Evaluate: d. `7(9)/(5) - 2 (2)/(5) - 1 (4)/(5)`

Answer

To evaluate the expression \( 7\frac{9}{5} - 2\frac{2}{5} - 1\frac{4}{5} \), we will follow these steps:

### Step 1: Convert mixed numbers to improper fractions
First, we need to convert each mixed number into an improper fraction.

1. **Convert \( 7\frac{9}{5} \)**:
\[ 7\frac{9}{5} = \frac{7 \times 5 + 9}{5} = \frac{35 + 9}{5} = \frac{44}{5} \]

2. **Convert \( 2\frac{2}{5} \)**:
\[ 2\frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{10 + 2}{5} = \frac{12}{5} \]

3. **Convert \( 1\frac{4}{5} \)**:
\[ 1\frac{4}{5} = \frac{1 \times 5 + 4}{5} = \frac{5 + 4}{5} = \frac{9}{5} \]

### Step 2: Rewrite the expression
Now we can rewrite the original expression using the improper fractions:
\[ \frac{44}{5} - \frac{12}{5} - \frac{9}{5} \]

### Step 3: Combine the fractions
Since all fractions have the same denominator, we can combine them directly:
\[ \frac{44 - 12 - 9}{5} \]

### Step 4: Perform the subtraction in the numerator
Now, we will perform the subtraction in the numerator:
\[ 44 - 12 = 32 \]
\[ 32 - 9 = 23 \]

### Step 5: Write the final result
Now we can write the final result:
\[ \frac{23}{5} \]

### Final Answer:
The evaluated expression is \( \frac{23}{5} \).

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