Simplify-
`5 7/8 div 3 1/4 xx 7 5/(16) + 7/8 ` of 16

Answer

To simplify the expression \( 5 \frac{7}{8} \div 3 \frac{1}{4} \times \frac{7 \frac{5}{16}}{16} + \frac{7}{8} \) of 16, we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
1. Convert \( 5 \frac{7}{8} \):
\[ 5 \frac{7}{8} = \frac{5 \times 8 + 7}{8} = \frac{40 + 7}{8} = \frac{47}{8} \]

2. Convert \( 3 \frac{1}{4} \):
\[ 3 \frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4} \]

3. Convert \( 7 \frac{5}{16} \):
\[ 7 \frac{5}{16} = \frac{7 \times 16 + 5}{16} = \frac{112 + 5}{16} = \frac{117}{16} \]

### Step 2: Rewrite the Expression
Now, rewrite the expression using the improper fractions:
\[ \frac{47}{8} \div \frac{13}{4} \times \frac{117}{16} + \frac{7}{8} \times 16 \]

### Step 3: Change Division to Multiplication
Change the division to multiplication by multiplying by the reciprocal:
\[ \frac{47}{8} \times \frac{4}{13} \times \frac{117}{16} + \frac{7}{8} \times 16 \]

### Step 4: Simplify Each Part
1. Simplify \( \frac{47}{8} \times \frac{4}{13} \):
\[ = \frac{47 \times 4}{8 \times 13} = \frac{188}{104} \]
Now simplify \( \frac{188}{104} \) by dividing both the numerator and denominator by 4:
\[ = \frac{47}{26} \]

2. Now multiply by \( \frac{117}{16} \):
\[ = \frac{47}{26} \times \frac{117}{16} = \frac{47 \times 117}{26 \times 16} \]
Calculate \( 47 \times 117 = 5499 \) and \( 26 \times 16 = 416 \):
\[ = \frac{5499}{416} \]

3. Simplify \( \frac{7}{8} \times 16 \):
\[ = \frac{7 \times 16}{8} = \frac{112}{8} = 14 \]

### Step 5: Combine the Results
Now combine \( \frac{5499}{416} + 14 \):
Convert 14 to a fraction with a denominator of 416:
\[ 14 = \frac{14 \times 416}{416} = \frac{5824}{416} \]
Now add:
\[ \frac{5499 + 5824}{416} = \frac{11323}{416} \]

### Step 6: Final Simplification
Now, we can check if \( \frac{11323}{416} \) can be simplified. Since 11323 and 416 have no common factors, this is the final answer.

### Final Answer:
\[ \frac{11323}{416} \]