3/20 + 7/15; 16/35 + 5/14;

To add the fractions, we need to find a common denominator for each pair before summing them.

For \( \frac{3}{20} + \frac{7}{15} \):

1. Find the least common multiple (LCM) of the denominators 20 and 15.

   • The prime factorization of 20 is \( 2^2 \times 5 \).
   • The prime factorization of 15 is \( 3 \times 5 \).
   • The LCM will take the highest powers:
     • \( 2^2 \) from 20,
     • \( 3^1 \) from 15,
     • \( 5^1 \) from both.
   • Thus, the LCM is \( 2^2 \times 3 \times 5 = 60 \).

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

   • For \( \frac{3}{20} \): \[ \frac{3}{20} = \frac{3 \times 3}{20 \times 3} = \frac{9}{60} \]
   • For \( \frac{7}{15} \): \[ \frac{7}{15} = \frac{7 \times 4}{15 \times 4} = \frac{28}{60} \]

3. Now add the fractions: \[ \frac{9}{60} + \frac{28}{60} = \frac{9 + 28}{60} = \frac{37}{60} \]

For \( \frac{16}{35} + \frac{5}{14} \):

1. Find the LCM of the denominators 35 and 14.

   • The prime factorization of 35 is \( 5 \times 7 \).
   • The prime factorization of 14 is \( 2 \times 7 \).
   • The LCM will take the highest powers:
     • \( 2^1 \) from 14,
     • \( 5^1 \) from 35,
     • \( 7^1 \) from both.
   • Thus, the LCM is \( 2 \times 5 \times 7 = 70 \).

2. Convert each fraction to have the common denominator of 70.

   • For \( \frac{16}{35} \): \[ \frac{16}{35} = \frac{16 \times 2}{35 \times 2} = \frac{32}{70} \]
   • For \( \frac{5}{14} \): \[ \frac{5}{14} = \frac{5 \times 5}{14 \times 5} = \frac{25}{70} \]

3. Now add the fractions: \[ \frac{32}{70} + \frac{25}{70} = \frac{32 + 25}{70} = \frac{57}{70} \]

Final Results:

• \( \frac{3}{20} + \frac{7}{15} = \frac{37}{60} \)
• \( \frac{16}{35} + \frac{5}{14} = \frac{57}{70} \)