Question

Com fração geratriz, efetue:

1,44444... + 0,15555...

Answer 1

$Ola'~~~\mathbb{BIANCA} \\ \\ 1,4444......+0,15555.... \\ \\ \underline{resoluc\~ao}~ \\ \\ \underbrace{1,4444....}_{ (\frac{14-1}{10-1}) }+\underbrace{0,1555...}_{ (\frac{15-1}{100-10}) } \\ \\ \frac{13}{9}+ \frac{14}{90} \\ \\ \frac{90.13+9.14}{9.90} = \frac{\not9(10.13+14)}{\not9.90}= \frac{10,13+14}{90} = \frac{\not2(5.13+7)}{\not2.45}= \boxed{\boxed{\frac{8}{5}} } \\ \\ \mathbb{ttttttttttttttttttttttttttttttt} \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Espero~ter~ajudado!!$

Answer 2

Com fração geratriz, efetue:

1,44444... + 0,15555...

     x      =   1,444... ( 10) multiplica
 10x      = 14,444...

10x = 14,444...
   x  =   1,444...
---------------------subtrai
  9x = 13,000...

9x = 13
x = 13/9

      x       =     0,1555...  ( 10) multiplica
  10x       =     1,555...    (10) multiplica
100x       =   15,555...

100x = 15,555...
  10x =   1,555... subtrai
----------------------------------
  90x = 14,000...

90x =14
x = 14/90

assim




1,44444... + 0,15555...

     13     14           (mmc) 9,90 | 2
 ------ + -----                      9,45| 3
      9      90                       3,15| 3
                                          1,  5| 5
 10(13) + 1(14)                   1,1/     = 2x3x3x5 =  90
--------------------
           90

130  + 14
--------------
      90

144                      144 : 18        8
------  simplifica -------------- = --------
 90                         90 : 18        5