To add the fractions \( \frac{5}{7} \) and \( \frac{1}{4} \), we need to find a common denominator. The least common multiple of 7 and 4 is 28.
Now, we will convert each fraction to have a denominator of 28:
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Convert \( \frac{5}{7} \): \[ \frac{5}{7} = \frac{5 \times 4}{7 \times 4} = \frac{20}{28} \]
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Convert \( \frac{1}{4} \): \[ \frac{1}{4} = \frac{1 \times 7}{4 \times 7} = \frac{7}{28} \]
Now we can add the fractions: \[ \frac{20}{28} + \frac{7}{28} = \frac{20 + 7}{28} = \frac{27}{28} \]
Therefore, \( \frac{5}{7} + \frac{1}{4} = \frac{27}{28} \).