Find the sum:
`4/(15)+3/(20)`

Answer

To find the sum of the fractions \( \frac{4}{15} + \frac{3}{20} \), we will follow these steps:

### Step 1: Find the LCM of the denominators
The denominators are 15 and 20. We need to find the Least Common Multiple (LCM) of these two numbers.

- **Factorization of 15**: \( 15 = 3 \times 5 \)
- **Factorization of 20**: \( 20 = 2 \times 2 \times 5 \)

Now, we take the highest power of each prime factor:
- The prime factors are 2, 3, and 5.
- The highest power of 2 is \( 2^2 \) (from 20).
- The highest power of 3 is \( 3^1 \) (from 15).
- The highest power of 5 is \( 5^1 \) (common in both).

So, the LCM is:
\[ LCM = 2^2 \times 3^1 \times 5^1 = 4 \times 3 \times 5 = 60 \]

### Step 2: Convert each fraction to have the same denominator
Now that we have the LCM, we will convert both fractions to have a denominator of 60.

- For \( \frac{4}{15} \):
\[ \frac{4}{15} = \frac{4 \times 4}{15 \times 4} = \frac{16}{60} \]

- For \( \frac{3}{20} \):
\[ \frac{3}{20} = \frac{3 \times 3}{20 \times 3} = \frac{9}{60} \]

### Step 3: Add the two fractions
Now we can add the two fractions:
\[ \frac{16}{60} + \frac{9}{60} = \frac{16 + 9}{60} = \frac{25}{60} \]

### Step 4: Simplify the fraction
Next, we simplify \( \frac{25}{60} \) by finding the greatest common divisor (GCD) of 25 and 60.

- The GCD of 25 and 60 is 5.

Now we divide both the numerator and the denominator by their GCD:
\[ \frac{25 \div 5}{60 \div 5} = \frac{5}{12} \]

### Final Answer
Thus, the sum of \( \frac{4}{15} + \frac{3}{20} \) is:
\[ \frac{5}{12} \]

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