#### Jomo

##### Elite Member

- Joined
- Dec 30, 2014

- Messages
- 3,526

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

What I did was say that (10a+b)/99 = a/b and then b(10a+b) = 99a.

Since the one's place on the lhs comes from b

Then by trial and error I found a=b=9. Of course after seeing the answer I realized that I should have seen that one immediately but probably not any others (if in fact there were any).

In any case I would like to see how others would have solved this.

Thanks,

Steven

What I did was say that (10a+b)/99 = a/b and then b(10a+b) = 99a.

Since the one's place on the lhs comes from b

^{2}I realized that a can only be 1, 4, 5, 6 and/or 9.Then by trial and error I found a=b=9. Of course after seeing the answer I realized that I should have seen that one immediately but probably not any others (if in fact there were any).

In any case I would like to see how others would have solved this.

Thanks,

Steven

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