Simplify: `9/32 + 11/12`

Answer

To simplify the expression \( \frac{9}{32} + \frac{11}{12} \), we will follow these steps:

### Step 1: Find the Least Common Multiple (LCM) of the Denominators
The denominators are 32 and 12.

To find the LCM:
- The prime factorization of 32 is \( 2^5 \).
- The prime factorization of 12 is \( 2^2 \times 3^1 \).

The LCM is found by taking the highest power of each prime factor:
- For 2, the highest power is \( 2^5 \).
- For 3, the highest power is \( 3^1 \).

Thus, the LCM is:
\[ LCM = 2^5 \times 3^1 = 32 \times 3 = 96 \]

### Step 2: Convert Each Fraction to Have the LCM as the Denominator
Now we convert each fraction to have a denominator of 96.

For \( \frac{9}{32} \):
\[ \frac{9}{32} = \frac{9 \times 3}{32 \times 3} = \frac{27}{96} \]

For \( \frac{11}{12} \):
\[ \frac{11}{12} = \frac{11 \times 8}{12 \times 8} = \frac{88}{96} \]

### Step 3: Add the Two Fractions
Now that both fractions have the same denominator, we can add them:
\[ \frac{27}{96} + \frac{88}{96} = \frac{27 + 88}{96} = \frac{115}{96} \]

### Step 4: Final Answer
The simplified result of \( \frac{9}{32} + \frac{11}{12} \) is:
\[ \frac{115}{96} \]