# 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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