Find :
a. `4 (5)/(13)- 3 (7)/(13) + 2 (8)/(13)`

Answer

To solve the expression \( 4 \frac{5}{13} - 3 \frac{7}{13} + 2 \frac{8}{13} \), we will follow these steps:

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

- For \( 4 \frac{5}{13} \):
\[ 4 \frac{5}{13} = \frac{4 \times 13 + 5}{13} = \frac{52 + 5}{13} = \frac{57}{13} \]

- For \( 3 \frac{7}{13} \):
\[ 3 \frac{7}{13} = \frac{3 \times 13 + 7}{13} = \frac{39 + 7}{13} = \frac{46}{13} \]

- For \( 2 \frac{8}{13} \):
\[ 2 \frac{8}{13} = \frac{2 \times 13 + 8}{13} = \frac{26 + 8}{13} = \frac{34}{13} \]

### Step 2: Substitute Back into the Expression
Now, we substitute these improper fractions back into the expression:
\[ \frac{57}{13} - \frac{46}{13} + \frac{34}{13} \]

### Step 3: Combine the Fractions
Since all fractions have the same denominator, we can combine them by subtracting and adding the numerators:
\[ \frac{57 - 46 + 34}{13} \]

### Step 4: Perform the Arithmetic in the Numerator
Now, we perform the arithmetic:
\[ 57 - 46 = 11 \]
Then add 34:
\[ 11 + 34 = 45 \]

So, we have:
\[ \frac{45}{13} \]

### Step 5: Convert Back to Mixed Number (if necessary)
To convert \( \frac{45}{13} \) back to a mixed number:
- Divide 45 by 13, which gives us 3 with a remainder of 6.
Thus, we can express it as:
\[ 3 \frac{6}{13} \]

### Final Answer
The final answer is:
\[ 3 \frac{6}{13} \]

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