To subtract \( 9 \frac{7}{10} - 6 \frac{1}{4} \), we first convert the mixed numbers into improper fractions.
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Convert \( 9 \frac{7}{10} \): \[ 9 \frac{7}{10} = 9 \times 10 + 7 = 90 + 7 = 97 \Rightarrow \frac{97}{10} \]
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Convert \( 6 \frac{1}{4} \): \[ 6 \frac{1}{4} = 6 \times 4 + 1 = 24 + 1 = 25 \Rightarrow \frac{25}{4} \]
Now we have the problem as: \[ \frac{97}{10} - \frac{25}{4} \]
Next, we need a common denominator to subtract these fractions. The least common multiple of 10 and 4 is 20.
Now, we convert both fractions:
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Convert \( \frac{97}{10} \) to have a denominator of 20: \[ \frac{97}{10} = \frac{97 \times 2}{10 \times 2} = \frac{194}{20} \]
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Convert \( \frac{25}{4} \) to have a denominator of 20: \[ \frac{25}{4} = \frac{25 \times 5}{4 \times 5} = \frac{125}{20} \]
Now we can perform the subtraction: \[ \frac{194}{20} - \frac{125}{20} = \frac{194 - 125}{20} = \frac{69}{20} \]
Finally, we can convert \( \frac{69}{20} \) back to a mixed number: \[ 69 \div 20 = 3 \quad \text{(remainder } 9\text{)} \] Thus: \[ \frac{69}{20} = 3 \frac{9}{20} \]
Therefore, the difference \( 9 \frac{7}{10} - 6 \frac{1}{4} \) is: \[ \boxed{3 \frac{9}{20}} \]