Well 22/7 isn't exactly pi, we just recognize it today as an approximation.

As for 6/21 * 11, this would of course be 22/7, as 6 factors to 2*3, 21 factors to 7*3, and 22 factors to 2*11.

So, 6/21 times 11 is (3*2*11)/(7*3) and if you cancel out the threes you get 2*11/7, or 22/7. Basically, 6/21 * 11 is just 22/7* (3/3).

It is must as simple to assume someone knew 22/7 as it is to assume they would use this other equation.