To find out how many practice sessions Adeline has, we need to divide the total practice time by the length of each session.
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Convert the session time to an improper fraction: \[ 1 \frac{3}{4} \text{ hours} = \frac{4 \times 1 + 3}{4} = \frac{7}{4} \text{ hours} \]
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Total practice time: \[ 21 \text{ hours} = \frac{21}{1} \]
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Divide the total hours by the length of each session: \[ \text{Number of sessions} = \frac{\text{Total hours}}{\text{Hours per session}} = \frac{\frac{21}{1}}{\frac{7}{4}} \]
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To divide by a fraction, multiply by its reciprocal: \[ \frac{21}{1} \times \frac{4}{7} = \frac{21 \times 4}{1 \times 7} = \frac{84}{7} \]
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Simplify the fraction: \[ \frac{84}{7} = 12 \]
Thus, Adeline has 12 practice sessions.
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