The image you provided contains exercise questions asking to express the mixed fractions in their proper fraction form. Let me work through each one for you:

1. $2 \frac{3}{4}$:
   This is a mixed number. To express it as an improper fraction: $2 \frac{3}{4} = \frac{(2 \times 4) + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4}$

2. $4 \frac{2}{3}$:
   Similarly, this is a mixed number. Converting to an improper fraction: $4 \frac{2}{3} = \frac{(4 \times 3) + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3}$

3. $3 \frac{3}{5}$:
   To convert to an improper fraction: $3 \frac{3}{5} = \frac{(3 \times 5) + 3}{5} = \frac{15 + 3}{5} = \frac{18}{5}$

4. $1 \frac{4}{6}$:
   Converting this to an improper fraction: $1 \frac{4}{6} = \frac{(1 \times 6) + 4}{6} = \frac{6 + 4}{6} = \frac{10}{6} = \frac{5}{3}$

5. $4 \frac{1}{2}$:
   Converting to an improper fraction: $4 \frac{1}{2} = \frac{(4 \times 2) + 1}{2} = \frac{8 + 1}{2} = \frac{9}{2}$

6. $2 \frac{4}{7}$:
   Converting to an improper fraction: $2 \frac{4}{7} = \frac{(2 \times 7) + 4}{7} = \frac{14 + 4}{7} = \frac{18}{7}$

Now all the mixed fractions are expressed as improper fractions.

Would you like further explanations or details on any of these? Feel free to ask!
Here are some related questions for further study:

1. How do you convert improper fractions back into mixed numbers?
2. What are the properties of improper fractions in addition and subtraction?
3. Can you simplify an improper fraction? If so, how?
4. How do you compare two improper fractions?
5. What is the role of denominators when adding fractions?

Tip: Always check that the numerator is greater than or equal to the denominator when working with improper fractions!