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We are given the ratio of the number of flowers (daisies to lilies to daffodils) in a bouquet as \( 4h : 9 : 2h \). 

To find the fraction of the flowers that are lilies:

### Step 1: Identify the parts for each type of flower
- Daisies: \( 4h \)
- Lilies: \( 9 \)
- Daffodils: \( 2h \)

### Step 2: Calculate the total number of flowers
The total number of flowers in the bouquet is the sum of the parts for each type of flower:
\[
4h + 9 + 2h = 6h + 9
\]

### Step 3: Find the fraction of lilies
The fraction of lilies is the number of lilies divided by the total number of flowers:
\[
\frac{\text{Lilies}}{\text{Total flowers}} = \frac{9}{6h + 9}
\]

### Step 4: Simplify the fraction
Factor the denominator:
\[
6h + 9 = 3(2h + 3)
\]
So, the fraction becomes:
\[
\frac{9}{3(2h + 3)} = \frac{3}{2h + 3}
\]

Thus, the fraction of the flowers that are lilies is \( \frac{3}{2h + 3} \).

Let me know if you'd like more details or have any questions! 

Here are five related questions you could explore:
1. What happens to the fraction of lilies if \( h = 2 \)?
2. How many total flowers are there if \( h = 1 \)?
3. What fraction of the flowers are daisies?
4. What fraction of the flowers are daffodils?
5. If the bouquet contains 30 flowers in total, how many of each flower are present?

**Tip:** Always try to simplify fractions by factoring both the numerator and denominator when possible!

A florist sells bouquets containing different flowers. The ratio of daisies to lilies to daffodils in a bouquet is 4h : 9 : 2h. What fraction of the flowers in the bouquet are lilies?

Learn how to calculate the fraction of lilies in a bouquet with a given ratio of daisies to lilies to daffodils. Understand the steps of simplification and factoring to express the final answer in its simplest form. Suitable for students in Grades 7-9.

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