Question

You make a large bowl of salad to share with your friends. Your brother eats 1/3 of it before they come over

Answer 1

Assume that the original amount of salad you made is "m".
Now, your brother ate 1/3 of the original amount.

This means that:
The amount left to be divided among your friends = m - (1/3) m = (2/3) m

Now, we need to divide this amount among the six friends of yours, therefore:
the amount that each friend gets can be calculated by dividing the (2/3) m which is the left portion of the salad by the number of friends as follows:
each friend receives = [(2/3) m] / 6 = (1/9) m