Question

find the difference:
$10\frac{1}{10} - 8\frac{5}{11}$

Explanation:

Step1: Convert to improper fractions

$10\frac{1}{10} = \frac{10\times10 +1}{10}=\frac{101}{10}$, $8\frac{5}{11}=\frac{8\times11 +5}{11}=\frac{93}{11}$

Step2: Find common denominator

The least common denominator of 10 and 11 is $10\times11=110$. Rewrite fractions:
$\frac{101}{10}=\frac{101\times11}{110}=\frac{1111}{110}$, $\frac{93}{11}=\frac{93\times10}{110}=\frac{930}{110}$

Step3: Subtract the fractions

$\frac{1111}{110}-\frac{930}{110}=\frac{1111-930}{110}=\frac{181}{110}$

Step4: Convert back to mixed number

$\frac{181}{110}=1\frac{71}{110}$

Answer:

$\boldsymbol{1\frac{71}{110}}$