Question

cercetati daca este reductibila fractia 8·10la puterea n +1 / 10 la puterea n + 26 , unde n ∈ N

Answer 1

   
[tex]\displaystyle\\ \frac{8 \times 10^n+ 1}{10^n+26}=\\\\\\ =\frac{8 \times 1\underbrace{0000000.....000000}_{\text{n zerouri}}+1}{1\underbrace{0000000.....000000}_{\text{n zerouri}}+26}=\\\\\\ =\frac{8\underbrace{0000000.....00000}_{\text{(n-1) zerouri}}1}{1\underbrace{0000000.....0000}_{\text{(n-2) zerouri}}26} =\boxed{\frac{80000000.....000001}{10000000.....000026} }\\\\\\ \text{Suma cifrelor de la numarator este: }~8+1=9\\ \text{Suma cifrelor de la numitor este: }~1+2+6=9[/tex]


Rezulta ca si numaratorul si numitorul sunt divizibili cu 9.
Rezulta ca fractia poaate fi simplificata cu 9.
Rezulta ca fractia este reductibila.