(1) Suppose x = 32.12353535... . Then 100x = 3212.353535... and 10000x = 321235.353535... .
Subtracting these gives
10000x - 100x = 321235.353535... - 3212.353535...
9900x = 321235 - 3212
9900x = 318023
x = 318023/9900
(2) By the same process as above, we start with
x = 2.333...
y = 4.151515...
Then
10x = 23.333...
==> 10x - x = 23.333... - 2.333...
==> 9x = 23 - 2
==> x = 21/9
and
100y = 415.151515...
==> 100y - y = 415.151515... - 4.151515
==> 99y = 415 - 4
==> y = 411/99
After this, we get
x + y = 2.333... + 4.151515...
==> x + y = 21/9 + 411/99
==> x + y = 231/99 + 411/99
==> x + y = 642/99 = 214/33