King Dasaratha gave half of the divine payasa broth to Queen Kaushalya, one third to Queen Sumitra and one eighth to Kaikeyi and then, after some thought, the remainder to Sumitra. So what proportion did each get in the end?

1/2 (Kaushalya) + 1/3 (Sumitra) + 1/8 (Kaikeyi) (first round) =
12/24 + 8/24 + 3/24 = 23/24

Left over for Sumitra therefore: 1/24
So Sumitra received in toto: 1/3 + 1/24 = 8/24 + 1/24 = 9/24 = 3/8

Therefore the final distribution was as follows:
1/2 + 3/8 + 1/8 = 4/8 (Kaushalya) + 3/8 (Sumitra) + 1/8 (Kaikeyi)
= 8/8 = 1