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:
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For \( \frac{1}{3} \): \[ \frac{1}{3} = \frac{1 \times 10}{3 \times 10} = \frac{10}{30} \]
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For \( \frac{5}{6} \): \[ \frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30} \]
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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: \[ \boxed{1} \quad \boxed{\frac{29}{30}} \]
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