To solve the expression \( \frac{14}{25} + 0.09 - \frac{1}{4} \), we'll first convert everything into a common format, which is easier if we use decimals.
Convert \( \frac{14}{25} \) to decimal: \[ \frac{14}{25} = 0.56 \]
Convert \( \frac{1}{4} \) to decimal: \[ \frac{1}{4} = 0.25 \]
Now, we can rewrite the expression: \[ 0.56 + 0.09 - 0.25 \]
Now, add \( 0.56 \) and \( 0.09 \): \[ 0.56 + 0.09 = 0.65 \]
Finally, subtract \( 0.25 \): \[ 0.65 - 0.25 = 0.40 \]
Therefore, the final result is: \[ \boxed{0.40} \]