when a fraction is divided by the difference of 1/2 and 1/6, we get 2/3. what is the fraction?

Difference of 1/2 and 1/6 = 3/6 - 1/6

                                    = 3-1/6

                                    = 2/6 (simplified to 1/3)

Let the fraction be x

Given, x divided by 1/3 = 2/3

To find x, we have to transpose 1/3 to RHS which then gives,

x = 1/3*2/3

x = 1*2/3*3

x = 2/9

Thus, the fraction is 2/9.

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 To verify the answer:

2/9 (the fraction x) divided by 1/3 (the difference of 1/2 and 1/6)

2/9 divided by 1/3

So, 2/9*3/1

Then, 2*3/9*1

Which gives, 6/9

Simplifying it gives, 2/3

Thats the fraction you gave in the question!

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