Explicație pas cu pas:
a)
[tex]3.1 + 3.(1) = \frac{31}{10} + \frac{31 - 3}{9} = \frac{^{9)} 31}{10} + \frac{^{10)}28}{9} = \frac{279 + 280}{90} = \frac{559}{90} = 6.2(1)[/tex]
b)
[tex]0.02 + 0.(02) = \frac{2}{100} + \frac{2}{99} = \frac{^{99)} 1}{50} + \frac{^{50)}2}{99} = \frac{99 + 100}{4950} = \frac{199}{4950} = 0.04(02)[/tex]
c)
[tex]2.(3) + 1.(2) = \frac{23 - 2}{9} + \frac{12 - 1}{9} = \frac{21}{9} + \frac{11}{9} = \frac{21 + 11}{9} = \frac{32}{9} = 3.(5)[/tex]
d)
[tex]0.(14) + 0.(41) = \frac{14}{99} + \frac{41}{99} = \frac{14 + 41}{99} = \frac{55}{99} = 0.(5)[/tex]
e)
[tex]0.(1) + 0.(12) + 0.(123) = \frac{^{1221)} 1}{9} + \frac{^{111)} 12}{99} + \frac{^{11)}123}{999} = \frac{1221 + 1332 + 1353}{10989} = \frac{3906}{10989} = \frac{434}{1221} = 0.(355446)[/tex]
f)
[tex]2.1(2) - 1.2(1) = \frac{212 - 21}{90} - \frac{121 - 12}{90} = \frac{191 - 109}{90} = \frac{82}{90} = \frac{41}{45} = 0.9(1)[/tex]
