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Let's break down the problem.

**Given:**
- The formula for 6 gallons of light green paint uses \( \frac{3}{8} \) gallon of white paint.
- Liam has \( \frac{9}{16} \) gallon of white paint.

**Part a:**
You are asked if Liam has enough white paint to make 8 gallons of light green paint. If not, how much more does he need?

**Step-by-step solution:**

1. **Find the amount of white paint needed for 1 gallon of light green paint:**

   \[
   \text{White paint needed per gallon} = \frac{3}{8} \div 6 = \frac{3}{8} \times \frac{1}{6} = \frac{3}{48} = \frac{1}{16} \, \text{gallons per gallon of light green paint}
   \]

2. **Find the amount of white paint needed for 8 gallons of light green paint:**

   \[
   \text{White paint for 8 gallons} = 8 \times \frac{1}{16} = \frac{8}{16} = \frac{1}{2} \, \text{gallons}
   \]

3. **Compare the amount of white paint Liam has with the required amount:**
   
   Liam has \( \frac{9}{16} \) gallon of white paint.

   The white paint required is \( \frac{1}{2} = \frac{8}{16} \).

   Since \( \frac{9}{16} \) is greater than \( \frac{8}{16} \), **Liam has enough white paint** to make 8 gallons of light green paint.

   **Conclusion:** Liam has \( \frac{9}{16} \) gallon of white paint, which is more than the \( \frac{8}{16} \) gallon needed. So, he does not need any more paint.

Would you like further details or explanations?

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**Here are 5 additional questions related to the problem:**

1. What is the total amount of white paint needed to make 10 gallons of light green paint?
2. How much more white paint would Liam need if he wanted to make 12 gallons of light green paint?
3. If Liam used \( \frac{1}{16} \) gallon of white paint per gallon of light green paint, how many gallons of light green paint can he make with \( \frac{9}{16} \) gallon of white paint?
4. How would the formula change if the ratio of white paint to light green paint increased to \( \frac{4}{8} \)?
5. What fraction of white paint does Liam have if he wants to make 5 gallons of light green paint?

**Tip:** When comparing fractions, it helps to express them with the same denominator to easily see which one is larger.

A formula for 6 gallons of light green paint uses 3/8 gallon of white paint. Liam has 9/16 gallon of white paint. Does Liam have enough white paint to make 8 gallons of light green paint? If not, how much more does he need?

Explore how to solve a proportional relationship problem involving fractions. This example shows how to determine if 9/16 gallons of white paint is enough to make 8 gallons of light green paint. Suitable for Grades 6-8 students learning about fractions and proportional reasoning.

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