To solve the equation \( 4 \frac{2}{5} + \left(-\frac{1}{10}\right) \), we first convert the mixed number \( 4 \frac{2}{5} \) into an improper fraction.
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Convert \( 4 \frac{2}{5} \): \[ 4 \frac{2}{5} = 4 \times 5 + 2 = 20 + 2 = 22 \] So, \( 4 \frac{2}{5} = \frac{22}{5} \).
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Now we have: \[ \frac{22}{5} + \left(-\frac{1}{10}\right) = \frac{22}{5} - \frac{1}{10} \]
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To subtract these fractions, we need a common denominator. The least common multiple of 5 and 10 is 10. We convert \( \frac{22}{5} \) to a fraction with a denominator of 10: \[ \frac{22}{5} = \frac{22 \times 2}{5 \times 2} = \frac{44}{10} \]
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Now we can perform the subtraction: \[ \frac{44}{10} - \frac{1}{10} = \frac{44 - 1}{10} = \frac{43}{10} \]
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Now, we can convert \( \frac{43}{10} \) back to a mixed number. Since \( 43 \div 10 = 4 \) with a remainder of 3: \[ \frac{43}{10} = 4 \frac{3}{10} \]
Thus, the final answer is: \[ 4 \quad 3/10 \]
So, the answer is \([4] [3]/[10]\).