`12(1)/(3)-(8)/(9)+(11)/(3)-4(11)/(9)=?`

Answer

To simplify the expression \( 12 \left( \frac{1}{3} \right) - \frac{8}{9} + \frac{11}{3} - 4 \left( \frac{11}{9} \right) \), we will follow these steps:

### Step 1: Convert Mixed Numbers and Fractions
First, we convert the mixed numbers into improper fractions:
- \( 12 \left( \frac{1}{3} \right) = \frac{12 \times 3 + 1}{3} = \frac{36 + 1}{3} = \frac{37}{3} \)
- \( 4 \left( \frac{11}{9} \right) = \frac{4 \times 11}{9} = \frac{44}{9} \)

Now, we rewrite the expression:
\[ \frac{37}{3} - \frac{8}{9} + \frac{11}{3} - \frac{44}{9} \]

### Step 2: Find a Common Denominator
The common denominator for the fractions is 9. We convert \( \frac{37}{3} \) and \( \frac{11}{3} \) to have a denominator of 9:
- \( \frac{37}{3} = \frac{37 \times 3}{3 \times 3} = \frac{111}{9} \)
- \( \frac{11}{3} = \frac{11 \times 3}{3 \times 3} = \frac{33}{9} \)

Now, the expression becomes:
\[ \frac{111}{9} - \frac{8}{9} + \frac{33}{9} - \frac{44}{9} \]

### Step 3: Combine the Fractions
Now, we can combine all the fractions since they have the same denominator:
\[ \frac{111 - 8 + 33 - 44}{9} \]

Calculating the numerator:
\[ 111 - 8 = 103 \\ 103 + 33 = 136 \\ 136 - 44 = 92 \]

So, we have:
\[ \frac{92}{9} \]

### Step 4: Final Answer
The simplified form of the expression is:
\[ \frac{92}{9} \]