Year 5 Maths: Subtracting Fractions

Understanding Subtracting Fractions

Hello, Year 5! Today, we are going to learn how to subtract fractions. Don’t worry; it’s easier than it sounds!

What are Fractions?

A fraction shows a part of a whole. It has two numbers: the top number (numerator) and the bottom number (denominator). For example, in the fraction $$\frac{3}{4}$$, 3 is the numerator (how many parts we have), and 4 is the denominator (how many parts make a whole).

Subtracting Fractions with the Same Denominator

When the fractions have the same denominator, it’s quite simple! You just subtract the numerators and keep the same denominator.

For example:

$$\frac{5}{8} – \frac{2}{8}$$

1. Subtract the numerators: $$5 – 2 = 3$$
2. Keep the same denominator: $$8$$

So, $$\frac{5}{8} – \frac{2}{8} = \frac{3}{8}$$.

Subtracting Fractions with Different Denominators

When the fractions have different denominators, we need to make them the same first. This is called finding a common denominator.

Steps to Subtract Fractions with Different Denominators:

1. Find a common denominator.
2. Convert each fraction to an equivalent fraction with the common denominator.
3. Subtract the numerators.
4. Keep the common denominator.
5. Simplify the fraction if possible.

Example:

Let’s subtract $$\frac{1}{4} – \frac{1}{6}$$.

1. Find a common denominator: The common denominator for 4 and 6 is 12.
2. Convert the fractions:
   • $$\frac{1}{4} = \frac{3}{12}$$ (because $$1 \times 3 = 3$$ and $$4 \times 3 = 12$$)
   • $$\frac{1}{6} = \frac{2}{12}$$ (because $$1 \times 2 = 2$$ and $$6 \times 2 = 12$$)
3. Subtract the numerators: $$3 – 2 = 1$$
4. Keep the common denominator: So, we have $$\frac{1}{12}$$.

Key Rules

• Same Denominator: Subtract numerators and keep the denominator.
• Different Denominators: Find a common denominator, convert fractions, then subtract.
• Always simplify your answer if you can!

Tips and Tricks

• Remember to always look for the smallest common denominator to make calculations easier.
• If you’re unsure, draw a picture to visually represent the fractions.
• Practice regularly to get comfortable with different scenarios.

Practice Questions

Easy Level (1-20)

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

Medium Level (21-40)

21. $$\frac{2}{3} – \frac{1}{6}$$
22. $$\frac{5}{12} – \frac{1}{4}$$
23. $$\frac{7}{10} – \frac{1}{5}$$
24. $$\frac{4}{5} – \frac{1}{2}$$
25. $$\frac{3}{8} – \frac{1}{4}$$
26. $$\frac{5}{6} – \frac{1}{3}$$
27. $$\frac{1}{2} – \frac{1}{8}$$
28. $$\frac{3}{4} – \frac{1}{2}$$
29. $$\frac{2}{5} – \frac{1}{10}$$
30. $$\frac{3}{10} – \frac{1}{5}$$
31. $$\frac{8}{15} – \frac{2}{15}$$
32. $$\frac{5}{8} – \frac{1}{4}$$
33. $$\frac{4}{9} – \frac{2}{9}$$
34. $$\frac{7}{12} – \frac{1}{6}$$
35. $$\frac{1}{4} – \frac{1}{8}$$
36. $$\frac{5}{6} – \frac{1}{2}$$
37. $$\frac{3}{5} – \frac{1}{10}$$
38. $$\frac{9}{10} – \frac{1}{5}$$
39. $$\frac{2}{3} – \frac{1}{9}$$
40. $$\frac{4}{7} – \frac{2}{7}$$

Hard Level (41-60)

41. $$\frac{5}{8} – \frac{1}{5}$$
42. $$\frac{7}{10} – \frac{1}{4}$$
43. $$\frac{11}{15} – \frac{2}{5}$$
44. $$\frac{3}{4} – \frac{1}{3}$$
45. $$\frac{8}{9} – \frac{2}{3}$$
46. $$\frac{5}{12} – \frac{1}{6}$$
47. $$\frac{2}{5} – \frac{1}{3}$$
48. $$\frac{9}{10} – \frac{3}{5}$$
49. $$\frac{4}{9} – \frac{1}{3}$$
50. $$\frac{7}{8} – \frac{5}{12}$$
51. $$\frac{1}{2} – \frac{2}{5}$$
52. $$\frac{3}{5} – \frac{2}{15}$$
53. $$\frac{11}{12} – \frac{1}{4}$$
54. $$\frac{5}{6} – \frac{1}{2}$$
55. $$\frac{7}{15} – \frac{1}{5}$$
56. $$\frac{3}{8} – \frac{1}{6}$$
57. $$\frac{5}{9} – \frac{1}{3}$$
58. $$\frac{4}{5} – \frac{1}{2}$$
59. $$\frac{8}{15} – \frac{2}{5}$$
60. $$\frac{2}{3} – \frac{1}{4}$$

Answers and Explanations

Easy Level Answers

1. $$\frac{2}{5}$$
2. $$\frac{3}{10}$$
3. $$\frac{3}{8}$$
4. $$\frac{3}{9}$$ (or $$\frac{1}{3}$$)
5. $$0$$
6. $$\frac{2}{4}$$ (or $$\frac{1}{2}$$)
7. $$\frac{2}{6}$$ (or $$\frac{1}{3}$$)
8. $$\frac{6}{12}$$ (or $$\frac{1}{2}$$)
9. $$\frac{3}{7}$$
10. $$\frac{5}{15}$$ (or $$\frac{1}{3}$$)
11. $$\frac{1}{5}$$
12. $$\frac{2}{6}$$ (or $$\frac{1}{3}$$)
13. $$\frac{4}{8}$$ (or $$\frac{1}{2}$$)
14. $$0$$
15. $$\frac{1}{10}$$
16. $$\frac{5}{20}$$ (or $$\frac{1}{4}$$)
17. $$\frac{2}{5}$$
18. $$\frac{3}{9}$$ (or $$\frac{1}{3}$$)
19. $$\frac{4}{11}$$
20. $$\frac{2}{12}$$ (or $$\frac{1}{6}$$)

Medium Level Answers

21. $$\frac{1}{2}$$
22. $$\frac{1}{3}$$
23. $$\frac{1}{2}$$
24. $$\frac{3}{10}$$
25. $$\frac{1}{8}$$
26. $$\frac{1}{2}$$
27. $$\frac{3}{8}$$
28. $$\frac{1}{4}$$
29. $$\frac{3}{10}$$
30. $$\frac{1}{10}$$
31. $$\frac{6}{15}$$ (or $$\frac{2}{5}$$)
32. $$\frac{3}{8}$$
33. $$\frac{2}{9}$$
34. $$\frac{1}{4}$$
35. $$\frac{1}{8}$$
36. $$\frac{1}{3}$$
37. $$\frac{5}{10}$$ (or $$\frac{1}{2}$$)
38. $$\frac{8}{10}$$ (or $$\frac{4}{5}$$)
39. $$\frac{5}{9}$$
40. $$\frac{2}{7}$$

Hard Level Answers

41. $$\frac{7}{40}$$
42. $$\frac{9}{20}$$
43. $$\frac{7}{15}$$
44. $$\frac{5}{12}$$
45. $$\frac{2}{9}$$
46. $$\frac{1}{4}$$
47. $$\frac{1}{15}$$
48. $$\frac{1}{10}$$
49. $$\frac{1}{9}$$
50. $$\frac{1}{24}$$
51. $$\frac{1}{10}$$
52. $$\frac{7}{15}$$
53. $$\frac{5}{12}$$
54. $$\frac{1}{3}$$
55. $$\frac{2}{15}$$
56. $$\frac{7}{24}$$
57. $$\frac{2}{9}$$
58. $$\frac{1}{10}$$
59. $$\frac{2}{15}$$
60. $$\frac{5}{12}$$

Keep practicing, and soon you’ll be a pro at subtracting fractions! Remember to always check your work!