To subtract \( 1 \frac{4}{5} - 5 \frac{1}{10} \), we first convert each mixed number to an improper fraction.
- Convert \( 1 \frac{4}{5} \):
\[ 1 \frac{4}{5} = 1 \times 5 + 4 = 5 + 4 = \frac{9}{5} \]
- Convert \( 5 \frac{1}{10} \):
\[ 5 \frac{1}{10} = 5 \times 10 + 1 = 50 + 1 = \frac{51}{10} \]
Now we need to subtract the two improper fractions:
\[ \frac{9}{5} - \frac{51}{10} \]
To do this, we need a common denominator. The least common denominator (LCD) of 5 and 10 is 10.
We'll 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:
\[ \frac{18}{10} - \frac{51}{10} = \frac{18 - 51}{10} = \frac{-33}{10} \]
Now, we need to express \( \frac{-33}{10} \) as a mixed number:
\[ -33 \div 10 = -3 \quad \text{(with a remainder of } -3 \text{)} \]
Thus:
\[ \frac{-33}{10} = -3 \frac{3}{10} \]
Therefore, the final answer in the form of \( [\text{whole number}] [\text{numerator}]/[\text{denominator}] \) is:
\[ -3 \frac{3}{10} \]
So we can write the answer as:
\[ [-3] [3]/[10] \]
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