Question

aratati ca fractia ab+bc+ca in baza zece supra ac+cb+ba in baza zece este echiunitara (PRIN DESCOMPUNERE)

Answer 1

ab + bc + ca      10 a + b + 10 b + c + 10 c + a      11 a + 11 b + 11 c
-----------------  = ----------------------------------------- = ------------------------  = 
ac + cb + ba       10 a + c + 10 c + b + 10 b + a      11 a + 11 b + 11 c 


    11 × ( a + b + c )      a + b + c 
= ----------------------- = --------------- → fractie echiunitara 
    11 × ( a + b + c )      a + b + c

Answer 2

10a+b+10b+c+10c+a=11a+11b+11c=11(a+b+c)
10a+c+10c+b+10b+a=11a+11c+11b=11(a+b+c)

11(a+b+c)/11(a+b+c)=1, C.C.T.D.