To solve these equations, we need to simplify the expressions and perform the necessary calculations.

A = 3/13 + 7/11 + 8/13 + 15/11 + 2/13

To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 13 * 11 = 143.

A = (3/13) * (11/11) + (7/11) * (13/13) + (8/13) * (11/11) + (15/11) * (13/13) + 2/13
= 33/143 + 91/143 + 88/143 + 195/143 + 2/13
= (33 + 91 + 88 + 195)/143 + 2/13
= 407/143 + 2/13

To add fractions with the same denominator, we simply add the numerators.

A = (407 + 2)/143
= 409/143

Therefore, A = 409/143.

B = (21/67) * (2/11) * (67/7)

To multiply fractions, we multiply the numerators and denominators.

B = (21 * 2 * 67)/(67 * 11 * 7)
= 282/5177

Therefore, B = 282/5177.

C = (4/7) * (31/11) - (4/7) * (9/11)

To subtract fractions, we need to find a common denominator. In this case, the common denominator is 7 * 11 = 77.

C = (4/7) * (31/11) - (4/7) * (9/11)
= (4/7) * (31/11 - 9/11)
= (4/7) * (22/11)
= 88/77

Therefore, C = 88/77.

D = (3 1/2) * (12/43) + (49/14) * (31/43) + 11/2

To multiply a mixed number by a fraction, we first convert the mixed number to an improper fraction.

D = (7/2) * (12/43) + (49/14) * (31/43) + 11/2
= (7/2) * (12/43) + (7/2) * (31/43) + 11/2

To add fractions with the same denominator, we simply add the numerators.

D = (7 * 12 + 7 * 31 + 11)/2
= (84 + 217 + 11)/2
= 312/2
= 156

Therefore, D = 156.

To summarize:
A = 409/143
B = 282/5177
C = 88/77
D = 156