# Squeezy fractions

Number Theory Level 5

Suppose $$a, b$$ are positive integers satisfying:

$$\frac {27}{197} < \frac {a}{b} < \frac {41}{299}$$.

Let $$B$$ (a positive integer) be the minimum value of $$b$$ such that there exists a positive integer value of $$a$$, say $$A$$ , such that this equation is satisfied.

Let D ( a positive integer) be the minimum value of d such that there exists a positive integer value of $$c$$ , satisfying the following inequality:

$$\frac {27}{197} < \frac {c}{d} < \frac {A}{B}$$.

Evaluate $$B+D$$.

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