If 5/6 is divided by a certain fraction a/b the result is 1/4. What is the fraction a/b?

To start, set up and equation using what you know.

(5/6) / (a/b) = (1/4)

Then, you need to isolate a/b. To do this multiply both sides by a/b and then divide by 1/4

5/6 = (a/b) (1/4)

(5/6) / (1/4) = (a/b)

Next, simplify the left side. To do this, take the inverse of 1/4 (which is 4) and multiply by 5/6 (this is also know as 'flip the second guy and multiply').

(5/6) • 4 = a/b

20/6 = a/b

Lastly, simplify to get the final answer.

10/3 = a/b