\( 1, \overline{23}-1,4= \) Hint: first convert \( 1, \overline{23} \) to its simplest ractional form.

To convert \( 1, \overline{23} \) into its simplest fractional form, we first express it as \( 1 + 0, \overline{23} \). The repeating decimal \( 0, \overline{23} \) can be transformed to a fraction by letting \( x = 0, \overline{23} \). Then, \( 100x = 23, \overline{23} \). By subtracting the two equations, we have \( 99x = 23 \), resulting in \( x = \frac{23}{99} \). So, \( 1, \overline{23} = 1 + \frac{23}{99} = \frac{99 + 23}{99} = \frac{122}{99} \). Now, substituting this into the original equation gives us: \[ \frac{122}{99} - 1.4 = \frac{122}{99} - \frac{14}{10} = \frac{122}{99} - \frac{139.6}{99} = \frac{122 - 139.6}{99} = \frac{-17.6}{99} \] To simplify further, we can express \(-17.6\) as \(-\frac{176}{10}\), leading to: \[ \frac{-176}{990} \text{ (after converting 17.6 to a fraction over 990)} \] So, the final simplified expression becomes \(\frac{-88}{495}\). Thus, the answer is \( \frac{-88}{495} \).