To solve \(1 \frac{4}{5} - 5 \frac{1}{10}\), we first convert the mixed numbers to improper fractions.
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Convert \(1 \frac{4}{5}\): \[ 1 \frac{4}{5} = 1 + \frac{4}{5} = \frac{5}{5} + \frac{4}{5} = \frac{9}{5} \]
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Convert \(5 \frac{1}{10}\): \[ 5 \frac{1}{10} = 5 + \frac{1}{10} = \frac{50}{10} + \frac{1}{10} = \frac{51}{10} \]
Now we need to subtract these improper fractions: \[ \frac{9}{5} - \frac{51}{10} \]
To perform the subtraction, we need a common denominator. The least common multiple of 5 and 10 is 10. We convert \(\frac{9}{5}\) to have a denominator of 10: \[ \frac{9}{5} = \frac{9 \times 2}{5 \times 2} = \frac{18}{10} \]
Now we can perform the subtraction: \[ \frac{18}{10} - \frac{51}{10} = \frac{18 - 51}{10} = \frac{-33}{10} \]
To express \(\frac{-33}{10}\) as a fraction in simplest form, we note that \(-33\) and \(10\) have no common factors (except 1). Thus, the simplest form of the fraction is: \[ \frac{-33}{10} \]
Therefore, the final answer is: \[ \frac{-33}{10} \]
So, in the form \([]/[]\), we have \([-33]/[10]\).