To solve \( 7 \frac{5}{10} - 1 \frac{6}{10} \), we can first convert the mixed numbers to improper fractions.
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Convert \( 7 \frac{5}{10} \) to an improper fraction: \[ 7 \frac{5}{10} = \frac{(7 \times 10) + 5}{10} = \frac{70 + 5}{10} = \frac{75}{10} \]
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Convert \( 1 \frac{6}{10} \) to an improper fraction: \[ 1 \frac{6}{10} = \frac{(1 \times 10) + 6}{10} = \frac{10 + 6}{10} = \frac{16}{10} \]
Now we will subtract the two improper fractions: \[ \frac{75}{10} - \frac{16}{10} = \frac{75 - 16}{10} = \frac{59}{10} \]
Finally, convert \( \frac{59}{10} \) back to a mixed number: \[ \frac{59}{10} = 5 \frac{9}{10} \]
So, the result of \( 7 \frac{5}{10} - 1 \frac{6}{10} \) is \( 5 \frac{9}{10} \).