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[tex] \frac{22}{33} ^{(11} + \frac{111}{333} ^{(111} + \frac{7777}{6666} ^{(1111} - \frac{1212}{7272} ^{(1212} = \\ \\ \frac{22 : 11}{33 : 11} + \frac{111 : 111}{333 : 111} + \frac{7777 : 1111}{6666 : 1111} - \frac{1212 : 1212}{7272 : 1212} = \\ \\ \frac{2}{3} + \frac{1}{3} + \frac{7}{6} - \frac{1}{6} = \\ \\ \frac{2 \times 2}{3 \times 2} + \frac{1 \times 2}{3 \times 2} + \frac{7}{6} - \frac{1}{6} = \\ \\ \frac{4}{6} + \frac{2}{6} + \frac{7}{6} - \frac{1}{6} = \\ \\ \frac{4 + 2 + 7 - 1}{6} = \\ \\ \frac{12}{6} = \\ \\ 2 [/tex]

22/33=(11*2)/(11*3) simplificat prin 11=2/3

111/333=111/(3*111) simplificat prin 111=1/3

7777/6666=(7*1111)/(6*1111) simplificat prin 1111=7/6

Imparti pe 1212 la grupul de cifre care se repeta, 12.

1212:12=101

12

__

==12

   12

   __

   ==

Analog cu 7272=>7272/72=101

1212/7272=(101*12)/(72*101) simplificat prin 101=12/72 simplificat prin 12=1/6

2/3+1/3+7/6-1/6=3/3+6/6=1+1=2