Why does rand() + rand() produce negative numbers?

I observed that rand() library function when it is called just once within a loop, it almost always produces positive numbers.

for (i = 0; i < 100; i++) {
    printf("%d\n", rand());
}

But when I add two rand() calls, the numbers generated now have more negative numbers.

for (i = 0; i < 100; i++) {
    printf("%d = %d\n", rand(), (rand() + rand()));
}

Can someone explain why I am seeing negative numbers in the second case?

PS: I initialize the seed before the loop as srand(time(NULL)).