Final answer:
Patrick spent a total of 3/4 of an hour waiting for his grandmother, which is equal to 45 minutes after adding 1/2 an hour on the phone and 1/4 of an hour listening to the radio.
Step-by-step explanation:
The question asks how long Patrick spent waiting for his grandmother if he spent 1/2 of an hour on the phone with a friend and 1/4 of an hour listening to the radio. To find the total time spent, we need to add the two fractions together. This involves finding a common denominator and then adding the numerators.
1/2 an hour is equivalent to 2/4 hours. Adding this to 1/4 hour gives us:
2/4 + 1/4 = 3/4 hour
Thus, Patrick spent 3/4 of an hour waiting for his grandmother.
To convert this into minutes, we multiply by 60 (since there are 60 minutes in an hour):
3/4 hour * 60 minutes/hour = 45 minutes
Therefore, Patrick waited for 45 minutes in total.