Answer :

Since both fractions have the same denominator, we can subtract them.  We only need to subtract the numerators, or the top numbers.  7-4=3.  We now have the fraction [tex]1 \frac{3}{9} [/tex]But 3 is a multiple of 9.  We can divide both 3 and 9 by three. 3÷3=1.  9÷3=3.  We just reduced the fraction.  [tex]1 \frac{1}{3} [/tex]That would be the fraction in simplest form.
This is how I solve mines. It might be different from how others solve it.

[tex] \frac{(1)(7)}{9} - \frac{4}{9} \\ \\ \frac{7}{9} - \frac{4}{9} = \frac{1}{3} [/tex]