To solve is:
[tex]1 \frac{1}{4} - 1 \frac{1}{5} [/tex]
making it into an improper fraction:
[tex] \frac{1+4}{4} - \frac{1+5}{5} [/tex]
[tex] \frac{5}{4} - \frac{6}{5} [/tex]
bringing to a common denominator (which is 20, since they have no factors in common)
[tex] \frac{5*5}{20} - \frac{6*4}{20} [/tex]
[tex] \frac{25}{20} - \frac{24}{20} [/tex]
the answer is then:
[tex]\frac{1}{20} [/tex]
