Question

Ayúdenme pls. Es pregunta de examen de admisión.

Answer 1

1. tratemos de racionalizar el número decimal

$0.52\overline{27}=0.52+0.00\overline{27}\\ \\\\0.52\overline{27}=0.52+0.\overline{27}\div100\\ \\\\0.52\overline{27}=\dfrac{52}{100}+\dfrac{27}{99}\times\dfrac{1}{100}\\ \\ \\0.52\overline{27}=\dfrac{1}{100}\left(52+\dfrac{27}{99}\right)\\ \\ \\\\0.52\overline{27}=\dfrac{1}{100}\left(52+\dfrac{3}{11}\right)\\ \\ \\\\\\0.52\overline{27}=\dfrac{1}{100}\times\dfrac{575}{11}\\ \\ \\\\0.52\overline{27}=\dfrac{575}{1100}$

2. Ahora traduzcamos el problema

$\dfrac{4k+11}{11k+11}=\dfrac{575}{1100}$

3. Resolvamos

$\dfrac{4k+11}{11k+11}=\dfrac{575}{1100}=\dfrac{23}{44}=\dfrac{23r}{44r}\\ \\\\4k+11=23r\wedge 11k+11=44r\\ \\4k+11=23r\wedge k+1=4r\\ \\4k+11=23r\wedge k=4r-1\\\\4(4r-1)+11=23r\wedge k=4r-1\\\\r=1\\ \\\\\text{Entonces la fracci\'on es: }\dfrac{23}{44}$

4. Respuesta 21