Question

If x = recurring 1.23 and y = recurring 12.3. Find x + y.

Answer 1

x= reccuring 1.23 can be written in a decimal fraction as a mixed fraction as 1 23/99
( to convert pure reccuring decimal fraction into simple fraction ,write down the repeated digits only once in numerator and place as many nines in denominator as the number of digits repeating eg; .23 = 23/99)
=( 99*1+23/99)
= 122/99
y= reccuring 12.3
= 12 3/9
=(12*9)+3/9
= 111/9
x+y = 122/99+111/9
= (122*9+99*111)/99*9
= 13.565656....
ie x+y = reccuring 13.56

or.
x= 1.23232323
y=12.33333333
x+y=13.5656565656