`15(7)/(8) xx 23(1)/(5) + 3(4)/(5) xx 5(1)/(8) = ?`

Answer

To solve the expression \( 15\frac{7}{8} \times 23\frac{1}{5} + 3\frac{4}{5} \times 5\frac{1}{8} \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
1. Convert \( 15\frac{7}{8} \) to an improper fraction:
\[ 15\frac{7}{8} = \frac{15 \times 8 + 7}{8} = \frac{120 + 7}{8} = \frac{127}{8} \]

2. Convert \( 23\frac{1}{5} \) to an improper fraction:
\[ 23\frac{1}{5} = \frac{23 \times 5 + 1}{5} = \frac{115 + 1}{5} = \frac{116}{5} \]

3. Convert \( 3\frac{4}{5} \) to an improper fraction:
\[ 3\frac{4}{5} = \frac{3 \times 5 + 4}{5} = \frac{15 + 4}{5} = \frac{19}{5} \]

4. Convert \( 5\frac{1}{8} \) to an improper fraction:
\[ 5\frac{1}{8} = \frac{5 \times 8 + 1}{8} = \frac{40 + 1}{8} = \frac{41}{8} \]

### Step 2: Rewrite the Expression
Now, we can rewrite the original expression using the improper fractions:
\[ \frac{127}{8} \times \frac{116}{5} + \frac{19}{5} \times \frac{41}{8} \]

### Step 3: Multiply the Fractions
1. Calculate \( \frac{127}{8} \times \frac{116}{5} \):
\[ \frac{127 \times 116}{8 \times 5} = \frac{14732}{40} \]

2. Calculate \( \frac{19}{5} \times \frac{41}{8} \):
\[ \frac{19 \times 41}{5 \times 8} = \frac{779}{40} \]

### Step 4: Add the Results
Now we add the two results:
\[ \frac{14732}{40} + \frac{779}{40} = \frac{14732 + 779}{40} = \frac{15511}{40} \]

### Step 5: Convert Back to Mixed Number
To convert \( \frac{15511}{40} \) back to a mixed number:
1. Divide \( 15511 \) by \( 40 \):
\[ 15511 \div 40 = 387 \quad \text{(whole number)} \]
Remainder:
\[ 15511 - (387 \times 40) = 11 \]
So, we have:
\[ 387\frac{11}{40} \]

### Final Answer
Thus, the final answer is:
\[ \boxed{387\frac{11}{40}} \]