To find out how much farther away Planet X is compared to Planet Y, we need to subtract the distance of Planet Y from the distance of Planet X.
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Convert the distances to the same format:
- Distance of Planet X: \(2 \frac{1}{2}\) light-years can be converted to an improper fraction: \[ 2 \frac{1}{2} = \frac{5}{2} \text{ light-years} \]
- Distance of Planet Y: \( \frac{8}{10} \) light-years can be simplified to: \[ \frac{8}{10} = \frac{4}{5} \text{ light-years} \]
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Find a common denominator to subtract the fractions.
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The least common denominator (LCD) of 2 and 5 is 10.
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Rewrite \( \frac{5}{2} \) with a denominator of 10: \[ \frac{5}{2} = \frac{5 \times 5}{2 \times 5} = \frac{25}{10} \]
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Rewrite \( \frac{4}{5} \) with a denominator of 10: \[ \frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10} \]
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Subtract the distances: \[ \frac{25}{10} - \frac{8}{10} = \frac{25 - 8}{10} = \frac{17}{10} \]
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Convert to a mixed number: \[ \frac{17}{10} = 1 \frac{7}{10} \text{ light-years} \]
Therefore, Planet X is \( \frac{17}{10} \) light-years or \( 1 \frac{7}{10} \) light-years farther away than Planet Y.