Question

Sarah practices the piano 1/3 hour in the morning, 5/6 hour in the afternoon, and 4/5 hour in the evening.

How many hours did Sarah practice in all?

Enter your answer as a mixed number in simplest form by filling in the boxes.

Answer 1

To find how many hours Sarah practiced in total, we will add the three time durations together:

- Morning practice: \( \frac{1}{3} \) hour
- Afternoon practice: \( \frac{5}{6} \) hour
- Evening practice: \( \frac{4}{5} \) hour

First, we need to find a common denominator for all three fractions. The denominators are 3, 6, and 5. The least common multiple (LCM) of these numbers can be calculated:

- The multiples of 3: 3, 6, 9, 12, 15
- The multiples of 6: 6, 12, 18, 24
- The multiples of 5: 5, 10, 15, 20

The smallest common multiple is 30.

Now, we will convert each fraction to have a denominator of 30:

1. For \( \frac{1}{3} \):
\[
\frac{1}{3} = \frac{1 \times 10}{3 \times 10} = \frac{10}{30}
\]

2. For \( \frac{5}{6} \):
\[
\frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30}
\]

3. For \( \frac{4}{5} \):
\[
\frac{4}{5} = \frac{4 \times 6}{5 \times 6} = \frac{24}{30}
\]

Now we can add these fractions together:
\[
\frac{10}{30} + \frac{25}{30} + \frac{24}{30} = \frac{10 + 25 + 24}{30} = \frac{59}{30}
\]

Next, we convert \( \frac{59}{30} \) to a mixed number:
- \( 30 \) goes into \( 59 \) one time (since \( 30 \times 1 = 30 \))
- The remainder is \( 59 - 30 = 29 \)

Thus, we can express \( \frac{59}{30} \) as:
\[
1 \frac{29}{30}
\]

Therefore, the total hours Sarah practiced in mixed number form is:
\[
\boxed{1} \quad \boxed{\frac{29}{30}}
\]