Question

Se a/b é uma fração geratriz periódica 75,2713713713, com a e b positivos e primos, o valor de a +b é

Answer 1

$\mathsf{x=75,\overline{2713}}\\\mathsf{x=75,2713713713...\times10000}\\\mathsf{10000x=752713,713713... \times1000}\\\mathsf{10000000x=752713713,713713...}$

$\mathsf{-\underline{\begin{cases}10000000x=752713713,\cancel{713713713... }\\10000x=752713,\cancel{713713713...}\end{cases}}}$

$\mathsf{9990000x=751961000}\\\mathsf{x=\dfrac{751961000}{9990000}}\\\mathsf{x=\dfrac{751961}{9990}}$ $a=751961\\b=9990$

$\boxed{\boxed{\mathsf{a+b=751961+9990=761951}}}$