Find:
`2(3)/(4)+5(5)/(6)`

Options

A. `8(7)/(12)`
B. `8(8)/(12)`
C. `8(9)/(12)`
D. `8(10)/(12)`

Answer

To solve the problem \( 2\frac{3}{4} + 5\frac{5}{6} \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

For \( 2\frac{3}{4} \):
- Multiply the whole number (2) by the denominator (4): \( 2 \times 4 = 8 \)
- Add the numerator (3): \( 8 + 3 = 11 \)
- So, \( 2\frac{3}{4} = \frac{11}{4} \)

For \( 5\frac{5}{6} \):
- Multiply the whole number (5) by the denominator (6): \( 5 \times 6 = 30 \)
- Add the numerator (5): \( 30 + 5 = 35 \)
- So, \( 5\frac{5}{6} = \frac{35}{6} \)

### Step 2: Add the Improper Fractions
Now we need to add \( \frac{11}{4} + \frac{35}{6} \). To do this, we need a common denominator.

### Step 3: Find the Least Common Multiple (LCM)
The denominators are 4 and 6. The LCM of 4 and 6 is 12.

### Step 4: Convert Each Fraction to Have the Common Denominator
Now we convert each fraction to have the denominator of 12.

For \( \frac{11}{4} \):
- Multiply the numerator and denominator by 3:
\[ \frac{11 \times 3}{4 \times 3} = \frac{33}{12} \]

For \( \frac{35}{6} \):
- Multiply the numerator and denominator by 2:
\[ \frac{35 \times 2}{6 \times 2} = \frac{70}{12} \]

### Step 5: Add the Converted Fractions
Now we can add the two fractions:
\[ \frac{33}{12} + \frac{70}{12} = \frac{33 + 70}{12} = \frac{103}{12} \]

### Final Answer
Thus, the final answer is:
\[ \frac{103}{12} \]

---