Sam spent StartFraction 5 Over 6 EndFraction of an hour at the dentist’s office. He spent StartFraction 1 Over 10 EndFraction of the time in the waiting room. How much time did he spend at the dentist’s office other than in the waiting room?

Question

StartFraction 1 Over 12 EndFraction of an hour
StartFraction 3 Over 25 EndFraction of an hour
Three-fourths of an hour
StartFraction 11 Over 12 EndFraction of an hour

Answer 1

To find out how much time Sam spent at the dentist's office other than in the waiting room, we need to calculate the time he spent in the waiting room and then subtract that from the total time.

1. Total time spent at the dentist's office: \( \frac{5}{6} \) hours.

2. Time spent in the waiting room: We know he spent \( \frac{1}{10} \) of the total time in the waiting room. Therefore, we can calculate this by multiplying:

\[ \text{Time in waiting room} = \frac{1}{10} \times \frac{5}{6} = \frac{5}{60} = \frac{1}{12} \text{ hours} \]

3. Time spent other than in the waiting room: Now, we subtract the time spent in the waiting room from the total time:

\[ \text{Time spent other than waiting room} = \frac{5}{6} - \frac{1}{12} \]

To perform the subtraction, we need a common denominator. The least common multiple of 6 and 12 is 12.

Convert \( \frac{5}{6} \) to twelfths:

\[ \frac{5}{6} = \frac{10}{12} \]

Now we can perform the subtraction:

\[ \frac{10}{12} - \frac{1}{12} = \frac{9}{12} = \frac{3}{4} \text{ hours} \]

Thus, Sam spent \( \frac{3}{4} \) of an hour at the dentist's office other than in the waiting room.

The answer is \( \frac{3}{4} \) of an hour.