To find out how much time Sam spent at the dentist’s office other than in the waiting room, we need to calculate how much time he spent in the waiting room and then subtract that from his total time at the dentist’s office.
- Total time at the dentist's office: \( \frac{5}{6} \) hours
- Time spent in the waiting room: \( \frac{1}{10} \) of the total time at the dentist's office
First, we calculate the time spent in the waiting room:
\[ \text{Time in waiting room} = \frac{1}{10} \times \frac{5}{6} \]
To multiply these fractions, we multiply the numerators and denominators:
\[ = \frac{1 \times 5}{10 \times 6} = \frac{5}{60} = \frac{1}{12} \text{ hours} \]
Now we can find the time spent at the dentist's office other than in the waiting room by subtracting the waiting room time from the total time:
\[ \text{Time other than waiting room} = \frac{5}{6} - \frac{1}{12} \]
To perform this subtraction, we need a common denominator. The least common multiple of 6 and 12 is 12. We convert \( \frac{5}{6} \) to twelfths:
\[ \frac{5}{6} = \frac{10}{12} \]
Now we can subtract:
\[ \frac{10}{12} - \frac{1}{12} = \frac{9}{12} = \frac{3}{4} \text{ hours} \]
So, Sam spent \( \frac{3}{4} \) of an hour at the dentist’s office other than in the waiting room.
The correct answer is:
Three-fourths of an hour.
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