## Solving the Fraction Problem: (6/4+5 1/6 of 3/7)/(5+2 1/3)

This problem involves a combination of fractions, mixed numbers, and operations. Let's break it down step-by-step:

### Step 1: Convert mixed numbers to improper fractions.

**5 1/6:**(5 * 6 + 1) / 6 = 31/6**2 1/3:**(2 * 3 + 1) / 3 = 7/3

### Step 2: Calculate "5 1/6 of 3/7".

- This means multiplying 31/6 by 3/7: (31/6) * (3/7) = 93/42

### Step 3: Simplify the numerator.

**(6/4 + 93/42):**Find a common denominator (84)- (6/4) * (21/21) = 126/84
- (93/42) * (2/2) = 186/84

- Add the fractions: 126/84 + 186/84 = 312/84

### Step 4: Simplify the denominator.

**(5 + 7/3):**Find a common denominator (3)- (5 * 3/3) = 15/3

- Add the fractions: 15/3 + 7/3 = 22/3

### Step 5: Divide the numerator by the denominator.

**(312/84) / (22/3):**Dividing by a fraction is the same as multiplying by its reciprocal.- (312/84) * (3/22) = 936/1848

### Step 6: Simplify the final fraction.

- Both the numerator and denominator are divisible by 12:
- (936/12) / (1848/12) =
**78/154**

- (936/12) / (1848/12) =

### Final Answer:

The simplified fraction for (6/4+5 1/6 of 3/7)/(5+2 1/3) is **78/154**.