Worksheet for comparing proper fractions using <, >, or = signs.
A worksheet titled "Comparing Proper Fractions (A)" with 50 problems requiring students to compare pairs of fractions using <, >, or = signs. The worksheet includes spaces for name, date, and score, and is sourced from Math-Drills.com.
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Show Answer Key & Explanations
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 solve each fraction comparison step by step. We’ll compare the two fractions in each pair and decide whether to use <, >, or =.
We can do this by:
- Finding a common denominator (if needed), or
- Converting to decimals (if easy), or
- Using cross-multiplication (multiply top of first with bottom of second, and vice versa — then compare those products).
I’ll go row by row, problem by problem.
---
Row 1:
1. ½ vs 4/5
Cross multiply: 1×5 = 5, 2×4 = 8 → 5 < 8 → so ½ < 4/5 → <
2. ½ vs ½ → same → =
3. ¼ vs 7/8
Cross: 1×8=8, 4×7=28 → 8 < 28 → ¼ < 7/8 → <
4. 1/10 vs 1/8
Same numerator? No. Cross: 1×8=8, 10×1=10 → 8 < 10 → 1/10 < 1/8 → <
5. 4/9 vs 1/6
Cross: 4×6=24, 9×1=9 → 24 > 9 → 4/9 > 1/6 → >
---
Row 2:
6. 1/5 vs 1/9
Cross: 1×9=9, 5×1=5 → 9 > 5 → 1/5 > 1/9 → >
7. 5/7 vs 2/11
Cross: 5×11=55, 7×2=14 → 55 > 14 → 5/7 > 2/11 → >
8. 1/4 vs 2/3
Cross: 1×3=3, 4×2=8 → 3 < 8 → 1/4 < 2/3 → <
9. 1/2 vs 7/9
Cross: 1×9=9, 2×7=14 → 9 < 14 → 1/2 < 7/9 → <
10. 10/12 vs 1/9
Simplify 10/12 = 5/6. Now compare 5/6 vs 1/9.
Cross: 5×9=45, 6×1=6 → 45 > 6 → 5/6 > 1/9 → >
---
Row 3:
11. 3/6 vs 4/8
Simplify both: 3/6 = 1/2, 4/8 = 1/2 → equal → =
12. 6/10 vs 2/5
Simplify 6/10 = 3/5. Compare 3/5 vs 2/5 → 3/5 > 2/5 → >
13. 4/5 vs 5/8
Cross: 4×8=32, 5×5=25 → 32 > 25 → 4/5 > 5/8 → >
14. 1/2 vs 3/5
Cross: 1×5=5, 2×3=6 → 5 < 6 → 1/2 < 3/5 → <
15. 1/9 vs 3/4
Cross: 1×4=4, 9×3=27 → 4 < 27 → 1/9 < 3/4 → <
---
Row 4:
16. 5/6 vs 8/9
Cross: 5×9=45, 6×8=48 → 45 < 48 → 5/6 < 8/9 → <
17. 1/2 vs 8/9
Cross: 1×9=9, 2×8=16 → 9 < 16 → 1/2 < 8/9 → <
18. 2/11 vs 3/5
Cross: 2×5=10, 11×3=33 → 10 < 33 → 2/11 < 3/5 → <
19. 4/10 vs 4/5
Same numerator? Yes. Smaller denominator means bigger fraction. 4/5 > 4/10 → <
Wait — we’re comparing 4/10 ___ 4/5 → since 4/5 is bigger, 4/10 < 4/5 → <
20. 3/10 vs 2/3
Cross: 3×3=9, 10×2=20 → 9 < 20 → 3/10 < 2/3 → <
---
Row 5:
21. 2/3 vs 1/8
Cross: 2×8=16, 3×1=3 → 16 > 3 → 2/3 > 1/8 → >
22. 2/3 vs 7/10
Cross: 2×10=20, 3×7=21 → 20 < 21 → 2/3 < 7/10 → <
23. 6/12 vs 5/6
Simplify 6/12 = 1/2. Compare 1/2 vs 5/6 → 1/2 = 3/6 < 5/6 → <
24. 2/6 vs 3/5
Simplify 2/6 = 1/3. Compare 1/3 vs 3/5 → cross: 1×5=5, 3×3=9 → 5 < 9 → 1/3 < 3/5 → <
25. 1/2 vs 2/7
Cross: 1×7=7, 2×2=4 → 7 > 4 → 1/2 > 2/7 → >
---
Row 6:
26. 2/5 vs 4/8
Simplify 4/8 = 1/2. Compare 2/5 vs 1/2 → cross: 2×2=4, 5×1=5 → 4 < 5 → 2/5 < 1/2 → <
27. 5/6 vs 9/11
Cross: 5×11=55, 6×9=54 → 55 > 54 → 5/6 > 9/11 → >
28. 2/8 vs 5/10
Simplify: 2/8 = 1/4, 5/10 = 1/2 → 1/4 < 1/2 → <
29. 2/3 vs 3/5
Cross: 2×5=10, 3×3=9 → 10 > 9 → 2/3 > 3/5 → >
30. 4/8 vs 1/5
Simplify 4/8 = 1/2. Compare 1/2 vs 1/5 → 1/2 > 1/5 → >
---
Row 7:
31. 1/6 vs 7/10
Cross: 1×10=10, 6×7=42 → 10 < 42 → 1/6 < 7/10 → <
32. 3/4 vs 1/8
Cross: 3×8=24, 4×1=4 → 24 > 4 → 3/4 > 1/8 → >
33. 8/9 vs 3/4
Cross: 8×4=32, 9×3=27 → 32 > 27 → 8/9 > 3/4 → >
34. 2/4 vs 1/3
Simplify 2/4 = 1/2. Compare 1/2 vs 1/3 → 1/2 > 1/3 → >
35. 3/7 vs 2/3
Cross: 3×3=9, 7×2=14 → 9 < 14 → 3/7 < 2/3 → <
---
Row 8:
36. 1/8 vs 1/6
Same numerator. Bigger denominator = smaller fraction → 1/8 < 1/6 → <
37. 4/8 vs 6/7
Simplify 4/8 = 1/2. Compare 1/2 vs 6/7 → 1/2 = 7/14, 6/7 = 12/14 → 7/14 < 12/14 → <
38. 4/11 vs 5/11
Same denominator → 4 < 5 → 4/11 < 5/11 → <
39. 1/9 vs 1/6
Same numerator → 1/9 < 1/6 → <
40. 1/6 vs 2/4
Simplify 2/4 = 1/2. Compare 1/6 vs 1/2 → 1/6 < 1/2 → <
---
Row 9:
41. 7/12 vs 7/9
Same numerator → bigger denominator = smaller fraction → 7/12 < 7/9 → <
42. 1/2 vs 3/7
Cross: 1×7=7, 2×3=6 → 7 > 6 → 1/2 > 3/7 → >
43. 3/10 vs 1/2
Cross: 3×2=6, 10×1=10 → 6 < 10 → 3/10 < 1/2 → <
44. 1/5 vs 1/3
Same numerator → 1/5 < 1/3 → <
45. 7/11 vs 3/6
Simplify 3/6 = 1/2. Compare 7/11 vs 1/2 → cross: 7×2=14, 11×1=11 → 14 > 11 → 7/11 > 1/2 → >
---
Row 10:
46. 2/10 vs 2/8
Same numerator → 2/10 < 2/8 → <
47. 7/9 vs 4/6
Simplify 4/6 = 2/3. Compare 7/9 vs 2/3 → 2/3 = 6/9 → 7/9 > 6/9 → >
48. 5/9 vs 1/5
Cross: 5×5=25, 9×1=9 → 25 > 9 → 5/9 > 1/5 → >
49. 2/9 vs 1/6
Cross: 2×6=12, 9×1=9 → 12 > 9 → 2/9 > 1/6 → >
50. 8/9 vs 5/11
Cross: 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. >
We can do this by:
- Finding a common denominator (if needed), or
- Converting to decimals (if easy), or
- Using cross-multiplication (multiply top of first with bottom of second, and vice versa — then compare those products).
I’ll go row by row, problem by problem.
---
Row 1:
1. ½ vs 4/5
Cross multiply: 1×5 = 5, 2×4 = 8 → 5 < 8 → so ½ < 4/5 → <
2. ½ vs ½ → same → =
3. ¼ vs 7/8
Cross: 1×8=8, 4×7=28 → 8 < 28 → ¼ < 7/8 → <
4. 1/10 vs 1/8
Same numerator? No. Cross: 1×8=8, 10×1=10 → 8 < 10 → 1/10 < 1/8 → <
5. 4/9 vs 1/6
Cross: 4×6=24, 9×1=9 → 24 > 9 → 4/9 > 1/6 → >
---
Row 2:
6. 1/5 vs 1/9
Cross: 1×9=9, 5×1=5 → 9 > 5 → 1/5 > 1/9 → >
7. 5/7 vs 2/11
Cross: 5×11=55, 7×2=14 → 55 > 14 → 5/7 > 2/11 → >
8. 1/4 vs 2/3
Cross: 1×3=3, 4×2=8 → 3 < 8 → 1/4 < 2/3 → <
9. 1/2 vs 7/9
Cross: 1×9=9, 2×7=14 → 9 < 14 → 1/2 < 7/9 → <
10. 10/12 vs 1/9
Simplify 10/12 = 5/6. Now compare 5/6 vs 1/9.
Cross: 5×9=45, 6×1=6 → 45 > 6 → 5/6 > 1/9 → >
---
Row 3:
11. 3/6 vs 4/8
Simplify both: 3/6 = 1/2, 4/8 = 1/2 → equal → =
12. 6/10 vs 2/5
Simplify 6/10 = 3/5. Compare 3/5 vs 2/5 → 3/5 > 2/5 → >
13. 4/5 vs 5/8
Cross: 4×8=32, 5×5=25 → 32 > 25 → 4/5 > 5/8 → >
14. 1/2 vs 3/5
Cross: 1×5=5, 2×3=6 → 5 < 6 → 1/2 < 3/5 → <
15. 1/9 vs 3/4
Cross: 1×4=4, 9×3=27 → 4 < 27 → 1/9 < 3/4 → <
---
Row 4:
16. 5/6 vs 8/9
Cross: 5×9=45, 6×8=48 → 45 < 48 → 5/6 < 8/9 → <
17. 1/2 vs 8/9
Cross: 1×9=9, 2×8=16 → 9 < 16 → 1/2 < 8/9 → <
18. 2/11 vs 3/5
Cross: 2×5=10, 11×3=33 → 10 < 33 → 2/11 < 3/5 → <
19. 4/10 vs 4/5
Same numerator? Yes. Smaller denominator means bigger fraction. 4/5 > 4/10 → <
Wait — we’re comparing 4/10 ___ 4/5 → since 4/5 is bigger, 4/10 < 4/5 → <
20. 3/10 vs 2/3
Cross: 3×3=9, 10×2=20 → 9 < 20 → 3/10 < 2/3 → <
---
Row 5:
21. 2/3 vs 1/8
Cross: 2×8=16, 3×1=3 → 16 > 3 → 2/3 > 1/8 → >
22. 2/3 vs 7/10
Cross: 2×10=20, 3×7=21 → 20 < 21 → 2/3 < 7/10 → <
23. 6/12 vs 5/6
Simplify 6/12 = 1/2. Compare 1/2 vs 5/6 → 1/2 = 3/6 < 5/6 → <
24. 2/6 vs 3/5
Simplify 2/6 = 1/3. Compare 1/3 vs 3/5 → cross: 1×5=5, 3×3=9 → 5 < 9 → 1/3 < 3/5 → <
25. 1/2 vs 2/7
Cross: 1×7=7, 2×2=4 → 7 > 4 → 1/2 > 2/7 → >
---
Row 6:
26. 2/5 vs 4/8
Simplify 4/8 = 1/2. Compare 2/5 vs 1/2 → cross: 2×2=4, 5×1=5 → 4 < 5 → 2/5 < 1/2 → <
27. 5/6 vs 9/11
Cross: 5×11=55, 6×9=54 → 55 > 54 → 5/6 > 9/11 → >
28. 2/8 vs 5/10
Simplify: 2/8 = 1/4, 5/10 = 1/2 → 1/4 < 1/2 → <
29. 2/3 vs 3/5
Cross: 2×5=10, 3×3=9 → 10 > 9 → 2/3 > 3/5 → >
30. 4/8 vs 1/5
Simplify 4/8 = 1/2. Compare 1/2 vs 1/5 → 1/2 > 1/5 → >
---
Row 7:
31. 1/6 vs 7/10
Cross: 1×10=10, 6×7=42 → 10 < 42 → 1/6 < 7/10 → <
32. 3/4 vs 1/8
Cross: 3×8=24, 4×1=4 → 24 > 4 → 3/4 > 1/8 → >
33. 8/9 vs 3/4
Cross: 8×4=32, 9×3=27 → 32 > 27 → 8/9 > 3/4 → >
34. 2/4 vs 1/3
Simplify 2/4 = 1/2. Compare 1/2 vs 1/3 → 1/2 > 1/3 → >
35. 3/7 vs 2/3
Cross: 3×3=9, 7×2=14 → 9 < 14 → 3/7 < 2/3 → <
---
Row 8:
36. 1/8 vs 1/6
Same numerator. Bigger denominator = smaller fraction → 1/8 < 1/6 → <
37. 4/8 vs 6/7
Simplify 4/8 = 1/2. Compare 1/2 vs 6/7 → 1/2 = 7/14, 6/7 = 12/14 → 7/14 < 12/14 → <
38. 4/11 vs 5/11
Same denominator → 4 < 5 → 4/11 < 5/11 → <
39. 1/9 vs 1/6
Same numerator → 1/9 < 1/6 → <
40. 1/6 vs 2/4
Simplify 2/4 = 1/2. Compare 1/6 vs 1/2 → 1/6 < 1/2 → <
---
Row 9:
41. 7/12 vs 7/9
Same numerator → bigger denominator = smaller fraction → 7/12 < 7/9 → <
42. 1/2 vs 3/7
Cross: 1×7=7, 2×3=6 → 7 > 6 → 1/2 > 3/7 → >
43. 3/10 vs 1/2
Cross: 3×2=6, 10×1=10 → 6 < 10 → 3/10 < 1/2 → <
44. 1/5 vs 1/3
Same numerator → 1/5 < 1/3 → <
45. 7/11 vs 3/6
Simplify 3/6 = 1/2. Compare 7/11 vs 1/2 → cross: 7×2=14, 11×1=11 → 14 > 11 → 7/11 > 1/2 → >
---
Row 10:
46. 2/10 vs 2/8
Same numerator → 2/10 < 2/8 → <
47. 7/9 vs 4/6
Simplify 4/6 = 2/3. Compare 7/9 vs 2/3 → 2/3 = 6/9 → 7/9 > 6/9 → >
48. 5/9 vs 1/5
Cross: 5×5=25, 9×1=9 → 25 > 9 → 5/9 > 1/5 → >
49. 2/9 vs 1/6
Cross: 2×6=12, 9×1=9 → 12 > 9 → 2/9 > 1/6 → >
50. 8/9 vs 5/11
Cross: 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 worksheet comparing fractions.
