Which of the following is equal to `(119)/171 + 7/9` ?

Options

A. `28/19`
B. `7/19`
C. `17/9`
D. `17/91`

Answer

To solve the problem \( \frac{119}{171} + \frac{7}{9} \), we will follow these steps:

### Step 1: Identify the fractions
We have two fractions:
- \( \frac{119}{171} \)
- \( \frac{7}{9} \)

### Step 2: Find the Least Common Multiple (LCM)
To add these fractions, we need a common denominator. The denominators are 171 and 9. The LCM of 171 and 9 is 171, since 171 is divisible by 9.

### Step 3: Rewrite the fractions with the common denominator
The first fraction is already over the common denominator:
- \( \frac{119}{171} \)

For the second fraction \( \frac{7}{9} \), we need to convert it:
\[ \frac{7}{9} = \frac{7 \times 19}{9 \times 19} = \frac{133}{171} \]

### Step 4: Add the fractions
Now we can add the two fractions:
\[ \frac{119}{171} + \frac{133}{171} = \frac{119 + 133}{171} = \frac{252}{171} \]

### Step 5: Simplify the resulting fraction
Next, we simplify \( \frac{252}{171} \). We can divide both the numerator and the denominator by their greatest common divisor (GCD).

To find the GCD, we can divide both numbers by 9:
\[ \frac{252 \div 9}{171 \div 9} = \frac{28}{19} \]

### Final Answer
Thus, the final answer is:
\[ \frac{28}{19} \]