Comparing Proper Fractions to Twelfths (A) - Free Printable
Educational worksheet: Comparing Proper Fractions to Twelfths (A). Download and print for classroom or home learning activities.
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Step-by-step solution for: Comparing Proper Fractions to Twelfths (A)
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Show Answer Key & Explanations
Step-by-step solution for: Comparing Proper Fractions to Twelfths (A)
Let’s go through each fraction pair one by one. We’ll compare them using <, >, or =.
To compare two fractions, we can:
- Find a common denominator and compare numerators.
- Or cross-multiply: if a/b vs c/d, then compare a×d and b×c.
- Or convert to decimals (if easy).
We’ll use cross-multiplication for most — it’s fast and works every time.
---
1. 1/2 □ 4/5
Cross multiply: 1×5 = 5, 2×4 = 8 → 5 < 8 → so 1/2 < 4/5
2. 1/2 □ 1/2
Same → =
3. 1/4 □ 7/8
1×8 = 8, 4×7 = 28 → 8 < 28 → 1/4 < 7/8
4. 1/10 □ 1/8
1×8 = 8, 10×1 = 10 → 8 < 10 → 1/10 < 1/8
5. 4/9 □ 1/6
4×6 = 24, 9×1 = 9 → 24 > 9 → 4/9 > 1/6
6. 1/5 □ 1/9
1×9 = 9, 5×1 = 5 → 9 > 5 → 1/5 > 1/9
7. 5/7 □ 2/11
5×11 = 55, 7×2 = 14 → 55 > 14 → 5/7 > 2/11
8. 1/4 □ 2/3
1×3 = 3, 4×2 = 8 → 3 < 8 → 1/4 < 2/3
9. 1/2 □ 7/9
1×9 = 9, 2×7 = 14 → 9 < 14 → 1/2 < 7/9
10. 10/12 □ 1/9
10×9 = 90, 12×1 = 12 → 90 > 12 → 10/12 > 1/9
11. 3/6 □ 4/8
Simplify both: 3/6 = 1/2, 4/8 = 1/2 → =
12. 6/10 □ 2/5
6/10 = 3/5, 2/5 stays → 3/5 > 2/5 → 6/10 > 2/5
13. 4/5 □ 5/8
4×8 = 32, 5×5 = 25 → 32 > 25 → 4/5 > 5/8
14. 1/2 □ 3/5
1×5 = 5, 2×3 = 6 → 5 < 6 → 1/2 < 3/5
15. 1/9 □ 3/4
1×4 = 4, 9×3 = 27 → 4 < 27 → 1/9 < 3/4
16. 5/6 □ 8/9
5×9 = 45, 6×8 = 48 → 45 < 48 → 5/6 < 8/9
17. 1/2 □ 8/9
1×9 = 9, 2×8 = 16 → 9 < 16 → 1/2 < 8/9
18. 2/11 □ 3/5
2×5 = 10, 11×3 = 33 → 10 < 33 → 2/11 < 3/5
19. 4/10 □ 4/5
4×5 = 20, 10×4 = 40 → 20 < 40 → 4/10 < 4/5
20. 3/10 □ 2/3
3×3 = 9, 10×2 = 20 → 9 < 20 → 3/10 < 2/3
21. 2/3 □ 1/8
2×8 = 16, 3×1 = 3 → 16 > 3 → 2/3 > 1/8
22. 2/3 □ 7/10
2×10 = 20, 3×7 = 21 → 20 < 21 → 2/3 < 7/10
23. 6/12 □ 5/6
6/12 = 1/2, 5/6 → 1/2 < 5/6 → 6/12 < 5/6
24. 2/6 □ 3/5
2×5 = 10, 6×3 = 18 → 10 < 18 → 2/6 < 3/5
25. 1/2 □ 2/7
1×7 = 7, 2×2 = 4 → 7 > 4 → 1/2 > 2/7
26. 2/5 □ 4/8
4/8 = 1/2 → 2/5 vs 1/2 → 2×2=4, 5×1=5 → 4<5 → 2/5 < 4/8
27. 5/6 □ 9/11
5×11=55, 6×9=54 → 55>54 → 5/6 > 9/11
28. 2/8 □ 5/10
2/8=1/4, 5/10=1/2 → 1/4 < 1/2 → 2/8 < 5/10
29. 2/3 □ 3/5
2×5=10, 3×3=9 → 10>9 → 2/3 > 3/5
30. 4/8 □ 1/5
4/8=1/2 → 1/2 > 1/5 → 4/8 > 1/5
31. 1/6 □ 7/10
1×10=10, 6×7=42 → 10<42 → 1/6 < 7/10
32. 3/4 □ 1/8
3×8=24, 4×1=4 → 24>4 → 3/4 > 1/8
33. 8/9 □ 3/4
8×4=32, 9×3=27 → 32>27 → 8/9 > 3/4
34. 2/4 □ 1/3
2/4=1/2 → 1/2 vs 1/3 → 1×3=3, 2×1=2 → 3>2 → 2/4 > 1/3
35. 3/7 □ 2/3
3×3=9, 7×2=14 → 9<14 → 3/7 < 2/3
36. 1/8 □ 1/6
1×6=6, 8×1=8 → 6<8 → 1/8 < 1/6
37. 4/8 □ 6/7
4/8=1/2 → 1/2 vs 6/7 → 1×7=7, 2×6=12 → 7<12 → 4/8 < 6/7
38. 4/11 □ 5/11
Same denominator → 4<5 → 4/11 < 5/11
39. 1/9 □ 1/6
1×6=6, 9×1=9 → 6<9 → 1/9 < 1/6
40. 1/6 □ 2/4
2/4=1/2 → 1/6 < 1/2 → 1/6 < 2/4
41. 7/12 □ 7/9
Same numerator → bigger denominator means smaller fraction → 12>9 → 7/12 < 7/9
42. 1/2 □ 3/7
1×7=7, 2×3=6 → 7>6 → 1/2 > 3/7
43. 3/10 □ 1/2
3×2=6, 10×1=10 → 6<10 → 3/10 < 1/2
44. 1/5 □ 1/3
1×3=3, 5×1=5 → 3<5 → 1/5 < 1/3
45. 7/11 □ 3/6
3/6=1/2 → 7/11 vs 1/2 → 7×2=14, 11×1=11 → 14>11 → 7/11 > 3/6
46. 2/10 □ 2/8
Same numerator → 10>8 → 2/10 < 2/8 → 2/10 < 2/8
47. 7/9 □ 4/6
4/6=2/3 → 7/9 vs 2/3 → 7×3=21, 9×2=18 → 21>18 → 7/9 > 4/6
48. 5/9 □ 1/5
5×5=25, 9×1=9 → 25>9 → 5/9 > 1/5
49. 2/9 □ 1/6
2×6=12, 9×1=9 → 12>9 → 2/9 > 1/6
50. 8/9 □ 5/11
8×11=88, 9×5=45 → 88>45 → 8/9 > 5/11
---
Final 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. >
To compare two fractions, we can:
- Find a common denominator and compare numerators.
- Or cross-multiply: if a/b vs c/d, then compare a×d and b×c.
- Or convert to decimals (if easy).
We’ll use cross-multiplication for most — it’s fast and works every time.
---
1. 1/2 □ 4/5
Cross multiply: 1×5 = 5, 2×4 = 8 → 5 < 8 → so 1/2 < 4/5
2. 1/2 □ 1/2
Same → =
3. 1/4 □ 7/8
1×8 = 8, 4×7 = 28 → 8 < 28 → 1/4 < 7/8
4. 1/10 □ 1/8
1×8 = 8, 10×1 = 10 → 8 < 10 → 1/10 < 1/8
5. 4/9 □ 1/6
4×6 = 24, 9×1 = 9 → 24 > 9 → 4/9 > 1/6
6. 1/5 □ 1/9
1×9 = 9, 5×1 = 5 → 9 > 5 → 1/5 > 1/9
7. 5/7 □ 2/11
5×11 = 55, 7×2 = 14 → 55 > 14 → 5/7 > 2/11
8. 1/4 □ 2/3
1×3 = 3, 4×2 = 8 → 3 < 8 → 1/4 < 2/3
9. 1/2 □ 7/9
1×9 = 9, 2×7 = 14 → 9 < 14 → 1/2 < 7/9
10. 10/12 □ 1/9
10×9 = 90, 12×1 = 12 → 90 > 12 → 10/12 > 1/9
11. 3/6 □ 4/8
Simplify both: 3/6 = 1/2, 4/8 = 1/2 → =
12. 6/10 □ 2/5
6/10 = 3/5, 2/5 stays → 3/5 > 2/5 → 6/10 > 2/5
13. 4/5 □ 5/8
4×8 = 32, 5×5 = 25 → 32 > 25 → 4/5 > 5/8
14. 1/2 □ 3/5
1×5 = 5, 2×3 = 6 → 5 < 6 → 1/2 < 3/5
15. 1/9 □ 3/4
1×4 = 4, 9×3 = 27 → 4 < 27 → 1/9 < 3/4
16. 5/6 □ 8/9
5×9 = 45, 6×8 = 48 → 45 < 48 → 5/6 < 8/9
17. 1/2 □ 8/9
1×9 = 9, 2×8 = 16 → 9 < 16 → 1/2 < 8/9
18. 2/11 □ 3/5
2×5 = 10, 11×3 = 33 → 10 < 33 → 2/11 < 3/5
19. 4/10 □ 4/5
4×5 = 20, 10×4 = 40 → 20 < 40 → 4/10 < 4/5
20. 3/10 □ 2/3
3×3 = 9, 10×2 = 20 → 9 < 20 → 3/10 < 2/3
21. 2/3 □ 1/8
2×8 = 16, 3×1 = 3 → 16 > 3 → 2/3 > 1/8
22. 2/3 □ 7/10
2×10 = 20, 3×7 = 21 → 20 < 21 → 2/3 < 7/10
23. 6/12 □ 5/6
6/12 = 1/2, 5/6 → 1/2 < 5/6 → 6/12 < 5/6
24. 2/6 □ 3/5
2×5 = 10, 6×3 = 18 → 10 < 18 → 2/6 < 3/5
25. 1/2 □ 2/7
1×7 = 7, 2×2 = 4 → 7 > 4 → 1/2 > 2/7
26. 2/5 □ 4/8
4/8 = 1/2 → 2/5 vs 1/2 → 2×2=4, 5×1=5 → 4<5 → 2/5 < 4/8
27. 5/6 □ 9/11
5×11=55, 6×9=54 → 55>54 → 5/6 > 9/11
28. 2/8 □ 5/10
2/8=1/4, 5/10=1/2 → 1/4 < 1/2 → 2/8 < 5/10
29. 2/3 □ 3/5
2×5=10, 3×3=9 → 10>9 → 2/3 > 3/5
30. 4/8 □ 1/5
4/8=1/2 → 1/2 > 1/5 → 4/8 > 1/5
31. 1/6 □ 7/10
1×10=10, 6×7=42 → 10<42 → 1/6 < 7/10
32. 3/4 □ 1/8
3×8=24, 4×1=4 → 24>4 → 3/4 > 1/8
33. 8/9 □ 3/4
8×4=32, 9×3=27 → 32>27 → 8/9 > 3/4
34. 2/4 □ 1/3
2/4=1/2 → 1/2 vs 1/3 → 1×3=3, 2×1=2 → 3>2 → 2/4 > 1/3
35. 3/7 □ 2/3
3×3=9, 7×2=14 → 9<14 → 3/7 < 2/3
36. 1/8 □ 1/6
1×6=6, 8×1=8 → 6<8 → 1/8 < 1/6
37. 4/8 □ 6/7
4/8=1/2 → 1/2 vs 6/7 → 1×7=7, 2×6=12 → 7<12 → 4/8 < 6/7
38. 4/11 □ 5/11
Same denominator → 4<5 → 4/11 < 5/11
39. 1/9 □ 1/6
1×6=6, 9×1=9 → 6<9 → 1/9 < 1/6
40. 1/6 □ 2/4
2/4=1/2 → 1/6 < 1/2 → 1/6 < 2/4
41. 7/12 □ 7/9
Same numerator → bigger denominator means smaller fraction → 12>9 → 7/12 < 7/9
42. 1/2 □ 3/7
1×7=7, 2×3=6 → 7>6 → 1/2 > 3/7
43. 3/10 □ 1/2
3×2=6, 10×1=10 → 6<10 → 3/10 < 1/2
44. 1/5 □ 1/3
1×3=3, 5×1=5 → 3<5 → 1/5 < 1/3
45. 7/11 □ 3/6
3/6=1/2 → 7/11 vs 1/2 → 7×2=14, 11×1=11 → 14>11 → 7/11 > 3/6
46. 2/10 □ 2/8
Same numerator → 10>8 → 2/10 < 2/8 → 2/10 < 2/8
47. 7/9 □ 4/6
4/6=2/3 → 7/9 vs 2/3 → 7×3=21, 9×2=18 → 21>18 → 7/9 > 4/6
48. 5/9 □ 1/5
5×5=25, 9×1=9 → 25>9 → 5/9 > 1/5
49. 2/9 □ 1/6
2×6=12, 9×1=9 → 12>9 → 2/9 > 1/6
50. 8/9 □ 5/11
8×11=88, 9×5=45 → 88>45 → 8/9 > 5/11
---
Final 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. >
Parent Tip: Review the logic above to help your child master the concept of fraction comparison worksheet.
