Seifert surface and crossing number

Question

i am sitting here with the problem of Seifert Surfaces. I know from a theorem that every knot does have a Seifert surface. We can also make a so called disc-and-band surface $F$ by gluing $v$ discs and $e$ bands together. Then we get $\chi(F)=v-e$ (this is a very simple fact). We can construct such a Seifert surface by the Seifert-algorithm such that we get the Seifert-discs. Then we can glue some bands to connect the discs. Then we want to conclude the following inequality:$$g(K)\leq\frac{c(K)}{2}$$ with $g(K)$ the genus of the knot $K$ and $c(K)$ the crossing-number. Can someone give a suggestion how to make such a estimate?! I can give the proof of the fact with $\chi(F)$ and also the inequality $u(K)\leq c(K)/2$ with u(K) the unknotting number. Can someone gibe a good proof?