First, we need to find out how many minutes she exercised for. Since she started at 4:05 and ended at 4:32, she exercised for 32-5=27 minutes. To write this as a fractional part of an hour, we need to write it as a fraction over 60 since there are 60 minutes in each hour. Then we'll reduce it to simplest form:
[tex]\frac{27}{60}=\frac{9}{20}[/tex] of an hour.