The common denominator for all fractions is 72.

Converting all fractions to have a denominator of 72:

(4/15) (4/4) = 16/60
(5/18) (4/4) = 20/72
(2/21) (3/3) = 6/63
(5/21) (3/3) = 15/63
(1/24) (3/3) = 3/72
(7/24) (3/3) = 21/72

Adding all the fractions together:

1/15 + 16/72 + 20/72 + 6/72 + 15/72 + 3/72 + 21/72 = 62/72 or 31/36