John ate 1/2 of pizza for lunch, and he are 1/3 of what was left for dinner. How much pizza did John eat for dinner?

Let X be the amount of pizza John had for lunch.

John ate X/2 for dinner.
John ate X - X/2 = X/2 for dinner. John ate X/2 * 1/3 = X/6 of pizza for dinner. Answer: \boxed{\frac{X}{6}}.

To find out how much pizza John ate for dinner, we need to follow these steps:

Step 1: Calculate the amount of pizza left after John ate 1/2 for lunch.

To do this, we subtract 1/2 from 1 whole pizza:

1 - 1/2 = 1/2.

So, there was 1/2 of pizza left after John ate for lunch.

Step 2: Calculate the amount of pizza John ate for dinner, which is 1/3 of what was left.

To do this, we multiply the amount left by 1/3:

1/2 * 1/3 = 1/6.

Therefore, John ate 1/6 of a pizza for dinner.