3/8+2/9 1/6+2/5 2/9+11/15 7/12+2/9

Let's calculate each of the fractions step by step.

1. Calculating \( \frac{3}{8} + \frac{2}{9} \):

   • The least common denominator (LCD) of 8 and 9 is 72.
   • Convert each fraction: \[ \frac{3}{8} = \frac{3 \times 9}{8 \times 9} = \frac{27}{72} \] \[ \frac{2}{9} = \frac{2 \times 8}{9 \times 8} = \frac{16}{72} \]
   • Now, add the fractions: \[ \frac{27}{72} + \frac{16}{72} = \frac{27 + 16}{72} = \frac{43}{72} \]

2. Calculating \( \frac{1}{6} + \frac{2}{5} \):

   • The LCD of 6 and 5 is 30.
   • Convert each fraction: \[ \frac{1}{6} = \frac{1 \times 5}{6 \times 5} = \frac{5}{30} \] \[ \frac{2}{5} = \frac{2 \times 6}{5 \times 6} = \frac{12}{30} \]
   • Now, add the fractions: \[ \frac{5}{30} + \frac{12}{30} = \frac{5 + 12}{30} = \frac{17}{30} \]

3. Calculating \( \frac{2}{9} + \frac{11}{15} \):

   • The LCD of 9 and 15 is 45.
   • Convert each fraction: \[ \frac{2}{9} = \frac{2 \times 5}{9 \times 5} = \frac{10}{45} \] \[ \frac{11}{15} = \frac{11 \times 3}{15 \times 3} = \frac{33}{45} \]
   • Now, add the fractions: \[ \frac{10}{45} + \frac{33}{45} = \frac{10 + 33}{45} = \frac{43}{45} \]

4. Calculating \( \frac{7}{12} + \frac{2}{9} \):

   • The LCD of 12 and 9 is 36.
   • Convert each fraction: \[ \frac{7}{12} = \frac{7 \times 3}{12 \times 3} = \frac{21}{36} \] \[ \frac{2}{9} = \frac{2 \times 4}{9 \times 4} = \frac{8}{36} \]
   • Now, add the fractions: \[ \frac{21}{36} + \frac{8}{36} = \frac{21 + 8}{36} = \frac{29}{36} \]

Summary of Results:

1. \( \frac{3}{8} + \frac{2}{9} = \frac{43}{72} \)
2. \( \frac{1}{6} + \frac{2}{5} = \frac{17}{30} \)
3. \( \frac{2}{9} + \frac{11}{15} = \frac{43}{45} \)
4. \( \frac{7}{12} + \frac{2}{9} = \frac{29}{36} \)