\\\\q) -2\frac{1}{4}=-\frac{2*4+1}{4}=-\frac{9}{4},invers = -\frac{4}{9}\\\\r) -1,1(6)=-\frac{116-11}{90}=-\frac{105}{90}=-\frac{21}{18}=-\frac{7}{6},invers =-\frac{6}{7}\\[/tex]
2.Mulțimea B conține opusele numerelor din mulțimea A:
Mulțimea C conține inversele numerelor din mulțimea A fără 0 :
[tex]\frac{1}{6} , invers=6\\\\-5,7=-\frac{57}{10},invers=\frac{10}{57}\\\\2,3=\frac{23}{10},invers=\frac{10}{23}\\\\1,(2)=\frac{12-1}{9}=\frac{11}{9}, invers=\frac{9}{11}\\\\-1,5=\frac{15}{10}=\frac{3}{2},invers=\frac{2}{3}\\\\3 , invers = \frac{1}{3}\\\\[/tex]
[tex]-\frac{5}{3},invers=-\frac{3}{5}\\\\0,91(6)=\frac{916-91}{900}=\frac{815}{900}=\frac{163}{180},invers=\frac{180}{163}\\\\-2\frac{3}{4}=-\frac{2*4+3}{4}=-\frac{11}{4},invers = -\frac{4}{11}\\\\-0,4 =-\frac{4/10}=-\frac{2}{5},invers = -\frac{5}{2}\\\\1\frac{1}{2}=\frac{1*2+1}{2}=\frac{3}{2},invers=\frac{2}{3} \\\\[/tex]
Atunci:
[tex]C=\{6;\frac{10}{57};\frac{10}{23};\frac{9}{11};\frac{2}{3};\frac{1}{3};-\frac{3}{5};\frac{180}{163};-\frac{4}{11};-\frac{5}{2};\frac{2}{3}\}[/tex]
