Let's assume that the packet of chalk contained a total of 1 unit. The first teacher received 2/5 of the chalk, which means that the remainder is 1 - 2/5 = 3/5. The second teacher received 2/15 of the remainder, which is (2/15) (3/5) = 2/25.

Therefore, the third teacher received the remaining fraction of the chalk, which is 3/5 - 2/25 = 15/25 - 2/25 = 13/25.

So, the third teacher received a fraction of 13/25 of the chalk.