5/12+9/20

To add the fractions \( \frac{5}{12} \) and \( \frac{9}{20} \), we need a common denominator.

1. Find the least common multiple (LCM) of the denominators (12 and 20).

   • The prime factorization of 12 is \( 2^2 \times 3 \).
   • The prime factorization of 20 is \( 2^2 \times 5 \).
   • The LCM is \( 2^2 \times 3 \times 5 = 60 \).

2. Convert each fraction to have the common denominator of 60:

   • For \( \frac{5}{12} \): \[ \frac{5}{12} = \frac{5 \times 5}{12 \times 5} = \frac{25}{60} \]
   • For \( \frac{9}{20} \): \[ \frac{9}{20} = \frac{9 \times 3}{20 \times 3} = \frac{27}{60} \]

3. Now add the fractions: \[ \frac{25}{60} + \frac{27}{60} = \frac{25 + 27}{60} = \frac{52}{60} \]

4. Simplify \( \frac{52}{60} \):

   • Both 52 and 60 can be divided by 4. \[ \frac{52 \div 4}{60 \div 4} = \frac{13}{15} \]

Thus, \( \frac{5}{12} + \frac{9}{20} = \frac{13}{15} \).