To solve \( 7 \frac{1}{2} - 1 \frac{5}{6} \), we'll first convert both mixed numbers to improper fractions.
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Convert \( 7 \frac{1}{2} \) to an improper fraction: \[ 7 \frac{1}{2} = 7 \times 2 + 1 = 14 + 1 = 15 \] So, \( 7 \frac{1}{2} = \frac{15}{2} \).
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Convert \( 1 \frac{5}{6} \) to an improper fraction: \[ 1 \frac{5}{6} = 1 \times 6 + 5 = 6 + 5 = 11 \] So, \( 1 \frac{5}{6} = \frac{11}{6} \).
Now we need to subtract \( \frac{11}{6} \) from \( \frac{15}{2} \). To do this, we need a common denominator. The least common multiple of 2 and 6 is 6.
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Convert \( \frac{15}{2} \) to have a denominator of 6: \[ \frac{15}{2} = \frac{15 \times 3}{2 \times 3} = \frac{45}{6} \]
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Now we can perform the subtraction: \[ \frac{45}{6} - \frac{11}{6} = \frac{45 - 11}{6} = \frac{34}{6} \]
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Finally, simplify \( \frac{34}{6} \): \[ \frac{34}{6} = \frac{17}{3} \]
Thus, \( 7 \frac{1}{2} - 1 \frac{5}{6} = \frac{17}{3} \).
So the final answer is: \[ \frac{17}{3} \] or \( [17]/[3] \).