a) 5/6 + 2/3 + 1/4
To add these fractions, we need to find a common denominator. The least common multiple of 6, 3, and 4 is 12.

5/6 = 10/12
2/3 = 8/12
1/4 = 3/12

Adding them together:
10/12 + 8/12 + 3/12 = 21/12 = 7/4

b) 3/2 + 6/7 - 3/14
To add these fractions, we need to find a common denominator. The least common multiple of 2, 7, and 14 is 14.

3/2 = 21/14
6/7 = 12/14
3/14 = 3/14

Adding them together:
21/14 + 12/14 - 3/14 = 30/14 = 15/7

c) 3/8 + 2/7 + 9/7 + 5/7
To add these fractions, we need to find a common denominator. The least common multiple of 8, 7, and 7 is 56.

3/8 = 21/56
2/7 = 8/56
9/7 = 72/56
5/7 = 40/56

Adding them together:
21/56 + 8/56 + 72/56 + 40/56 = 141/56 = 63/28 = 9/4

d) 5/4 - 2/44 + 3/11
To add these fractions, we need to find a common denominator. The least common multiple of 4, 44, and 11 is 44.

5/4 = 55/44
2/44 = 2/44
3/11 = 12/44

Adding them together:
55/44 - 2/44 + 12/44 = 65/44 = 13/8