Find:
` 7/(12)+9/(16)`

Answer

To solve the problem \( \frac{7}{12} + \frac{9}{16} \), we will follow these steps:

### Step 1: Find the Least Common Multiple (LCM) of the Denominators
The denominators are 12 and 16. We need to find the LCM of these two numbers.

- **Prime factorization of 12**: \( 12 = 2^2 \times 3^1 \)
- **Prime factorization of 16**: \( 16 = 2^4 \)

To find the LCM, we take the highest power of each prime factor:
- For \( 2 \): the highest power is \( 2^4 \)
- For \( 3 \): the highest power is \( 3^1 \)

Thus, the LCM is:
\[ LCM = 2^4 \times 3^1 = 16 \times 3 = 48 \]

### Step 2: Convert Each Fraction to Have the Same Denominator
Now we will convert both fractions to have a denominator of 48.

For \( \frac{7}{12} \):
\[ \frac{7}{12} = \frac{7 \times 4}{12 \times 4} = \frac{28}{48} \]

For \( \frac{9}{16} \):
\[ \frac{9}{16} = \frac{9 \times 3}{16 \times 3} = \frac{27}{48} \]

### Step 3: Add the Two Fractions
Now that both fractions have the same denominator, we can add them:
\[ \frac{28}{48} + \frac{27}{48} = \frac{28 + 27}{48} = \frac{55}{48} \]

### Step 4: Convert to Mixed Number (if necessary)
The fraction \( \frac{55}{48} \) is an improper fraction. To convert it to a mixed number:
- Divide 55 by 48, which gives 1 with a remainder of 7.
Thus, we can write:
\[ \frac{55}{48} = 1 \frac{7}{48} \]

### Final Answer
The final answer is:
\[ 1 \frac{7}{48} \]

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