Let's analyze the image and solve the questions step-by-step.

Problem 1: How many groups of $\frac{1}{4}$ are in 6?

To find how many groups of $\frac{1}{4}$ are in 6, we need to divide 6 by $\frac{1}{4}$:

$6 \div \frac{1}{4}$

Dividing by a fraction is equivalent to multiplying by its reciprocal:

$6 \times \frac{4}{1} = 6 \times 4 = 24$

So, there are 24 groups of $\frac{1}{4}$ in 6.

Problem 2: Evaluate $6 \div \frac{5}{4}$

To evaluate $6 \div \frac{5}{4}$, we need to multiply 6 by the reciprocal of $\frac{5}{4}$:

$6 \times \frac{4}{5} = \frac{24}{5}$

Now, we convert $\frac{24}{5}$ to a mixed number:

$\frac{24}{5} = 4 \frac{4}{5}$

So, $6 \div \frac{5}{4} = 4 \frac{4}{5}$.

Summary of Answers:

1. There are 24 groups of $\frac{1}{4}$ in 6.
2. $6 \div \frac{5}{4} = 4 \frac{4}{5}$.

Would you like more details on any of these solutions, or do you have any further questions?

Here are 5 related questions to expand your understanding:

1. What is the reciprocal of a fraction, and why is it used in division problems?
2. How can we visually represent dividing whole numbers by fractions using a number line?
3. How do we convert improper fractions to mixed numbers?
4. What is the process for solving problems involving division of fractions?
5. Can you provide more examples of dividing a whole number by a fraction?

Tip: When dividing by a fraction, remember to multiply by its reciprocal!