The fraction a/b is equals the repeating decimal 0.ababab. If a and b are single-digit positive integers, what is the value of a + b.

Answer 1

If a number equal .abababab..., then this number can be written as (10a+b)/99

So (10a+b)/99 = a/b

or (10a+b) = 99a/b

or b(10a+b) = 99a

Since a is a positive single digit number just try to solve for b when a=1, then a=2,....until you find a b that is allowable (b is also a positive single digit)

Note that on the lhs the constant will come from b² and the constant on the rhs will come from 9*a. This will rule out many values for a!