To subtract the mixed numbers \(3 \frac{2}{5}\) and \(1 \frac{3}{5}\), we can follow these steps:
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Convert the mixed numbers to improper fractions.
For \(3 \frac{2}{5}\): \[ 3 \frac{2}{5} = \frac{3 \times 5 + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5} \]
For \(1 \frac{3}{5}\): \[ 1 \frac{3}{5} = \frac{1 \times 5 + 3}{5} = \frac{5 + 3}{5} = \frac{8}{5} \]
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Subtract the improper fractions.
\[ \frac{17}{5} - \frac{8}{5} = \frac{17 - 8}{5} = \frac{9}{5} \]
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Convert the improper fraction back to a mixed number.
\(\frac{9}{5}\) can be converted to a mixed number by dividing \(9\) by \(5\):
- \(5\) goes into \(9\) once with a remainder of \(4\).
- So, \(9 \div 5 = 1\) remainder \(4\).
Thus, we have:
\[ \frac{9}{5} = 1 \frac{4}{5} \]
So,
\[ 3 \frac{2}{5} - 1 \frac{3}{5} = 1 \frac{4}{5}. \]