While waiting for his grandma to arrive, Patrick spent \( \frac{1}{2} \) of an hour on the phone with a friend and \( \frac{1}{4} \) of an hour listening to music. How long did Patrick spend waiting or his grandma? Write your answer both in minutes and as a fraction of an hour.

To find out how long Patrick spent waiting for his grandma, we need to sum the time he spent on the phone and listening to music. Patrick spent \( \frac{1}{2} \) hour on the phone and \( \frac{1}{4} \) hour listening to music. First, convert both fractions to have a common denominator, which in this case is 4: \[ \frac{1}{2} = \frac{2}{4} \] Now, add the two fractions: \[ \frac{2}{4} + \frac{1}{4} = \frac{3}{4} \] So, Patrick spent \( \frac{3}{4} \) of an hour waiting for his grandma. Now, to convert \( \frac{3}{4} \) of an hour into minutes, remember that 1 hour equals 60 minutes: \[ \frac{3}{4} \times 60 = 45 \] Thus, Patrick spent 45 minutes waiting for his grandma, which is also \( \frac{3}{4} \) of an hour.