To convert the mixed number \( 11 \frac{5}{10} \) into its simplest form, first convert the mixed number into an improper fraction.
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Convert \( 11 \frac{5}{10} \) to an improper fraction: \[ 11 \frac{5}{10} = \frac{11 \times 10 + 5}{10} = \frac{110 + 5}{10} = \frac{115}{10} \]
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Now simplify \( \frac{115}{10} \):
- Find the greatest common divisor (GCD) of 115 and 10, which is 5.
- Divide both the numerator and the denominator by their GCD: \[ \frac{115 \div 5}{10 \div 5} = \frac{23}{2} \]
So, the mixed number \( 11 \frac{5}{10} \) in simplest form is \( \frac{23}{2} \). Alternatively, it can also be expressed as a mixed number \( 11 \frac{1}{2} \) since \( \frac{23}{2} = 11 \frac{1}{2} \).