`5 (2)/(9) - 2(4)/(9) - 1(1)/(9)`

Options

A. `= 1 (1)/(3)`
B. `= 1 (2)/(7)`
C. `= 1 (2)/(3)`
D. `= 1 (2)/(11)`

Answer

To solve the expression \(5 \frac{2}{9} - 2 \frac{4}{9} - 1 \frac{1}{9}\), we can follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert each mixed number into an improper fraction.

1. For \(5 \frac{2}{9}\):
\[ 5 \frac{2}{9} = \frac{5 \times 9 + 2}{9} = \frac{45 + 2}{9} = \frac{47}{9} \]

2. For \(2 \frac{4}{9}\):
\[ 2 \frac{4}{9} = \frac{2 \times 9 + 4}{9} = \frac{18 + 4}{9} = \frac{22}{9} \]

3. For \(1 \frac{1}{9}\):
\[ 1 \frac{1}{9} = \frac{1 \times 9 + 1}{9} = \frac{9 + 1}{9} = \frac{10}{9} \]

### Step 2: Rewrite the Expression
Now we can rewrite the original expression using the improper fractions:
\[ \frac{47}{9} - \frac{22}{9} - \frac{10}{9} \]

### Step 3: Combine the Fractions
Since all fractions have the same denominator, we can combine them by subtracting the numerators:
\[ \frac{47 - 22 - 10}{9} \]

### Step 4: Perform the Subtraction
Now we perform the subtraction in the numerator:
1. First, calculate \(47 - 22\):
\[ 47 - 22 = 25 \]
2. Then subtract \(10\) from \(25\):
\[ 25 - 10 = 15 \]

So, we have:
\[ \frac{15}{9} \]

### Step 5: Simplify the Fraction
Now, we can simplify \(\frac{15}{9}\):
1. Both the numerator and the denominator can be divided by \(3\):
\[ \frac{15 \div 3}{9 \div 3} = \frac{5}{3} \]

### Final Answer
Thus, the final answer is:
\[ \frac{5}{3} \]

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