Subtraction of fractions is a fundamental mathematical skill taught during Key Stage 3 in England and Wales, covering students aged 11 to 14. Mastering this topic is essential for developing a solid foundation in arithmetic and preparing for more advanced mathematical concepts.

Understanding Subtraction of Fractions

What Are Fractions?

Fractions represent parts of a whole and consist of a numerator (the top number) and a denominator (the bottom number). For example, in the fraction (\frac{3}{4}), 3 is the numerator, and 4 is the denominator.

Why Subtract Fractions?

Subtracting fractions allows us to determine the difference between two quantities that are parts of a whole. This skill is crucial in various real-life situations, such as calculating distances, managing finances, and measuring ingredients in cooking.

Steps to Subtract Fractions

1. Ensure Common Denominators: To subtract fractions, they must have the same denominator. If they don’t, find the least common denominator (LCD) and convert the fractions accordingly.
2. Subtract the Numerators: Once the denominators are the same, subtract the numerators while keeping the denominator unchanged.
3. Simplify the Fraction: If possible, reduce the resulting fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Example

Subtract (\frac{2}{3}) from (\frac{5}{6}):

1. Find Common Denominator: The LCD of 3 and 6 is 6.
2. Convert Fractions:
   [
   \frac{2}{3} = \frac{4}{6}
   ]
   [
   \frac{5}{6} = \frac{5}{6}
   ]
3. Subtract Numerators:
   [
   \frac{5}{6} – \frac{4}{6} = \frac{1}{6}
   ]
4. Simplify: (\frac{1}{6}) is already in its simplest form.

Practice Questions

Easy Level

1. (\frac{3}{4} – \frac{1}{4} = ?)
2. (\frac{5}{6} – \frac{2}{6} = ?)
3. (\frac{7}{8} – \frac{3}{8} = ?)
4. (\frac{2}{5} – \frac{1}{5} = ?)
5. (\frac{4}{9} – \frac{2}{9} = ?)
6. (\frac{6}{7} – \frac{1}{7} = ?)
7. (\frac{5}{10} – \frac{2}{10} = ?)
8. (\frac{9}{12} – \frac{3}{12} = ?)
9. (\frac{8}{15} – \frac{2}{15} = ?)
10. (\frac{10}{20} – \frac{5}{20} = ?)
11. (\frac{1}{2} – \frac{1}{4} = ?)
12. (\frac{3}{5} – \frac{1}{5} = ?)
13. (\frac{7}{10} – \frac{2}{10} = ?)
14. (\frac{4}{6} – \frac{2}{6} = ?)
15. (\frac{5}{8} – \frac{3}{8} = ?)
16. (\frac{6}{9} – \frac{2}{9} = ?)
17. (\frac{2}{3} – \frac{1}{3} = ?)
18. (\frac{4}{5} – \frac{2}{5} = ?)
19. (\frac{3}{7} – \frac{1}{7} = ?)
20. (\frac{5}{12} – \frac{2}{12} = ?)

Medium Level

21. (\frac{5}{6} – \frac{1}{3} = ?)
22. (\frac{7}{8} – \frac{2}{5} = ?)
23. (\frac{9}{10} – \frac{4}{15} = ?)
24. (\frac{11}{12} – \frac{5}{18} = ?)
25. (\frac{3}{4} – \frac{2}{3} = ?)
26. (\frac{5}{9} – \frac{1}{6} = ?)
27. (\frac{7}{10} – \frac{3}{5} = ?)
28. (\frac{4}{7} – \frac{2}{9} = ?)
29. (\frac{5}{8} – \frac{1}{4} = ?)
30. (\frac{6}{11} – \frac{2}{3} = ?)
31. (\frac{8}{9} – \frac{3}{4} = ?)
32. (\frac{10}{12} – \frac{1}{3} = ?)
33. (\frac{7}{15} – \frac{2}{5} = ?)
34. (\frac{9}{14} – \frac{3}{7} = ?)
35. (\frac{11}{16} – \frac{5}{8} = ?)
36. (\frac{13}{20} – \frac{3}{10} = ?)
37. (\frac{5}{6} – \frac{1}{2} = ?)
38. (\frac{3}{5} – \frac{1}{10} = ?)
39. (\frac{4}{9} – \frac{1}{3} = ?)
40. (\frac{7}{12} – \frac{2}{4} = ?)

Hard Level

41. (\frac{5}{6} – \frac{7}{12} = ?)
42. (\frac{11}{15} – \frac{2}{5} = ?)
43. (\frac{13}{20} – \frac{3}{4} = ?)
44. (\frac{17}{18} – \frac{5}{9} = ?)
45. (\frac{19}{24} – \frac{7}{12} = ?)
46. (\frac{23}{30} – \frac{4}{5} = ?)
47. (\frac{7}{8} – \frac{5}{12} = ?)
48. (\frac{9}{10} – \frac{11}{15} = ?)
49. (\frac{14}{21} – \frac{2}{3} = ?)
50. (\frac{16}{25} – \frac{3}{5} = ?)
51. (\frac{22}{27} – \frac{4}{9} = ?)
52. (\frac{5}{6} – \frac{7}{18} = ?)
53. (\frac{8}{13} – \frac{3}{26} = ?)
54. (\frac{19}{28} – \frac{5}{14} = ?)
55. (\frac{24}{35} – \frac{9}{35} = ?)
56. (\frac{7}{10} – \frac{11}{20} = ?)
57. (\frac{15}{16} – \frac{3}{8} = ?)
58. (\frac{21}{22} – \frac{5}{11} = ?)
59. (\frac{18}{25} – \frac{2}{5} = ?)
60. (\frac{13}{17} – \frac{4}{17} = ?)

Answers and Explanations

Easy Level

1. (\frac{3}{4} – \frac{1}{4} = \frac{2}{4} = \frac{1}{2})
2. (\frac{5}{6} – \frac{2}{6} = \frac{3}{6} = \frac{1}{2})
3. (\frac{7}{8} – \frac{3}{8} = \frac{4}{8} = \frac{1}{2})
4. (\frac{2}{5} – \frac{1}{5} = \frac{1}{5})
5. (\frac{4}{9} – \frac{2}{9} = \frac{2}{9})
6. (\frac{6}{7} – \frac{1}{7} = \frac{5}{7})
7. (\frac{5}{10} – \frac{2}{10} = \frac{3}{10})
8. (\frac{9}{12} – \frac{3}{12} = \frac{6}{12} = \frac{1}{2})
9. (\frac{8}{15} – \frac{2}{15} = \frac{6}{15} = \frac{2}{5})
10. (\frac{10}{20} – \frac{5}{20} = \frac{5}{20} = \frac{1}{4})
11. (\frac{1}{2} – \frac{1}{4} = \frac{2}{4} – \frac{1}{4} = \frac{1}{4})
12. (\frac{3}{5} – \frac{1}{5} = \frac{2}{5})
13. (\frac{7}{10} – \frac{2}{10} = \frac{5}{10} = \frac{1}{2})
14. (\frac{4}{6} – \frac{2}{6} = \frac{2}{6} = \frac{1}{3})
15. (\frac{5}{8} – \frac{3}{8} = \frac{2}{8} = \frac{1}{4})
16. (\frac{6}{9} – \frac{2}{9} = \frac{4}{9})
17. (\frac{2}{3} – \frac{1}{3} = \frac{1}{3})
18. (\frac{4}{5} – \frac{2}{5} = \frac{2}{5})
19. (\frac{3}{7} – \frac{1}{7} = \frac{2}{7})
20. (\frac{5}{12} – \frac{2}{12} = \frac{3}{12} = \frac{1}{4})

Medium Level

21. (\frac{5}{6} – \frac{1}{3} = \frac{5}{6} – \frac{2}{6} = \frac{3}{6} = \frac{1}{2})
22. (\frac{7}{8} – \frac{2}{5} = \frac{35}{40} – \frac{16}{40} = \frac{19}{40})
23. (\frac{9}{10} – \frac{4}{15} = \frac{27}{30} – \frac{8}{30} = \frac{19}{30})
24. (\frac{11}{12} – \frac{5}{18} = \frac{33}{36} – \frac{10}{36} = \frac{23}{36})
25. (\frac{3}{4} – \frac{2}{3} = \frac{9}{12} – \frac{8}{12} = \frac{1}{12})
26. (\frac{5}{9} – \frac{1}{6} = \frac{10}{18} – \frac{3}{18} = \frac{7}{18})
27. (\frac{7}{10} – \frac{3}{5} = \frac{7}{10} – \frac{6}{10} = \frac{1}{10})
28. (\frac{4}{7} – \frac{2}{9} = \frac{36}{63} – \frac{14}{63} = \frac{22}{63})
29. (\frac{5}{8} – \frac{1}{4} = \frac{5}{8} – \frac{2}{8} = \frac{3}{8})
30. (\frac{6}{11} – \frac{2}{3} = \frac{18}{33} – \frac{22}{33} = -\frac{4}{33}) (Note: Negative result)
31. (\frac{8}{9} – \frac{3}{4} = \frac{32}{36} – \frac{27}{36} = \frac{5}{36})
32. (\frac{10}{12} – \frac{1}{3} = \frac{10}{12} – \frac{4}{12} = \frac{6}{12} = \frac{1}{2})
33. (\frac{7}{15} – \frac{2}{5} = \frac{7}{15} – \frac{6}{15} = \frac{1}{15})
34. (\frac{9}{14} – \frac{3}{7} = \frac{9}{14} – \frac{6}{14} = \frac{3}{14})
35. (\frac{11}{16} – \frac{5}{8} = \frac{11}{16} – \frac{10}{16} = \frac{1}{16})
36. (\frac{13}{20} – \frac{3}{10} = \frac{13}{20} – \frac{6}{20} = \frac{7}{20})
37. (\frac{5}{6} – \frac{1}{2} = \frac{5}{6} – \frac{3}{6} = \frac{2}{6} = \frac{1}{3})
38. (\frac{3}{5} – \frac{1}{10} = \frac{6}{10} – \frac{1}{10} = \frac{5}{10} = \frac{1}{2})
39. (\frac{4}{9} – \frac{1}{3} = \frac{4}{9} – \frac{3}{9} = \frac{1}{9})
40. (\frac{7}{12} – \frac{2}{4} = \frac{7}{12} – \frac{6}{12} = \frac{1}{12})

Hard Level

41. (\frac{5}{6} – \frac{7}{12} = \frac{10}{12} – \frac{7}{12} = \frac{3}{12} = \frac{1}{4})
42. (\frac{11}{15} – \frac{2}{5} = \frac{11}{15} – \frac{6}{15} = \frac{5}{15} = \frac{1}{3})
43. (\frac{13}{20} – \frac{3}{4} = \frac{13}{20} – \frac{15}{20} = -\frac{2}{20} = -\frac{1}{10}) (Negative result)
44. (\frac{17}{18} – \frac{5}{9} = \frac{17}{18} – \frac{10}{18} = \frac{7}{18})
45. (\frac{19}{24} – \frac{7}{12} = \frac{19}{24} – \frac{14}{24} = \frac{5}{24})
46. (\frac{23}{30} – \frac{4}{5} = \frac{23}{30} – \frac{24}{30} = -\frac{1}{30}) (Negative result)
47. (\frac{7}{8} – \frac{5}{12} = \frac{21}{24} – \frac{10}{24} = \frac{11}{24})
48. (\frac{9}{10} – \frac{11}{15} = \frac{27}{30} – \frac{22}{30} = \frac{5}{30} = \frac{1}{6})
49. (\frac{14}{21} – \frac{2}{3} = \frac{14}{21} – \frac{14}{21} = 0)
50. (\frac{16}{25} – \frac{3}{5} = \frac{16}{25} – \frac{15}{25} = \frac{1}{25})
51. (\frac{22}{27} – \frac{4}{9} = \frac{22}{27} – \frac{12}{27} = \frac{10}{27})
52. (\frac{5}{6} – \frac{7}{18} = \frac{15}{18} – \frac{7}{18} = \frac{8}{18} = \frac{4}{9})
53. (\frac{8}{13} – \frac{3}{26} = \frac{16}{26} – \frac{3}{26} = \frac{13}{26} = \frac{1}{2})
54. (\frac{19}{28} – \frac{5}{14} = \frac{19}{28} – \frac{10}{28} = \frac{9}{28})
55. (\frac{24}{35} – \frac{9}{35} = \frac{15}{35} = \frac{3}{7})
56. (\frac{7}{10} – \frac{11}{20} = \frac{14}{20} – \frac{11}{20} = \frac{3}{20})
57. (\frac{15}{16} – \frac{3}{8} = \frac{15}{16} – \frac{6}{16} = \frac{9}{16})
58. (\frac{21}{22} – \frac{5}{11} = \frac{21}{22} – \frac{10}{22} = \frac{11}{22} = \frac{1}{2})
59. (\frac{18}{25} – \frac{2}{5} = \frac{18}{25} – \frac{10}{25} = \frac{8}{25})
60. (\frac{13}{17} – \frac{4}{17} = \frac{9}{17})

Note: Questions 30, 43, and 46 result in negative fractions, indicating that the subtracted fraction is larger than the original.