Fraction equivalence worksheet for students to determine if pairs of fractions are equal.

Let's solve the problem step by step.

Task:

Determine which of the given equations show equivalent fractions.
We need to check each equation and mark (or identify) those where the two fractions are equivalent.

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How to Check if Two Fractions Are Equivalent:

Two fractions $ \frac{a}{b} $ and $ \frac{c}{d} $ are equivalent if:
$$
\frac{a}{b} = \frac{c}{d} \quad \text{when} \quad a \cdot d = b \cdot c
$$
Alternatively, simplify both fractions and see if they reduce to the same value.

We'll go through each pair and check.

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List of Equations:

1. $ \frac{5}{11} = \frac{25}{55} $
→ Simplify $ \frac{25}{55} = \frac{5}{11} $ ✔ Equivalent

2. $ \frac{5}{5} = \frac{10}{10} $
→ Both equal 1 ✔ Equivalent

3. $ \frac{6}{9} = \frac{30}{45} $
→ $ \frac{6}{9} = \frac{2}{3}, \frac{30}{45} = \frac{2}{3} $ ✔ Equivalent

4. $ \frac{8}{12} = \frac{32}{48} $
→ $ \frac{8}{12} = \frac{2}{3}, \frac{32}{48} = \frac{2}{3} $ ✔ Equivalent

5. $ \frac{6}{11} = \frac{18}{33} $
→ $ \frac{18}{33} = \frac{6}{11} $ ✔ Equivalent

6. $ \frac{3}{4} = \frac{9}{12} $
→ $ \frac{9}{12} = \frac{3}{4} $ ✔ Equivalent

7. $ \frac{5}{9} = \frac{10}{18} $
→ $ \frac{10}{18} = \frac{5}{9} $ ✔ Equivalent

8. $ \frac{6}{6} = \frac{30}{30} $
→ Both equal 1 ✔ Equivalent

9. $ \frac{5}{10} = \frac{15}{30} $
→ Both equal $ \frac{1}{2} $ ✔ Equivalent

10. $ \frac{10}{10} = \frac{30}{30} $
→ Both equal 1 ✔ Equivalent

11. $ \frac{4}{6} = \frac{20}{18} $
→ $ \frac{4}{6} = \frac{2}{3}, \frac{20}{18} = \frac{10}{9} $ ✘ Not equivalent

12. $ \frac{1}{3} = \frac{2}{6} $
→ $ \frac{2}{6} = \frac{1}{3} $ ✔ Equivalent

13. $ \frac{7}{8} = \frac{35}{40} $
→ $ \frac{35}{40} = \frac{7}{8} $ ✔ Equivalent

14. $ \frac{3}{9} = \frac{9}{36} $
→ $ \frac{3}{9} = \frac{1}{3}, \frac{9}{36} = \frac{1}{4} $ ✘ Not equivalent

15. $ \frac{2}{8} = \frac{10}{40} $
→ $ \frac{2}{8} = \frac{1}{4}, \frac{10}{40} = \frac{1}{4} $ ✔ Equivalent

16. $ \frac{4}{5} = \frac{12}{15} $
→ $ \frac{12}{15} = \frac{4}{5} $ ✔ Equivalent

17. $ \frac{2}{7} = \frac{10}{14} $
→ $ \frac{10}{14} = \frac{5}{7} \neq \frac{2}{7} $ ✘ Not equivalent

18. $ \frac{4}{8} = \frac{12}{32} $
→ $ \frac{4}{8} = \frac{1}{2}, \frac{12}{32} = \frac{3}{8} $ ✘ Not equivalent

19. $ \frac{1}{2} = \frac{2}{10} $
→ $ \frac{2}{10} = \frac{1}{5} \neq \frac{1}{2} $ ✘ Not equivalent

20. $ \frac{5}{11} = \frac{15}{33} $
→ $ \frac{15}{33} = \frac{5}{11} $ ✔ Equivalent

21. $ \frac{3}{10} = \frac{12}{40} $
→ $ \frac{12}{40} = \frac{3}{10} $ ✔ Equivalent

22. $ \frac{3}{7} = \frac{6}{14} $
→ $ \frac{6}{14} = \frac{3}{7} $ ✔ Equivalent

23. $ \frac{7}{9} = \frac{21}{27} $
→ $ \frac{21}{27} = \frac{7}{9} $ ✔ Equivalent

24. $ \frac{1}{6} = \frac{5}{30} $
→ $ \frac{5}{30} = \frac{1}{6} $ ✔ Equivalent

25. $ \frac{9}{9} = \frac{18}{18} $
→ Both equal 1 ✔ Equivalent

26. $ \frac{5}{9} = \frac{10}{18} $
→ Already checked above ✔ Equivalent

27. $ \frac{1}{2} = \frac{2}{10} $
→ Already checked ✘ Not equivalent

28. $ \frac{4}{7} = \frac{8}{14} $
→ $ \frac{8}{14} = \frac{4}{7} $ ✔ Equivalent

29. $ \frac{6}{8} = \frac{18}{32} $
→ $ \frac{6}{8} = \frac{3}{4}, \frac{18}{32} = \frac{9}{16} $ ✘ Not equivalent

30. $ \frac{5}{11} = \frac{15}{33} $
→ Already checked ✔ Equivalent

31. $ \frac{6}{6} = \frac{24}{30} $
→ $ \frac{6}{6} = 1, \frac{24}{30} = \frac{4}{5} $ ✘ Not equivalent

32. $ \frac{1}{2} = \frac{4}{4} $
→ $ \frac{4}{4} = 1 \neq \frac{1}{2} $ ✘ Not equivalent

33. $ \frac{1}{7} = \frac{5}{35} $
→ $ \frac{5}{35} = \frac{1}{7} $ ✔ Equivalent

34. $ \frac{3}{5} = \frac{9}{15} $
→ $ \frac{9}{15} = \frac{3}{5} $ ✔ Equivalent

35. $ \frac{2}{2} = \frac{8}{10} $
→ $ \frac{2}{2} = 1, \frac{8}{10} = \frac{4}{5} $ ✘ Not equivalent

36. $ \frac{3}{3} = \frac{15}{9} $
→ $ \frac{3}{3} = 1, \frac{15}{9} = \frac{5}{3} $ ✘ Not equivalent

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✔ Final Answer: Mark the following as equivalent:

1. $ \frac{5}{11} = \frac{25}{55} $
2. $ \frac{5}{5} = \frac{10}{10} $
3. $ \frac{6}{9} = \frac{30}{45} $
4. $ \frac{8}{12} = \frac{32}{48} $
5. $ \frac{6}{11} = \frac{18}{33} $
6. $ \frac{3}{4} = \frac{9}{12} $
7. $ \frac{5}{9} = \frac{10}{18} $
8. $ \frac{6}{6} = \frac{30}{30} $
9. $ \frac{5}{10} = \frac{15}{30} $
10. $ \frac{10}{10} = \frac{30}{30} $
12. $ \frac{1}{3} = \frac{2}{6} $
13. $ \frac{7}{8} = \frac{35}{40} $
15. $ \frac{2}{8} = \frac{10}{40} $
16. $ \frac{4}{5} = \frac{12}{15} $
20. $ \frac{5}{11} = \frac{15}{33} $
21. $ \frac{3}{10} = \frac{12}{40} $
22. $ \frac{3}{7} = \frac{6}{14} $
23. $ \frac{7}{9} = \frac{21}{27} $
24. $ \frac{1}{6} = \frac{5}{30} $
25. $ \frac{9}{9} = \frac{18}{18} $
26. $ \frac{5}{9} = \frac{10}{18} $
28. $ \frac{4}{7} = \frac{8}{14} $
30. $ \frac{5}{11} = \frac{15}{33} $
33. $ \frac{1}{7} = \frac{5}{35} $
34. $ \frac{3}{5} = \frac{9}{15} $

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✘ Not Equivalent:

- #11: $ \frac{4}{6} = \frac{20}{18} $
- #14: $ \frac{3}{9} = \frac{9}{36} $
- #17: $ \frac{2}{7} = \frac{10}{14} $
- #18: $ \frac{4}{8} = \frac{12}{32} $
- #19: $ \frac{1}{2} = \frac{2}{10} $
- #27: $ \frac{1}{2} = \frac{2}{10} $
- #29: $ \frac{6}{8} = \frac{18}{32} $
- #31: $ \frac{6}{6} = \frac{24}{30} $
- #32: $ \frac{1}{2} = \frac{4}{4} $
- #35: $ \frac{2}{2} = \frac{8}{10} $
- #36: $ \frac{3}{3} = \frac{15}{9} $

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✔ Summary:

Mark all the ones with ✔ above — these are the equivalent fractions.

Let me know if you'd like this in a checklist format or printable version!