discrete mathematics - Prove two sets have same Cardinality by writing down bijection

a. Prove that the interval $A = [1,3]$ has the same cardinality as $B = [1,5]$ by writing down a bijection from $A \to B$. Don't prove it is a bijection.

b. Consider the following infinite set: $A = {1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4},..., \frac{1}{n}}$, Prove the set $A$ has the same cardinality as the integers by writing down a . bijection from $A$ onto $Z$.

I don't know how to find a function that is a bijection from one set to another. Can anyone help by explaining the thought process behind it, I've been having trouble with these types of problems? Thanks.