Math worksheet for practicing equivalent fractions and identifying improper fractions.

Problem Overview:

The worksheet focuses on equivalent fractions and comparing fractions. Here's a breakdown of the tasks:

1. Finding Equivalent Fractions: Fill in the missing numerators or denominators to create equivalent fractions.
2. Comparing Fractions: Use the symbols `>`, `<`, or `=` to compare pairs of fractions.

---

Solution:

#### Part 1: Finding Equivalent Fraactions

To find equivalent fractions, we use the principle that multiplying or dividing both the numerator and the denominator by the same non-zero number results in an equivalent fraction.

##### Step-by-Step Solutions:

1. $\frac{3}{3} = \frac{\_\_}{9}$
- Multiply both numerator and denominator by 3: $\frac{3 \times 3}{3 \times 3} = \frac{9}{9}$.
- Answer: $\boxed{9}$

2. $\frac{2}{8} = \frac{\_\_}{32}$
- Multiply both numerator and denominator by 4: $\frac{2 \times 4}{8 \times 4} = \frac{8}{32}$.
- Answer: $\boxed{8}$

3. $\frac{4}{7} = \frac{\_\_}{28}$
- Multiply both numerator and denominator by 4: $\frac{4 \times 4}{7 \times 4} = \frac{16}{28}$.
- Answer: $\boxed{16}$

4. $\frac{4}{9} = \frac{\_\_}{45}$
- Multiply both numerator and denominator by 5: $\frac{4 \times 5}{9 \times 5} = \frac{20}{45}$.
- Answer: $\boxed{20}$

5. $\frac{3}{4} = \frac{\_\_}{36}$
- Multiply both numerator and denominator by 9: $\frac{3 \times 9}{4 \times 9} = \frac{27}{36}$.
- Answer: $\boxed{27}$

6. $\frac{1}{8} = \frac{\_\_}{48}$
- Multiply both numerator and denominator by 6: $\frac{1 \times 6}{8 \times 6} = \frac{6}{48}$.
- Answer: $\boxed{6}$

7. $\frac{2}{9} = \frac{12}{\_\_}$
- Divide both numerator and denominator by 2: $\frac{12 \div 6}{54 \div 6} = \frac{2}{9}$.
- Answer: $\boxed{54}$

8. $\frac{3}{10} = \frac{21}{\_\_}$
- Multiply both numerator and denominator by 7: $\frac{3 \times 7}{10 \times 7} = \frac{21}{70}$.
- Answer: $\boxed{70}$

9. $\frac{4}{3} = \frac{\_\_}{18}$
- Multiply both numerator and denominator by 6: $\frac{4 \times 6}{3 \times 6} = \frac{24}{18}$.
- Answer: $\boxed{24}$

10. $\frac{2}{6} = \frac{\_\_}{60}$
- Simplify $\frac{2}{6}$ to $\frac{1}{3}$, then multiply by 20: $\frac{1 \times 20}{3 \times 20} = \frac{20}{60}$.
- Answer: $\boxed{20}$

11. $\frac{6}{5} = \frac{18}{\_\_}$
- Divide both numerator and denominator by 3: $\frac{18 \div 3}{x \div 3} = \frac{6}{5}$.
- Answer: $\boxed{15}$

12. $\frac{4}{7} = \frac{24}{\_\_}$
- Multiply both numerator and denominator by 6: $\frac{4 \times 6}{7 \times 6} = \frac{24}{42}$.
- Answer: $\boxed{42}$

13. $\frac{5}{12} = \frac{\_\_}{60}$
- Multiply both numerator and denominator by 5: $\frac{5 \times 5}{12 \times 5} = \frac{25}{60}$.
- Answer: $\boxed{25}$

14. $\frac{7}{11} = \frac{28}{\_\_}$
- Multiply both numerator and denominator by 4: $\frac{7 \times 4}{11 \times 4} = \frac{28}{44}$.
- Answer: $\boxed{44}$

15. $\frac{5}{4} = \frac{35}{\_\_}$
- Multiply both numerator and denominator by 7: $\frac{5 \times 7}{4 \times 7} = \frac{35}{28}$.
- Answer: $\boxed{28}$

16. $\frac{11}{12} = \frac{\_\_}{72}$
- Multiply both numerator and denominator by 6: $\frac{11 \times 6}{12 \times 6} = \frac{66}{72}$.
- Answer: $\boxed{66}$

17. $\frac{4}{9} = \frac{\_\_}{81}$
- Multiply both numerator and denominator by 9: $\frac{4 \times 9}{9 \times 9} = \frac{36}{81}$.
- Answer: $\boxed{36}$

18. $\frac{9}{10} = \frac{54}{\_\_}$
- Multiply both numerator and denominator by 6: $\frac{9 \times 6}{10 \times 6} = \frac{54}{60}$.
- Answer: $\boxed{60}$

19. $\frac{4}{13} = \frac{\_\_}{52}$
- Multiply both numerator and denominator by 4: $\frac{4 \times 4}{13 \times 4} = \frac{16}{52}$.
- Answer: $\boxed{16}$

20. $\frac{8}{3} = \frac{24}{\_\_}$
- Multiply both numerator and denominator by 3: $\frac{8 \times 3}{3 \times 3} = \frac{24}{9}$.
- Answer: $\boxed{9}$

21. $\frac{3}{10} = \frac{\_\_}{60}$
- Multiply both numerator and denominator by 6: $\frac{3 \times 6}{10 \times 6} = \frac{18}{60}$.
- Answer: $\boxed{18}$

22. $\frac{5}{2} = \frac{\_\_}{12}$
- Multiply both numerator and denominator by 6: $\frac{5 \times 6}{2 \times 6} = \frac{30}{12}$.
- Answer: $\boxed{30}$

23. $\frac{9}{12} = \frac{3}{\_\_}$
- Simplify $\frac{9}{12}$ to $\frac{3}{4}$.
- Answer: $\boxed{4}$

24. $\frac{5}{\_\_} = \frac{30}{54}$
- Simplify $\frac{30}{54}$ to $\frac{5}{9}$.
- Answer: $\boxed{9}$

---

#### Part 2: Comparing Fractions

To compare fractions, we can either:
1. Find a common denominator.
2. Convert fractions to decimals.
3. Cross-multiply.

##### Step-by-Step Solutions:

25. $\frac{3}{7} \_\_ \frac{10}{14}$
- Simplify $\frac{10}{14}$ to $\frac{5}{7}$.
- Compare $\frac{3}{7}$ and $\frac{5}{7}$: $\frac{3}{7} < \frac{5}{7}$.
- Answer: $\boxed{<}$

26. $\frac{2}{3} \_\_ \frac{8}{15}$
- Find a common denominator (15): $\frac{2}{3} = \frac{10}{15}$.
- Compare $\frac{10}{15}$ and $\frac{8}{15}$: $\frac{10}{15} > \frac{8}{15}$.
- Answer: $\boxed{>}$

27. $\frac{1}{2} \_\_ \frac{12}{20}$
- Simplify $\frac{12}{20}$ to $\frac{3}{5}$.
- Compare $\frac{1}{2}$ and $\frac{3}{5}$: $\frac{1}{2} = 0.5$, $\frac{3}{5} = 0.6$.
- Answer: $\boxed{<}$

28. $\frac{4}{5} \_\_ \frac{16}{20}$
- Simplify $\frac{16}{20}$ to $\frac{4}{5}$.
- Compare $\frac{4}{5}$ and $\frac{4}{5}$: $\frac{4}{5} = \frac{4}{5}$.
- Answer: $\boxed{=}$

29. $\frac{3}{7} \_\_ \frac{5}{14}$
- Find a common denominator (14): $\frac{3}{7} = \frac{6}{14}$.
- Compare $\frac{6}{14}$ and $\frac{5}{14}$: $\frac{6}{14} > \frac{5}{14}$.
- Answer: $\boxed{>}$

30. $\frac{4}{9} \_\_ \frac{8}{18}$
- Simplify $\frac{8}{18}$ to $\frac{4}{9}$.
- Compare $\frac{4}{9}$ and $\frac{4}{9}$: $\frac{4}{9} = \frac{4}{9}$.
- Answer: $\boxed{=}$

31. $\frac{1}{6} \_\_ \frac{3}{24}$
- Simplify $\frac{3}{24}$ to $\frac{1}{8}$.
- Compare $\frac{1}{6}$ and $\frac{1}{8}$: $\frac{1}{6} > \frac{1}{8}$.
- Answer: $\boxed{>}$

32. $\frac{2}{3} \_\_ \frac{7}{9}$
- Find a common denominator (9): $\frac{2}{3} = \frac{6}{9}$.
- Compare $\frac{6}{9}$ and $\frac{7}{9}$: $\frac{6}{9} < \frac{7}{9}$.
- Answer: $\boxed{<}$

---

Final Answers:

1. $\boxed{9}$
2. $\boxed{8}$
3. $\boxed{16}$
4. $\boxed{20}$
5. $\boxed{27}$
6. $\boxed{6}$
7. $\boxed{54}$
8. $\boxed{70}$
9. $\boxed{24}$
10. $\boxed{20}$
11. $\boxed{15}$
12. $\boxed{42}$
13. $\boxed{25}$
14. $\boxed{44}$
15. $\boxed{28}$
16. $\boxed{66}$
17. $\boxed{36}$
18. $\boxed{60}$
19. $\boxed{16}$
20. $\boxed{9}$
21. $\boxed{18}$
22. $\boxed{30}$
23. $\boxed{4}$
24. $\boxed{9}$
25. $\boxed{<}$
26. $\boxed{>}$
27. $\boxed{<}$
28. $\boxed{=}$
29. $\boxed{>}$
30. $\boxed{=}$
31. $\boxed{>}$
32. $\boxed{<}$

---

Final Answer Box:

$$
\boxed{9, 8, 16, 20, 27, 6, 54, 70, 24, 20, 15, 42, 25, 44, 28, 66, 36, 60, 16, 9, 18, 30, 4, 9, <, >, <, =, >, =, >, <}
$$