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

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

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

1. Find the least common denominator (LCD):

   • The denominators are 20 and 15.
   • The prime factorization of 20 is \( 2^2 \times 5 \) and for 15 is \( 3 \times 5 \).
   • The LCD is \( 2^2 \times 3 \times 5 = 60 \).

2. Convert each fraction:

   • 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. Add the fractions: \[ \frac{9}{60} + \frac{28}{60} = \frac{37}{60} \]

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

1. Find the least common denominator (LCD):

   • The denominators are 35 and 14.
   • The prime factorization of 35 is \( 5 \times 7 \) and for 14 is \( 2 \times 7 \).
   • The LCD is \( 2 \times 5 \times 7 = 70 \).

2. Convert each fraction:

   • 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. Add the fractions: \[ \frac{32}{70} + \frac{25}{70} = \frac{57}{70} \]

Final Results:

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