To convert the mixed number \( 1 \frac{7}{8} \) to an improper fraction, follow these steps:
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Multiply the whole number part by the denominator of the fractional part: \[ 1 \times 8 = 8 \]
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Add the result to the numerator of the fractional part: \[ 8 + 7 = 15 \]
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Place that sum over the original denominator: \[ \frac{15}{8} \]
Thus, \( 1 \frac{7}{8} \) as an improper fraction is \( \frac{15}{8} \).
So, the answer is: \[ \frac{15}{8} \]