Find:
`4/(7)+8/(13)`

Options

A. `108/(91)`
B. `109/(91)`
C. `110/(91)`
D. `111/(91)`

Answer

To solve the problem \( \frac{4}{7} + \frac{8}{13} \), we will follow these steps:

### Step 1: Find the LCM of the denominators
The denominators are 7 and 13. Since both 7 and 13 are prime numbers, their least common multiple (LCM) is simply their product:
\[ \text{LCM}(7, 13) = 7 \times 13 = 91 \]

### Step 2: Convert each fraction to have the common denominator
Now we need to convert each fraction to have the denominator of 91.

For \( \frac{4}{7} \):
- To convert \( \frac{4}{7} \) to a fraction with a denominator of 91, we multiply both the numerator and the denominator by 13 (since \( 91 \div 7 = 13 \)):
\[ \frac{4}{7} = \frac{4 \times 13}{7 \times 13} = \frac{52}{91} \]

For \( \frac{8}{13} \):
- To convert \( \frac{8}{13} \) to a fraction with a denominator of 91, we multiply both the numerator and the denominator by 7 (since \( 91 \div 13 = 7 \)):
\[ \frac{8}{13} = \frac{8 \times 7}{13 \times 7} = \frac{56}{91} \]

### Step 3: Add the two fractions
Now that both fractions have the same denominator, we can add them:
\[ \frac{52}{91} + \frac{56}{91} = \frac{52 + 56}{91} = \frac{108}{91} \]

### Step 4: Simplify the result (if necessary)
The fraction \( \frac{108}{91} \) cannot be simplified further since 108 and 91 have no common factors other than 1.

### Final Answer
Thus, the final result is:
\[ \frac{4}{7} + \frac{8}{13} = \frac{108}{91} \]

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