The problem provides the ratio of daises to lilies to daffodils in a bouquet as $4h : 9 : 2h$.

We are tasked with finding the fraction of the flowers in the bouquet that are lilies.

Step 1: Write the ratio values

The ratio of the flowers is:

• Daisies = $4h$
• Lilies = $9$
• Daffodils = $2h$

The total number of flowers in terms of $h$ is the sum of all parts: $4h + 9 + 2h = 6h + 9$

Step 2: Find the fraction of lilies

The lilies part of the ratio is $9$. Therefore, the fraction of flowers that are lilies is: $\text{Fraction of lilies} = \frac{\text{Lilies}}{\text{Total flowers}} = \frac{9}{6h + 9}.$

Step 3: Simplify the fraction

Factorize the denominator $6h + 9$: $6h + 9 = 3(2h + 3).$

Thus, the fraction becomes: $\frac{9}{6h + 9} = \frac{9}{3(2h + 3)}.$

Simplify by dividing both numerator and denominator by 3: $\frac{9}{3(2h + 3)} = \frac{3}{2h + 3}.$

Final Answer:

The fraction of the flowers in the bouquet that are lilies is: $\frac{3}{2h + 3}.$

Would you like me to explore a specific part of the solution further?

Here are 5 related questions to extend the understanding:

1. How would the fraction change if the ratio of lilies doubled?
2. What is the total number of flowers if $h = 2$?
3. If the ratio changes to $5h : 10 : 2h$, what is the fraction of lilies?
4. How would you determine the fraction of daisies in this bouquet?
5. Can you express the fraction of lilies as a percentage?

Tip: Always factorize expressions in ratios to simplify fractions.