To find the difference between \( 9 \frac{7}{10} \) and \( \frac{6}{14} \), we should first convert everything to a common fraction format.
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Convert the mixed number to an improper fraction: \[ 9 \frac{7}{10} = 9 + \frac{7}{10} = \frac{9 \times 10}{10} + \frac{7}{10} = \frac{90}{10} + \frac{7}{10} = \frac{90 + 7}{10} = \frac{97}{10} \]
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Simplify \( \frac{6}{14} \): \[ \frac{6}{14} = \frac{3}{7} \quad \text{(by dividing both numerator and denominator by 2)} \]
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Find a common denominator for \( \frac{97}{10} \) and \( \frac{3}{7} \):
- The least common multiple of 10 and 7 is 70.
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Convert both fractions to have a denominator of 70:
- Convert \( \frac{97}{10} \): \[ \frac{97}{10} \times \frac{7}{7} = \frac{97 \times 7}{70} = \frac{679}{70} \]
- Convert \( \frac{3}{7} \): \[ \frac{3}{7} \times \frac{10}{10} = \frac{3 \times 10}{70} = \frac{30}{70} \]
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Subtract the two fractions: \[ \frac{679}{70} - \frac{30}{70} = \frac{679 - 30}{70} = \frac{649}{70} \]
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Convert back to a mixed number (if needed):
- To convert \( \frac{649}{70} \) to a mixed number, divide 649 by 70: \[ 649 \div 70 = 9 \quad \text{(since \( 70 \times 9 = 630 \))} \] The remainder is \( 649 - 630 = 19 \), so we can express it as: \[ 9 \frac{19}{70} \]
Thus, the difference \( 9 \frac{7}{10} - \frac{6}{14} = \frac{649}{70} \) or as a mixed number, \( 9 \frac{19}{70} \).