In Brian's pencil case, 1/2 of all writing implements are pencils. Of the pencil's, 2/3 are lead pencils. What fraction of Brian's pencil case is lead pencils?

In the question it is already given that 1/2 of all writing implements are pencils. So we do not require the number of other materials in the pencil box. among the 1/2 of the pencils present, 2/3 are lead pencils.

Then

The number of lead pencils in the box = (1/2) * (2/3)

= 1/3

So 1/3 of the total 1/2 of the pencils are lead pencils.

Since we are not aware about the total number of materials in the box, so reaching the specific answer is impossible.