To solve the expression \( 11 \frac{2}{9} - 10 - \frac{1}{9} - 8 \), we will first convert the mixed number \( 11 \frac{2}{9} \) to an improper fraction:
\[ 11 \frac{2}{9} = \frac{11 \times 9 + 2}{9} = \frac{99 + 2}{9} = \frac{101}{9} \]
Now, rewrite the expression using the improper fraction:
\[ \frac{101}{9} - 10 - \frac{1}{9} - 8 \]
Next, convert the whole numbers 10 and 8 to fractions over 9:
\[ 10 = \frac{90}{9}, \quad 8 = \frac{72}{9} \]
Now substitute these values into the expression:
\[ \frac{101}{9} - \frac{90}{9} - \frac{1}{9} - \frac{72}{9} \]
Now combine the fractions:
\[ \frac{101 - 90 - 1 - 72}{9} = \frac{101 - 163}{9} = \frac{-62}{9} \]
Thus, the expression \( 11 \frac{2}{9} - 10 - \frac{1}{9} - 8 \) simplifies to:
\[ \frac{-62}{9} \]
Since \(-62\) and \(9\) have no common factors other than 1, this fraction is in its simplest form:
\[ \boxed{\frac{-62}{9}} \]
18 answers