# Fractions with sum 1 Using all numbers 0 to 9 only once, form two fractions whose sum is 1.I have tried every possible combination but with no luck. I believe the fractions must be xx/xx + xxx/xxx but I am not sure. Any ideas are most welcome. I even tried getting all different ways to select 3 out of 10 digits, then omitting all the primes and trying to make fractions with simple values 1/3, 1/4, 2/5 etc using only different digits but again with no luck! By the way, two years ago I was given a similar one, with three fractions and without the digit 0, for which I found a solution 7/68+9/12+5/34 but now I am stuck!!

Fractions with sum 1
Using all numbers 0 to 9 only once, form two fractions whose sum is 1.
I have tried every possible combination but with no luck. I believe the fractions must be xx/xx + xxx/xxx but I am not sure. Any ideas are most welcome. I even tried getting all different ways to select 3 out of 10 digits, then omitting all the primes and trying to make fractions with simple values 1/3, 1/4, 2/5 etc using only different digits but again with no luck! By the way, two years ago I was given a similar one, with three fractions and without the digit 0, for which I found a solution 7/68+9/12+5/34 but now I am stuck!!
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$\frac{27}{054}+\frac{69}{138}=\frac{1}{2}+\frac{1}{2}=1$
Or if a leading zero is not allowed.
$\frac{135}{270}+\frac{48}{96}=\frac{1}{2}+\frac{1}{2}=1$