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Let's go over the questions one by one.

### Problem 9: Find the LCD and GCF for the following word problem
The problem involves two fractions:

- The baby weighed \(8 \frac{1}{6}\) pounds at birth.
- A month later, she weighed \(9 \frac{1}{2}\) pounds.

The first step is to find how much weight the baby gained, which requires subtracting the two mixed fractions. To subtract:

- Convert each mixed number to an improper fraction:
  - \( 8 \frac{1}{6} = \frac{49}{6} \)
  - \( 9 \frac{1}{2} = \frac{19}{2} \)
  
- To subtract these fractions, we need the **Least Common Denominator (LCD)** between 6 and 2. The LCD of 6 and 2 is 6.
  
- Next, rewrite both fractions with a denominator of 6:
  - \( \frac{19}{2} = \frac{57}{6} \)

- Now subtract the two fractions:
  - \( \frac{57}{6} - \frac{49}{6} = \frac{8}{6} \)
  
- Simplify the fraction \( \frac{8}{6} = \frac{4}{3} \).

The baby gained \( \frac{4}{3} \) pounds.

- **LCD = 6**
- Since \( \frac{4}{3} \) is in its simplest form, **GCF = 1**.

### Problem 10: Solve the word problem and simplify if possible

We are given:

- One floorboard is \( 6 \frac{1}{3} \) feet long.
- Another floorboard is \( 2 \frac{5}{9} \) feet long.
- The total length of the floor is \( 12 \frac{2}{9} \) feet.
- We need to find how long the third board must be to cover the total length.

Steps:

1. Convert all mixed numbers to improper fractions:
   - \( 6 \frac{1}{3} = \frac{19}{3} \)
   - \( 2 \frac{5}{9} = \frac{23}{9} \)
   - \( 12 \frac{2}{9} = \frac{110}{9} \)

2. Add the lengths of the two given boards:
   - \( \frac{19}{3} = \frac{57}{9} \) (convert to a denominator of 9)
   - Now add \( \frac{57}{9} + \frac{23}{9} = \frac{80}{9} \)

3. Subtract the total length of the two boards from the total floor length:
   - \( \frac{110}{9} - \frac{80}{9} = \frac{30}{9} \)
   - Simplify \( \frac{30}{9} = \frac{10}{3} \)

The third board must be \( \frac{10}{3} = 3 \frac{1}{3} \) feet long.

Therefore, the correct answer is **\( 3 \frac{1}{3} \) feet**.

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Would you like further details on the steps or any clarifications? Here are five related questions:

1. How do you find the LCD of two fractions with different denominators?
2. How do you convert a mixed number into an improper fraction?
3. What are the steps to simplify fractions?
4. How do you handle word problems involving fractions and mixed numbers?
5. What methods can you use to verify your answer in a subtraction or addition of fractions?

**Tip**: Always simplify fractions to their lowest terms after performing arithmetic operations to get the most accurate answer.

Choose the LCD and the GCF for the following word problem. A baby weighed 8 1/6 pounds at birth. A month later, she weighed 9 1/2 pounds. How much weight did she gain? Solve the word problem: A floorboard was 6 1/3 feet long. Another floorboard that was 2 5/9 feet long was added. If the total length of the floor is 12 2/9 feet, how long must a third board be to cover the entire length of the floor?

Solve two word problems involving fractions and mixed numbers. Calculate the weight gained by a baby from 8 1/6 to 9 1/2 pounds by finding the Least Common Denominator (LCD) and Greatest Common Factor (GCF). Learn how to add two floorboards of lengths 6 1/3 and 2 5/9 feet and determine the required length of a third board to reach 12 2/9 feet. This exercise covers key concepts in fractions and mixed numbers.

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