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The problem involves a portion of a pizza being eaten, and then a third of the remaining pizza given away to a friend. The question asks how much of the pizza you ate, given that a quarter of the pizza was left after sharing with your friend.

Let's break it down step by step:

1. You ate a portion of the pizza, which we'll call \( p \) (the portion you ate).
2. You then gave away \( \frac{1}{3} \) of the remaining pizza to your friend.
3. After giving away that third to your friend, a quarter (\( \frac{1}{4} \)) of the pizza was left.

If \( x \) is the portion of the pizza that remains after you ate, the problem states that after giving away \( \frac{1}{3} \) of that portion to your friend, a quarter was left. This can be expressed as:

\[
x - \frac{1}{3}x = \frac{1}{4}
\]

Solving for \( x \):

\[
\frac{2}{3}x = \frac{1}{4}
\]

Multiply both sides by \( \frac{3}{2} \):

\[
x = \frac{3}{2} \times \frac{1}{4} = \frac{3}{8}
\]

So, \( \frac{3}{8} \) of the pizza was left after you ate your portion.

Now, to find out how much you ate, we subtract \( \frac{3}{8} \) from the whole pizza (which is 1 pizza):

\[
1 - \frac{3}{8} = \frac{8}{8} - \frac{3}{8} = \frac{5}{8}
\]

Therefore, you ate **5/8** of the pizza.

Would you like further details on this solution or have any other questions?

Here are some related questions:
1. How would the calculation change if you gave away half of the remaining pizza instead of a third?
2. What would happen if there was only 1/8 of the pizza left after giving to your friend?
3. Can we generalize this problem for other fractions of the remaining pizza given away?
4. How much pizza would your friend get if you ate 5/8 of it?
5. What is the total fraction of the pizza consumed by both you and your friend?

**Tip:** When working with fractions, it’s often easier to solve if you set up an equation and isolate the variable step by step.

If there was a quarter of the pizza left after I gave some to my friend, how much of the pizza did I eat?

Solve this fraction pizza problem where a person eats a portion of pizza, gives away a third of the remaining pizza, and is left with a quarter. Learn how to determine how much pizza was eaten using algebra and fraction arithmetic.

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