Steven G
Elite Member
- Joined
- Dec 30, 2014
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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 b2 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
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 b2 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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