To find the total distance Alice roller skates, we need to add the two distances together:
- Convert the mixed numbers to improper fractions:
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For \( 4 \frac{1}{4} \): \[ 4 \frac{1}{4} = \frac{4 \times 4 + 1}{4} = \frac{16 + 1}{4} = \frac{17}{4} \]
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For \( 4 \frac{3}{5} \): \[ 4 \frac{3}{5} = \frac{4 \times 5 + 3}{5} = \frac{20 + 3}{5} = \frac{23}{5} \]
- Now add the two fractions: To add \( \frac{17}{4} \) and \( \frac{23}{5} \), we need a common denominator. The least common multiple of 4 and 5 is 20.
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Convert \( \frac{17}{4} \) to a denominator of 20: \[ \frac{17}{4} = \frac{17 \times 5}{4 \times 5} = \frac{85}{20} \]
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Convert \( \frac{23}{5} \) to a denominator of 20: \[ \frac{23}{5} = \frac{23 \times 4}{5 \times 4} = \frac{92}{20} \]
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Now, add the two fractions: \[ \frac{85}{20} + \frac{92}{20} = \frac{85 + 92}{20} = \frac{177}{20} \]
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If you'd like to convert this back to a mixed number: \[ \frac{177}{20} = 8 \frac{17}{20} \]
So, the total distance Alice roller skates is: \[ \frac{177}{20} \text{ kilometers or } 8 \frac{17}{20} \text{ kilometers.} \]