The sum of the fraction `2/9,4/3` and `6/18`is

Options

A. `17/9`
B. `16/9`
C. `2/5`
D. `11/18`

Answer

To find the sum of the fractions \( \frac{2}{9} \), \( \frac{4}{3} \), and \( \frac{6}{18} \), we will follow these steps:

### Step 1: Find a common denominator
The denominators of the fractions are 9, 3, and 18. The least common multiple (LCM) of these numbers is 18.

### Step 2: Convert each fraction to have the common denominator
- The fraction \( \frac{2}{9} \) can be converted to have a denominator of 18:
\[ \frac{2}{9} = \frac{2 \times 2}{9 \times 2} = \frac{4}{18} \]

- The fraction \( \frac{4}{3} \) can also be converted:
\[ \frac{4}{3} = \frac{4 \times 6}{3 \times 6} = \frac{24}{18} \]

- The fraction \( \frac{6}{18} \) already has the common denominator:
\[ \frac{6}{18} = \frac{6}{18} \]

### Step 3: Add the fractions
Now that all fractions have the same denominator, we can add them:
\[ \frac{4}{18} + \frac{24}{18} + \frac{6}{18} = \frac{4 + 24 + 6}{18} = \frac{34}{18} \]

### Step 4: Simplify the result
We can simplify \( \frac{34}{18} \) by finding the greatest common divisor (GCD) of 34 and 18, which is 2:
\[ \frac{34 \div 2}{18 \div 2} = \frac{17}{9} \]

### Final Answer
The sum of the fractions \( \frac{2}{9} \), \( \frac{4}{3} \), and \( \frac{6}{18} \) is \( \frac{17}{9} \).

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