You should know that

\[ \frac{a}{b} + \frac{c}{d} \ne \frac{a+c}{b+d}.\]

However, if \(a, b, c, d \) are positive integers that satisfy \(\frac{a}{b} < \frac{c}{d},\) what can we say about \(\frac{a+c}{b+d} ?\)

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