3/20+2/15

To add the fractions \( \frac{3}{20} \) and \( \frac{2}{15} \), we first need to find a common denominator. The least common multiple (LCM) of 20 and 15 can help us with this.

The prime factorization of each number is:

• 20 = \( 2^2 \times 5^1 \)
• 15 = \( 3^1 \times 5^1 \)

The LCM will take the highest power of each prime factor:

• For \( 2 \): \( 2^2 \)
• For \( 3 \): \( 3^1 \)
• For \( 5 \): \( 5^1 \)

So, the LCM = \( 2^2 \times 3^1 \times 5^1 = 60 \).

Now we can rewrite each fraction with a denominator of 60:

1. Convert \( \frac{3}{20} \): \[ \frac{3}{20} = \frac{3 \times 3}{20 \times 3} = \frac{9}{60} \]

2. Convert \( \frac{2}{15} \): \[ \frac{2}{15} = \frac{2 \times 4}{15 \times 4} = \frac{8}{60} \]

Now, we can add the two fractions: \[ \frac{9}{60} + \frac{8}{60} = \frac{9 + 8}{60} = \frac{17}{60} \]

So, the answer is: \[ \frac{3}{20} + \frac{2}{15} = \frac{17}{60} \]