1/6 represents a fraction that has been reduced. The original answer will contain a multiple of 6 as the denominator. Since unit fractions always have the number 1 as a numerator you can write the problem this way:
1/x + 1/y = 2/xy
We know the final answer is 1/6 so we can say:
2/xy=1/6
Solve for xy:
xy=6/1 x 2/1
xy=12
Final answer (2/xy) is 2/12 which reduces to 1/6
There are only two possible combinations of unit fraction that could equal 1/16 they are:
1/12 + 1/12 = 2/12 (reduces to 1/6)
1/18 + 1/9 = 3/18 (reduces to 1/6)
