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### Problem 4:
**Question:** Tess measures out two pieces of wood trim for her art project. One piece is \(4 \frac{1}{2}\) inches long and the other is \(5 \frac{3}{4}\) inches long. Which of the following represents the total length of wood trim that Tess measures?

The options provided are:
1. \(9 \frac{3}{4}\)
2. \(9 \frac{5}{8}\)
3. \(10 \frac{5}{16}\)
4. \(11 \frac{1}{4}\)

**Solution:**
To find the total length of wood trim, we add the two lengths together:
\[
4 \frac{1}{2} + 5 \frac{3}{4} = \left(4 + \frac{1}{2}\right) + \left(5 + \frac{3}{4}\right)
\]

Convert the mixed numbers to improper fractions for easier addition:
\[
4 \frac{1}{2} = \frac{9}{2}, \quad 5 \frac{3}{4} = \frac{23}{4}
\]

To add these fractions, we first convert them to have a common denominator:
\[
\frac{9}{2} = \frac{18}{4}, \quad \frac{23}{4} = \frac{23}{4}
\]

Now add the fractions:
\[
\frac{18}{4} + \frac{23}{4} = \frac{41}{4} = 10 \frac{1}{4}
\]

So, the correct answer is \(10 \frac{1}{4}\) inches.

**None of the options exactly match this calculation**. It seems the correct total should be \(10 \frac{1}{4}\), not any of the options provided. Double-checking the problem might be necessary to ensure no mistakes were made.

### Problem 5:
**Question:** Theo adds two-thirds of a cup of water to a pancake recipe and then decides to add an additional quarter cup of water. Theo knows he added almost a total cup of water. How much less than a cup did Theo add? Justify your answer.

**Solution:**
First, add the two fractions:
\[
\frac{2}{3} + \frac{1}{4}
\]

To add these, find a common denominator:
\[
\frac{2}{3} = \frac{8}{12}, \quad \frac{1}{4} = \frac{3}{12}
\]
\[
\frac{8}{12} + \frac{3}{12} = \frac{11}{12}
\]

Theo added \(\frac{11}{12}\) cups of water. Since a full cup is \(1\) or \(\frac{12}{12}\), the difference is:
\[
1 - \frac{11}{12} = \frac{1}{12}
\]

So, Theo added \(\frac{1}{12}\) cup less than a full cup.

### Problem 6:
**Question:** At the beginning of the evening there were four and one-eighth chocolate bars left. Over the course of the evening, three and three-quarters chocolate bars were eaten. How much chocolate is left at the end of the evening? Justify.

**Solution:**
First, convert the mixed numbers to improper fractions:
\[
4 \frac{1}{8} = \frac{33}{8}, \quad 3 \frac{3}{4} = \frac{15}{4} = \frac{30}{8}
\]

Now subtract:
\[
\frac{33}{8} - \frac{30}{8} = \frac{3}{8}
\]

So, \(\frac{3}{8}\) of a chocolate bar is left.

### Problem on GCF:
**Question:** What is the greatest common factor (GCF) of 32 and 80?

The work shown involves prime factorization:
\[
32 = 2^5, \quad 80 = 2^4 \times 5
\]

The common factors are \(2^4\), so the GCF is \(2^4 = 16\).

**Conclusion:** The greatest common factor of 32 and 80 is 16.

---

Would you like more detailed explanations on any of these solutions or have any questions? Here are some related questions you might find interesting:

1. How do you convert mixed numbers to improper fractions and back?
2. What are some methods for finding the least common denominator when adding fractions?
3. Can you explain more about the process of finding the greatest common factor (GCF)?
4. How would the solution change if Theo added a different fraction of water?
5. How would you handle subtraction if one fraction has a larger denominator than the other?

**Tip:** When dealing with mixed numbers, converting them to improper fractions can simplify operations like addition, subtraction, and comparison.

Tess measures out two pieces of wood trim for her art project. One piece is 4 1/2 inches long and the other is 5 3/4 inches long. Which of the following represents the total length of wood trim that Tess measures? Theo adds two-thirds of a cup of water to a pancake recipe and then decides to add an additional quarter cup of water. Theo knows he added almost a total cup of water. How much less than a cup did Theo add? At the beginning of the evening there were four and one-eighth chocolate bars left. Over the course of the evening, three and three-quarters chocolate bars were eaten. How much chocolate is left at the end of the evening?

Learn how to solve problems involving addition and subtraction of fractions and finding the greatest common factor (GCF). This includes real-life examples such as calculating wood trim lengths, adding water to a pancake recipe, and determining how much chocolate remains. Suitable for students in Grades 5-7.

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