To solve the expression \( 6 \frac{1}{2} - \frac{9}{10} \), we first convert \( 6 \frac{1}{2} \) into an improper fraction.
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Convert \( 6 \frac{1}{2} \) to an improper fraction: \[ 6 \frac{1}{2} = 6 \times 2 + 1 = 12 + 1 = 13 \] So, \( 6 \frac{1}{2} = \frac{13}{2} \).
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Now we need to subtract \( \frac{9}{10} \) from \( \frac{13}{2} \). To do this, we need a common denominator. The least common multiple of 2 and 10 is 10.
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Convert \( \frac{13}{2} \) to have a denominator of 10: \[ \frac{13}{2} = \frac{13 \times 5}{2 \times 5} = \frac{65}{10} \]
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Now we can perform the subtraction: \[ \frac{65}{10} - \frac{9}{10} = \frac{65 - 9}{10} = \frac{56}{10} \]
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Simplify \( \frac{56}{10} \): \[ \frac{56}{10} = \frac{28}{5} \]
Thus, the final result is: \[ 5 \frac{3}{5} \text{ (because }\frac{28}{5} = 5 \text{ whole and } 3 \text{ remainder)} \] This can be represented in the format requested: \[ \boxed{5} \quad \boxed{3} \quad \boxed{5} \]