[tex]1,1+1,(1)-1,1(1)=1 \frac{1}{10}+1 \frac{1}{9}-1 \frac{11-1}{90}= \frac{11}{10}+ \frac{10}{9}- \frac{100}{90}\\
\text{numitor comun 90}\\
\frac{99+100-100}{90}= \frac{99}{90}= \frac{11}{10} [/tex][tex]1,2(3)+2,02(03)-3,1(012)=1 \frac{23-2}{90}+2 \frac{203-2}{9900}-3 \frac{1012-1}{9990}....
[/tex][tex]0,(3)\cdot1,2:2,1(6)= \frac{3}{9}\cdot \frac{12}{10}:2 \frac{16-1}{90}= \frac{3}{9}\cdot \frac{12}{10}\cdot \frac{90}{195}= \frac{3\cdot12}{195}= \frac{36}{195} [/tex]
[tex]2,(2):2,2\cdot2,2(2)=2 \frac{2}{9}\cdot \frac{10}{22}\cdot2 \frac{22-2}{90}= \frac{20}{9}\cdot \frac{10}{22}\cdot \frac{200}{90}= \frac{2000}{981} [/tex]
[tex]3,1=3\frac{1}{10}= \frac{31}{10}\\
3,(1)=3 \frac{1}{9}= \frac{28}{9} \\
3,1+3,(1)= \frac{31}{10}+ \frac{28}{9}. \\
\text{Amplificam I fractie cu 9, a doua cu 10. Numitor comun 90}\\
\frac{279+280}{90}= \frac{559}{90}
[/tex]
[tex]0.02+0.(02)= \frac{2}{100}+ \frac{2}{99}= \frac{198+200}{9900}= \frac{398}{9900} [/tex]
[tex]2,(3)+1,(2)=2 \frac{3}{9}+1 \frac{2}{9}= \frac{21}{9}+ \frac{11}{9}= \frac{32}{9}[/tex]
[tex]0.(14)+0,(41)= \frac{14}{99}+ \frac{41}{99}= \frac{55}{99} [/tex]
[tex]0,(1)+0,(12)+0,(123)= \frac{1}{9}+ \frac{12}{99}+ \frac{123}{999}\\
\text{numitor comun 9x11x111, prima se amplifica cu 11x111 adica 1221}\\
\text{a doua cu 111, a treia cu 11}\\
\frac{1221+1331+1353}{10989}= \frac{3905}{10989}[/tex]
[tex]2,1(2)-1,2(1)=2 \frac{12-1}{90}-1 \frac{21-2}{90}= \frac{191}{90}- \frac{111}{90}= \frac{80}{90}= \frac{8}{9} [/tex]
[tex]2,0(1)+2,01(12)-1,2(102)=2 \frac{1}{90}+2 \frac{112-1}{9900}-1 \frac{2102-2}{9990}= \\
\frac{181}{90}+ \frac{19911}{9900}- \frac{12000}{9990}\\
\text{Numitor comun 100x9x11x111, adica 1 098 900}\\
\text{prima fractie se amplifica cu 12 210, a doua cu 111, a treia cu 110}\\
\frac{2210010+2210121-1320000}{1098900}= \frac{3100131}{1098900}
[/tex]
