Express 1.32̅ + 0.3̅5̅ as a fraction in its simplest form

Answer :

We can express 1.32  + 0. 35  as a fraction As  :

Firsts we convert 1.32  into fraction form , As  :

1.32  =  1.32222222.....

1.322222222...  =  1.3  + 0.02222222..... 
Now we multiply and divide by 10 , in number 1.3 and get

1.3222222222... = 1310 + 0.02222222.....    --------------- ( 1  )

Now Let

x  =  0.02222222......  ------------- ( 2 )

Now we multiply by 100 on both hand side and get 

100x =  2.2222222......  ------------ ( 3 )

Now we subtract equation 2 from equation 3 and get

99x  =  2.2

Now we multiply by 10 on both hand side , we get

990x  =  22

Now we divide by 22 on both hand side , we get

45x  =  1

So,

145  , So

0.02222222.....  =  145 

Substitute that value in equation and get

1.3222222222... = 1310 + 145      Taking LCM we get

1.3222222222... = 13 × 9 + 2×190 = 117 +290  = 11990

Now we convert 0. 35  into fraction form , As  :

0. 35  =  0.353535353535...

Now Let

y  =  0.353535353535...  ------------- ( A )

Now we multiply by 100 on both hand side and get 

100y =  35.353535353535...  ------------ ( B )

Now we subtract equation 2 from equation 3 and get

99 y  =  35

y  = 3599
So,
0. 35  = 3599

Now we get

1.32  + 0. 35  = 11990  + 3599  taking LCM we get

1.32  + 0. 35  = 119 × 11 + 35 × 10990 

1.32  + 0. 35  = 1309 + 350990 

1.32  + 0. 35  = 1659990  ( Ans )

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