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The problem involves Gavin's writing rate, which is \( \frac{2}{3} \) of a page every 15 minutes (which is \( \frac{1}{4} \) of an hour). We are asked to find which of the given statements are true. Let’s break it down:

1. **Gavin’s writing rate**: 
   Gavin writes \( \frac{2}{3} \) of a page in 15 minutes. Therefore, in 1 hour (60 minutes), he writes \( \frac{2}{3} \times 4 = \frac{8}{3} \) pages.

Now, let’s analyze each statement:

**A. "Gavin writes \( \frac{2}{3} \) of a page every \( \frac{1}{4} \) hour."**
- This is correct. Gavin writes \( \frac{2}{3} \) of a page in 15 minutes, and 15 minutes is \( \frac{1}{4} \) of an hour.

**B. "If he writes for \( 3 \frac{1}{2} \) hours, then Gavin will write \( 2 \frac{1}{3} \) pages."**
- To calculate the number of pages Gavin writes in \( 3 \frac{1}{2} \) hours, multiply the rate of \( \frac{8}{3} \) pages per hour by \( 3 \frac{1}{2} \) hours:
  \[
  \frac{8}{3} \times \frac{7}{2} = \frac{56}{6} = \frac{28}{3} \approx 9 \frac{1}{3} \text{ pages.}
  \]
  The statement is false.

**C. "Every hour, Gavin writes \( 2 \frac{2}{3} \) pages."**
- In 1 hour, Gavin writes \( \frac{8}{3} \) pages, which is \( 2 \frac{2}{3} \) pages. This statement is true.

**D. "Gavin writes \( \frac{1}{3} \) page in half an hour."**
- In 1 hour, he writes \( \frac{8}{3} \) pages. In half an hour (which is half of the rate), he would write:
  \[
  \frac{8}{3} \times \frac{1}{2} = \frac{4}{3} \text{ pages}.
  \]
  So, this statement is false.

**E. "If Gavin wrote \( 6 \frac{2}{3} \) pages at one sitting, then he wrote for \( 2 \frac{1}{2} \) hours."**
- To determine how long it took Gavin to write \( 6 \frac{2}{3} \) pages, divide the pages by his rate:
  \[
  \frac{20}{3} \div \frac{8}{3} = \frac{20}{3} \times \frac{3}{8} = \frac{20}{8} = 2.5 \text{ hours.}
  \]
  This statement is true.

### True Statements:
- A
- C
- E

Do you want further details or have any questions?

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Here are 5 related questions you might find useful:
1. How would the answers change if Gavin wrote \( \frac{1}{2} \) a page every 15 minutes?
2. If Gavin increased his rate by 50%, how many pages would he write in 3 hours?
3. How many pages would Gavin write if he wrote continuously for 10 hours?
4. If Gavin writes for 45 minutes, how many pages will he complete?
5. How much time does Gavin take to write 10 pages?

**Tip**: When solving rate problems, converting time units (e.g., minutes to hours) can help simplify the calculations.

When writing in his notebook, Gavin writes at a rate of 2/3 of a page every 15 minutes. Which of these statements are true? Choose the THREE correct answers.

Analyze Gavin's writing rate, where he writes 2/3 of a page every 15 minutes. Find the correct true statements based on rate, pages, and time relationships. Suitable for students in Grades 6-8.

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