To add these fractions, first find a common denominator:

The least common multiple of 9, 8, and 7 is 504.

Convert each fraction to have a denominator of 504:

(4/9)(56/56) = 224/504
(3/8)(63/63) = 189/504
(2/7)(72/72) = 144/504
(5/7)(72/72) = 360/504
(5/8)(63/63) = 315/504
(5/9)(56/56) = 280/504

Now add them all together:

224/504 + 189/504 + 144/504 + 360/504 + 315/504 + 280/504 = 1512/504 = 3

Therefore, the sum of the fractions is 3.