Answer :
For this case we have missing [tex]\frac {2} {7}[/tex]of fence to be painted.
To paint [tex]\frac {5} {7}[/tex] of fence we used:
[tex]1 \frac {1} {4} = \frac {4 * 1 + 1} {4} = \frac {5} {4}[/tex]gallons of paint. So, we make a rule of three:
[tex]\frac {5} {4} ------------> \frac {5} {7}\\x --------------------------> \frac {2} {7}[/tex]
Where the variable "x" represents the gallons of paint needed to paint the missing fence
[tex]x = \frac {\frac {2} {7} * \frac {5} {4}} {\frac {5} {7}}\\x = \frac {70} {140} = \frac {1} {2} = 0.5[/tex]
Thus, 0.5 gallons of paint is missing for the missing fence.
Answer
0.5 gallons