Comparing Proper, Improper and Mixed Fractions to Twelfths (A) - Free Printable

Let's solve the worksheet titled "Comparing Proper, Improper and Mixed Fractions (A)" step by step.

We are to compare each pair of fractions using <, >, or =. We'll go through each problem carefully, converting mixed numbers to improper fractions where needed, simplifying when possible, and comparing numerators and denominators.

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Step-by-step Solutions:

1. $ \frac{2}{4} \quad \boxed{<} \quad \frac{3}{4} $
→ Same denominator; 2 < 3 → <

2. $ 1\frac{1}{11} \quad \boxed{<} \quad \frac{19}{11} $
→ Convert $1\frac{1}{11} = \frac{12}{11}$; $ \frac{12}{11} < \frac{19}{11} $ → <

3. $ \frac{6}{10} \quad \boxed{>} \quad \frac{2}{6} $
→ Simplify: $ \frac{6}{10} = \frac{3}{5}, \frac{2}{6} = \frac{1}{3} $. Compare: $ \frac{3}{5} = 0.6, \frac{1}{3} \approx 0.333 $ → >

4. $ \frac{3}{6} \quad \boxed{=} \quad 1\frac{1}{8} $
→ $ \frac{3}{6} = \frac{1}{2} = 0.5 $, $ 1\frac{1}{8} = 1.125 $ → <? Wait — no:
$ \frac{1}{2} < 1.125 $ → So actually $ \frac{3}{6} < 1\frac{1}{8} $ → <

✔ Correction: $ \frac{3}{6} = 0.5 $, $ 1\frac{1}{8} = 1.125 $ → <

5. $ \frac{5}{6} \quad \boxed{>} \quad \frac{2}{3} $
→ $ \frac{2}{3} = \frac{4}{6} $, $ \frac{5}{6} > \frac{4}{6} $ → >

6. $ \frac{4}{6} \quad \boxed{<} \quad \frac{3}{10} $
→ $ \frac{4}{6} = \frac{2}{3} \approx 0.666 $, $ \frac{3}{10} = 0.3 $ → $ 0.666 > 0.3 $ → >

✘ Wait: $ \frac{4}{6} > \frac{3}{10} $ → So should be >, not <

7. $ \frac{10}{6} \quad \boxed{>} \quad \frac{4}{5} $
→ $ \frac{10}{6} = \frac{5}{3} \approx 1.666 $, $ \frac{4}{5} = 0.8 $ → >

8. $ 1\frac{8}{9} \quad \boxed{>} \quad \frac{2}{9} $
→ $ 1\frac{8}{9} = \frac{17}{9} $, $ \frac{2}{9} $ → clearly $ \frac{17}{9} > \frac{2}{9} $ → >

9. $ \frac{5}{8} \quad \boxed{>} \quad 1\frac{9}{12} $
→ $ 1\frac{9}{12} = 1\frac{3}{4} = 1.75 $, $ \frac{5}{8} = 0.625 $ → $ 0.625 < 1.75 $ → <

10. $ 1\frac{3}{12} \quad \boxed{>} \quad 1\frac{4}{5} $
→ $ 1\frac{3}{12} = 1\frac{1}{4} = 1.25 $, $ 1\frac{4}{5} = 1.8 $ → $ 1.25 < 1.8 $ → <

11. $ \frac{1}{3} \quad \boxed{<} \quad \frac{1}{2} $
→ $ \frac{1}{3} \approx 0.333, \frac{1}{2} = 0.5 $ → <

12. $ \frac{3}{4} \quad \boxed{>} \quad 1\frac{1}{6} $
→ $ \frac{3}{4} = 0.75 $, $ 1\frac{1}{6} \approx 1.166 $ → $ 0.75 < 1.166 $ → <

13. $ 1\frac{1}{4} \quad \boxed{>} \quad \frac{8}{12} $
→ $ 1\frac{1}{4} = 1.25 $, $ \frac{8}{12} = \frac{2}{3} \approx 0.666 $ → >

14. $ \frac{3}{4} \quad \boxed{>} \quad \frac{7}{10} $
→ $ \frac{3}{4} = 0.75, \frac{7}{10} = 0.7 $ → $ 0.75 > 0.7 $ → >

15. $ \frac{4}{3} \quad \boxed{>} \quad \frac{6}{4} $
→ $ \frac{4}{3} \approx 1.333, \frac{6}{4} = 1.5 $ → $ 1.333 < 1.5 $ → <

16. $ 1 \quad \boxed{>} \quad \frac{2}{8} $
→ $ \frac{2}{8} = \frac{1}{4} = 0.25 $, $ 1 > 0.25 $ → >

17. $ 1\frac{3}{4} \quad \boxed{>} \quad 1\frac{6}{12} $
→ $ 1\frac{3}{4} = 1.75 $, $ 1\frac{6}{12} = 1\frac{1}{2} = 1.5 $ → $ 1.75 > 1.5 $ → >

18. $ \frac{2}{3} \quad \boxed{<} \quad \frac{6}{11} $
→ $ \frac{2}{3} \approx 0.666, \frac{6}{11} \approx 0.545 $ → $ 0.666 > 0.545 $ → >

19. $ \frac{1}{3} \quad \boxed{<} \quad \frac{9}{7} $
→ $ \frac{1}{3} \approx 0.333, \frac{9}{7} \approx 1.285 $ → <

20. $ 1\frac{2}{5} \quad \boxed{>} \quad \frac{11}{6} $
→ $ 1\frac{2}{5} = 1.4 $, $ \frac{11}{6} \approx 1.833 $ → $ 1.4 < 1.833 $ → <

21. $ \frac{1}{8} \quad \boxed{<} \quad \frac{2}{3} $
→ $ \frac{1}{8} = 0.125, \frac{2}{3} \approx 0.666 $ → <

22. $ 1\frac{2}{3} \quad \boxed{>} \quad \frac{3}{9} $
→ $ 1\frac{2}{3} = 1.666 $, $ \frac{3}{9} = \frac{1}{3} \approx 0.333 $ → >

23. $ \frac{6}{8} \quad \boxed{>} \quad 1\frac{7}{12} $
→ $ \frac{6}{8} = 0.75 $, $ 1\frac{7}{12} \approx 1.583 $ → $ 0.75 < 1.583 $ → <

24. $ \frac{3}{7} \quad \boxed{<} \quad \frac{1}{7} $
→ $ \frac{3}{7} > \frac{1}{7} $ → >

25. $ \frac{21}{11} \quad \boxed{>} \quad \frac{15}{11} $
→ Same denominator: 21 > 15 → >

26. $ \frac{14}{12} \quad \boxed{>} \quad \frac{2}{9} $
→ $ \frac{14}{12} = \frac{7}{6} \approx 1.166 $, $ \frac{2}{9} \approx 0.222 $ → >

27. $ \frac{11}{10} \quad \boxed{>} \quad 1\frac{3}{4} $
→ $ \frac{11}{10} = 1.1 $, $ 1\frac{3}{4} = 1.75 $ → $ 1.1 < 1.75 $ → <

28. $ \frac{9}{5} \quad \boxed{>} \quad 1\frac{1}{12} $
→ $ \frac{9}{5} = 1.8 $, $ 1\frac{1}{12} \approx 1.083 $ → >

29. $ \frac{3}{7} \quad \boxed{<} \quad 1\frac{1}{2} $
→ $ \frac{3}{7} \approx 0.428 $, $ 1\frac{1}{2} = 1.5 $ → <

30. $ \frac{8}{6} \quad \boxed{>} \quad \frac{4}{11} $
→ $ \frac{8}{6} = \frac{4}{3} \approx 1.333 $, $ \frac{4}{11} \approx 0.363 $ → >

31. $ \frac{3}{2} \quad \boxed{>} \quad \frac{1}{2} $
→ $ \frac{3}{2} = 1.5 > 0.5 $ → >

32. $ \frac{3}{8} \quad \boxed{<} \quad \frac{1}{3} $
→ $ \frac{3}{8} = 0.375 $, $ \frac{1}{3} \approx 0.333 $ → $ 0.375 > 0.333 $ → >

33. $ \frac{6}{7} \quad \boxed{>} \quad \frac{13}{9} $
→ $ \frac{6}{7} \approx 0.857 $, $ \frac{13}{9} \approx 1.444 $ → $ 0.857 < 1.444 $ → <

34. $ \frac{6}{12} \quad \boxed{<} \quad 1\frac{4}{5} $
→ $ \frac{6}{12} = 0.5 $, $ 1\frac{4}{5} = 1.8 $ → <

35. $ 1\frac{1}{2} \quad \boxed{>} \quad \frac{6}{5} $
→ $ 1\frac{1}{2} = 1.5 $, $ \frac{6}{5} = 1.2 $ → >

36. $ \frac{17}{12} \quad \boxed{>} \quad 1\frac{1}{3} $
→ $ \frac{17}{12} \approx 1.416 $, $ 1\frac{1}{3} = 1.333 $ → >

37. $ \frac{9}{6} \quad \boxed{>} \quad 1\frac{1}{2} $
→ $ \frac{9}{6} = 1.5 $, $ 1\frac{1}{2} = 1.5 $ → =

38. $ \frac{4}{5} \quad \boxed{<} \quad 1\frac{6}{7} $
→ $ \frac{4}{5} = 0.8 $, $ 1\frac{6}{7} \approx 1.857 $ → <

39. $ \frac{4}{5} \quad \boxed{>} \quad \frac{6}{11} $
→ $ \frac{4}{5} = 0.8 $, $ \frac{6}{11} \approx 0.545 $ → >

40. $ \frac{1}{5} \quad \boxed{<} \quad 1\frac{2}{7} $
→ $ \frac{1}{5} = 0.2 $, $ 1\frac{2}{7} \approx 1.285 $ → <

41. $ \frac{1}{11} \quad \boxed{<} \quad 1\frac{2}{3} $
→ $ \frac{1}{11} \approx 0.09 $, $ 1\frac{2}{3} \approx 1.666 $ → <

42. $ \frac{3}{2} \quad \boxed{>} \quad \frac{6}{8} $
→ $ \frac{3}{2} = 1.5 $, $ \frac{6}{8} = 0.75 $ → >

43. $ \frac{19}{11} \quad \boxed{>} \quad 1\frac{5}{6} $
→ $ \frac{19}{11} \approx 1.727 $, $ 1\frac{5}{6} \approx 1.833 $ → $ 1.727 < 1.833 $ → <

44. $ 1\frac{4}{9} \quad \boxed{>} \quad \frac{5}{7} $
→ $ 1\frac{4}{9} \approx 1.444 $, $ \frac{5}{7} \approx 0.714 $ → >

45. $ 1\frac{2}{5} \quad \boxed{>} \quad \frac{6}{8} $
→ $ 1\frac{2}{5} = 1.4 $, $ \frac{6}{8} = 0.75 $ → >

46. $ 1\frac{10}{12} \quad \boxed{>} \quad \frac{4}{7} $
→ $ 1\frac{10}{12} = 1\frac{5}{6} \approx 1.833 $, $ \frac{4}{7} \approx 0.571 $ → >

47. $ \frac{2}{3} \quad \boxed{>} \quad \frac{2}{7} $
→ $ \frac{2}{3} \approx 0.666 $, $ \frac{2}{7} \approx 0.285 $ → >

48. $ \frac{16}{11} \quad \boxed{>} \quad \frac{1}{8} $
→ $ \frac{16}{11} \approx 1.454 $, $ \frac{1}{8} = 0.125 $ → >

49. $ \frac{1}{5} \quad \boxed{<} \quad \frac{10}{8} $
→ $ \frac{1}{5} = 0.2 $, $ \frac{10}{8} = 1.25 $ → <

50. $ \frac{2}{5} \quad \boxed{<} \quad \frac{5}{7} $
→ $ \frac{2}{5} = 0.4 $, $ \frac{5}{7} \approx 0.714 $ → <

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✔ Final Answers:

| # | Answer |
|---|--------|
| 1 | < |
| 2 | < |
| 3 | > |
| 4 | < |
| 5 | > |
| 6 | > |
| 7 | > |
| 8 | > |
| 9 | < |
|10 | < |
|11 | < |
|12 | < |
|13 | > |
|14 | > |
|15 | < |
|16 | > |
|17 | > |
|18 | > |
|19 | < |
|20 | < |
|21 | < |
|22 | > |
|23 | < |
|24 | > |
|25 | > |
|26 | > |
|27 | < |
|28 | > |
|29 | < |
|30 | > |
|31 | > |
|32 | > |
|33 | < |
|34 | < |
|35 | > |
|36 | > |
|37 | = |
|38 | < |
|39 | > |
|40 | < |
|41 | < |
|42 | > |
|43 | < |
|44 | > |
|45 | > |
|46 | > |
|47 | > |
|48 | > |
|49 | < |
|50 | < |

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🔍 Summary Tips:

- Convert mixed numbers to improper fractions or decimals.
- Compare like denominators directly.
- Use common denominators or decimal equivalents for clarity.
- Always check if fractions are simplified.

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