media aritmetica a nr 0,(2) si 0,(6) este... (cu rezolvare va rog, 30 pnt)

Salut!

0,(a)=a/9

Dupa regula asta facem si la restul:

0,(2)=2/9

0,(6)=6/9(aici am putea sa simplificam, dar la media aritmetica ar trebui iar sa amplific ca sa se poata aduma)

Ma=(a+b)/2

Ma=(2/9 + 6/9)/2

Ma=8/9 / 2

Ma= 8/9 x 1/2

Ma=4/9

Succes!

Scriem sub forma de faractii numerele

0,(2) = 2/9

0,(6) = 6/9 = 2/3

[tex]\bf Ma = \dfrac{\dfrac{2}{9}+\dfrac{6}{9} }{2}[/tex]

[tex]\bf Ma = \dfrac{\dfrac{2+6}{9}}{2}[/tex]

[tex]\bf Ma = \dfrac{\dfrac{8}{9}}{2}\\\\\\\bf Ma = \dfrac{8}{9}:\dfrac{2}{1}\\\\\\\bf Ma = \dfrac{8}{9}\cdot\dfrac{1}{2}\\\\\\\bf Ma = \dfrac{\not8}{9}\cdot\dfrac{1}{\not2}\\\\\\\bf Ma = \dfrac{4\cdot1}{9\cdot1}\\\\\\\boxed{\bf Ma = \dfrac{4}{9}}[/tex]