To solve \( 8 \frac{2}{5} - 3 \frac{7}{10} \), we first convert the mixed numbers into improper fractions.
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Convert \( 8 \frac{2}{5} \): \[ 8 \frac{2}{5} = \frac{8 \times 5 + 2}{5} = \frac{40 + 2}{5} = \frac{42}{5} \]
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Convert \( 3 \frac{7}{10} \): \[ 3 \frac{7}{10} = \frac{3 \times 10 + 7}{10} = \frac{30 + 7}{10} = \frac{37}{10} \]
Now we have the improper fractions: \[ \frac{42}{5} - \frac{37}{10} \]
To subtract these fractions, we need a common denominator. The least common multiple of 5 and 10 is 10. So, we convert \( \frac{42}{5} \) to have the denominator of 10: \[ \frac{42}{5} = \frac{42 \times 2}{5 \times 2} = \frac{84}{10} \]
Now we can subtract: \[ \frac{84}{10} - \frac{37}{10} = \frac{84 - 37}{10} = \frac{47}{10} \]
Now, convert \( \frac{47}{10} \) back to a mixed number: \[ \frac{47}{10} = 4 \frac{7}{10} \]
So, the final answer is: \[ 4 \frac{7}{10} = [4] [7]/[10] \]
Thus, the answer is \([4] [7]/[10]\).