Question

sabendo que K vale 0,222..+4/9 - 45,444..., calcule o valor de K

Answer 1

0,222........ = 2/9 ****
45,444.....   = ( 454 - 45 )9  = 409/9  
2/9 + 4/9- 409/9 =
mmc = 9
( 2 + 4 - 409)/9 = - 403/9 ***

Answer 2

x = 0,2222...
10x = 2,2222...
10x = 2 + 0,22222...
10x = 2 + x
10x - x = 2
9x = 2

$x= \dfrac{2}{9}$

45,444...
45 + 0,4444...

y = 0,44444... 
10y = 4,44444...
10y = 4 + 0,44444...
10y = 4 + y
10y - y = 4
9y = 4

$y= \dfrac{4}{9}$

$45+ \dfrac{4}{9}\\\\\\ \dfrac{405+4}{9}\\\\\\ \dfrac{409}{9}$


$\dfrac{2}{9}+ \dfrac{4}{9}- \dfrac{409}{9}\\\\\\ k=-\dfrac{403}{9}$