Evaluate the sum:
` 6/(13)+3/(4)`

Answer

To evaluate the sum \( \frac{6}{13} + \frac{3}{4} \), we will follow these steps:

### Step 1: Find the Least Common Multiple (LCM) of the denominators
The denominators are 13 and 4. Since 13 is a prime number, we can find the LCM by multiplying the two numbers together.

- The prime factorization of 4 is \( 2^2 \).
- The prime factorization of 13 is \( 13^1 \).

The LCM is calculated as:
\[ \text{LCM} = 2^2 \times 13 = 4 \times 13 = 52 \]

### Step 2: Convert each fraction to have the common denominator
Now that we have the LCM, we will convert each fraction to have a denominator of 52.

For \( \frac{6}{13} \):
- We need to multiply the numerator and denominator by 4 (since \( 52 \div 13 = 4 \)):
\[ \frac{6}{13} = \frac{6 \times 4}{13 \times 4} = \frac{24}{52} \]

For \( \frac{3}{4} \):
- We need to multiply the numerator and denominator by 13 (since \( 52 \div 4 = 13 \)):
\[ \frac{3}{4} = \frac{3 \times 13}{4 \times 13} = \frac{39}{52} \]

### Step 3: Add the two fractions
Now that both fractions have the same denominator, we can add them:
\[ \frac{24}{52} + \frac{39}{52} = \frac{24 + 39}{52} = \frac{63}{52} \]

### Step 4: Simplify the result (if necessary)
The fraction \( \frac{63}{52} \) is already in its simplest form, as 63 and 52 have no common factors other than 1.

### Final Answer
Thus, the sum \( \frac{6}{13} + \frac{3}{4} = \frac{63}{52} \).

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