Evaluate the sum:
`3/(5)+4/(9)`

Answer

To evaluate the sum \( \frac{3}{5} + \frac{4}{9} \), we will follow these steps:

### Step 1: Find the LCM of the Denominators
The denominators are 5 and 9. To add the fractions, we need a common denominator, which is the least common multiple (LCM) of 5 and 9.

- **Prime factorization of 5**: \( 5 = 5^1 \)
- **Prime factorization of 9**: \( 9 = 3^2 \)

To find the LCM, we take the highest power of each prime number:

- For 5, the highest power is \( 5^1 \).
- For 3, the highest power is \( 3^2 \).

Thus, the LCM is:
\[ LCM = 5^1 \times 3^2 = 5 \times 9 = 45 \]

### Step 2: Convert Each Fraction to Have the Common Denominator
Now we will convert each fraction to have the denominator of 45.

1. For \( \frac{3}{5} \):
\[ \frac{3}{5} = \frac{3 \times 9}{5 \times 9} = \frac{27}{45} \]

2. For \( \frac{4}{9} \):
\[ \frac{4}{9} = \frac{4 \times 5}{9 \times 5} = \frac{20}{45} \]

### Step 3: Add the Converted Fractions
Now that both fractions have the same denominator, we can add them:
\[ \frac{27}{45} + \frac{20}{45} = \frac{27 + 20}{45} = \frac{47}{45} \]

### Final Answer
The sum \( \frac{3}{5} + \frac{4}{9} \) is:
\[ \frac{47}{45} \]

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