Among all fractions x that have a positive integer numerator and denominator and satisfy 9/11 ≤ x ≤ 11/13 which fraction has the smallest denominator?
plz wiil mark brainiest

We want to find a fraction a/b such that

This is true if and only if

We can choose a value for a only if the two extremes include at least one integer, i.e. if

Solving for b, we have

So, the smallest fraction is given for . We have

Solving for a, we have a=30.

The fraction 30/36 can be simplified to 5/6. So, we have

and this is the smallest possible denominator.

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.