To solve the problem \(3 \frac{3}{10} - 1 \frac{4}{5}\), we first convert the mixed numbers into improper fractions.
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Convert \(3 \frac{3}{10}\) to an improper fraction: \[ 3 \frac{3}{10} = \frac{(3 \times 10) + 3}{10} = \frac{30 + 3}{10} = \frac{33}{10} \]
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Convert \(1 \frac{4}{5}\) to an improper fraction: \[ 1 \frac{4}{5} = \frac{(1 \times 5) + 4}{5} = \frac{5 + 4}{5} = \frac{9}{5} \]
Now, we need to subtract the two improper fractions: \[ \frac{33}{10} - \frac{9}{5} \]
To perform the subtraction, we need a common denominator. The least common multiple of 10 and 5 is 10. We can rewrite \(\frac{9}{5}\) with a denominator of 10: \[ \frac{9}{5} = \frac{9 \times 2}{5 \times 2} = \frac{18}{10} \]
Now we have: \[ \frac{33}{10} - \frac{18}{10} = \frac{33 - 18}{10} = \frac{15}{10} \]
Next, we can simplify \(\frac{15}{10}\): \[ \frac{15}{10} = \frac{3}{2} \]
Finally, we convert \(\frac{3}{2}\) to a mixed number: \[ \frac{3}{2} = 1 \frac{1}{2} \]
Therefore, the answer is: \[ 1 \quad \frac{1}{2} \]
In the requested format: \[ [1] [1]/[2] \]