Year 6 Maths: Subtracting Fractions

Introduction to Subtracting Fractions

Hello, Year 6! Today, we’re going to learn how to subtract fractions. This is an important skill that will help you with many math problems. Don’t worry! We’ll go through it step by step.

What Are Fractions?

A fraction represents a part of a whole. For example, if you have a pizza that is divided into 4 equal slices, and you eat 1 slice, you have eaten $$\frac{1}{4}$$ of the pizza.

Parts of a Fraction

• Numerator: The number on the top (how many parts you have).
• Denominator: The number on the bottom (how many equal parts the whole is divided into).

Subtracting Fractions with the Same Denominator

Step 1: Check the Denominator

When subtracting fractions, the first thing you need to do is check if the denominators are the same.

Step 2: Subtract the Numerators

If the denominators are the same, subtract the numerators and keep the denominator the same.

Example:

$$\frac{3}{5} – \frac{1}{5}$$

• Both fractions have a denominator of 5.
• Subtract the numerators: $$3 – 1 = 2$$ .
• Keep the denominator the same: $$\frac{2}{5}$$ .

Key Rule:

If the denominators are the same:

$$\frac{a}{c} – \frac{b}{c} = \frac{a – b}{c}$$

Subtracting Fractions with Different Denominators

Step 1: Find a Common Denominator

If the denominators are different, you need to find a common denominator. This is a number that both denominators can divide into.

Step 2: Convert the Fractions

Convert both fractions to have the same denominator.

Step 3: Subtract the Numerators

Once the fractions have the same denominator, subtract the numerators and keep the denominator the same.

Example:

$$\frac{1}{3} – \frac{1}{6}$$

• The common denominator of 3 and 6 is 6.
• Convert $$\frac{1}{3}$$ to $$\frac{2}{6}$$ (because $$\frac{1 \times 2}{3 \times 2} = \frac{2}{6}$$ ).
• Now we have: $$\frac{2}{6} – \frac{1}{6}$$ .
• Subtract the numerators: $$2 – 1 = 1$$ .
• Keep the denominator the same: $$\frac{1}{6}$$ .

Key Rule:

If the denominators are different:

1. Find a common denominator.
2. Convert the fractions.
3. Subtract the numerators.

Tips and Tricks

1. Practice Finding Common Denominators: Knowing your times tables can help!
2. Use Visuals: Drawing fraction bars can help you see the fractions better.
3. Simplify Your Answer: If you can, simplify the fraction after you subtract.

Questions

Easy Level (1-20)

1. $$\frac{2}{4} – \frac{1}{4}$$
2. $$\frac{3}{5} – \frac{1}{5}$$
3. $$\frac{4}{8} – \frac{2}{8}$$
4. $$\frac{5}{10} – \frac{3}{10}$$
5. $$\frac{7}{9} – \frac{2}{9}$$
6. $$\frac{1}{2} – \frac{1}{2}$$
7. $$\frac{6}{12} – \frac{3}{12}$$
8. $$\frac{8}{8} – \frac{5}{8}$$
9. $$\frac{9}{10} – \frac{4}{10}$$
10. $$\frac{5}{25} – \frac{2}{25}$$
11. $$\frac{3}{6} – \frac{1}{6}$$
12. $$\frac{2}{3} – \frac{1}{3}$$
13. $$\frac{7}{14} – \frac{3}{14}$$
14. $$\frac{4}{6} – \frac{2}{6}$$
15. $$\frac{1}{8} – \frac{1}{8}$$
16. $$\frac{5}{15} – \frac{4}{15}$$
17. $$\frac{2}{10} – \frac{1}{10}$$
18. $$\frac{3}{7} – \frac{2}{7}$$
19. $$\frac{10}{20} – \frac{5}{20}$$
20. $$\frac{6}{18} – \frac{3}{18}$$

Medium Level (21-40)

21. $$\frac{2}{5} – \frac{1}{10}$$
22. $$\frac{3}{4} – \frac{1}{2}$$
23. $$\frac{5}{6} – \frac{1}{3}$$
24. $$\frac{7}{8} – \frac{1}{4}$$
25. $$\frac{9}{10} – \frac{3}{5}$$
26. $$\frac{1}{2} – \frac{1}{3}$$
27. $$\frac{3}{5} – \frac{1}{4}$$
28. $$\frac{7}{12} – \frac{1}{3}$$
29. $$\frac{4}{9} – \frac{2}{3}$$
30. $$\frac{5}{8} – \frac{1}{2}$$
31. $$\frac{11}{12} – \frac{1}{4}$$
32. $$\frac{5}{7} – \frac{2}{7}$$
33. $$\frac{10}{15} – \frac{4}{15}$$
34. $$\frac{7}{10} – \frac{1}{5}$$
35. $$\frac{8}{9} – \frac{2}{3}$$
36. $$\frac{3}{5} – \frac{2}{10}$$
37. $$\frac{12}{15} – \frac{4}{15}$$
38. $$\frac{5}{12} – \frac{1}{4}$$
39. $$\frac{6}{8} – \frac{1}{2}$$
40. $$\frac{9}{12} – \frac{3}{12}$$

Hard Level (41-60)

41. $$\frac{5}{6} – \frac{2}{9}$$
42. $$\frac{7}{10} – \frac{1}{5}$$
43. $$\frac{11}{15} – \frac{1}{3}$$
44. $$\frac{4}{5} – \frac{1}{4}$$
45. $$\frac{8}{15} – \frac{2}{5}$$
46. $$\frac{9}{14} – \frac{1}{7}$$
47. $$\frac{3}{8} – \frac{1}{4}$$
48. $$\frac{10}{12} – \frac{1}{3}$$
49. $$\frac{13}{15} – \frac{2}{5}$$
50. $$\frac{5}{9} – \frac{1}{3}$$
51. $$\frac{11}{18} – \frac{1}{6}$$
52. $$\frac{9}{16} – \frac{1}{4}$$
53. $$\frac{7}{10} – \frac{3}{20}$$
54. $$\frac{14}{21} – \frac{2}{7}$$
55. $$\frac{15}{24} – \frac{5}{12}$$
56. $$\frac{13}{20} – \frac{1}{5}$$
57. $$\frac{6}{11} – \frac{1}{11}$$
58. $$\frac{5}{7} – \frac{2}{14}$$
59. $$\frac{17}{30} – \frac{1}{2}$$
60. $$\frac{8}{12} – \frac{1}{3}$$

Answers

Easy Level Answers

1. $$\frac{1}{4}$$
2. $$\frac{2}{5}$$
3. $$\frac{2}{8}$$
4. $$\frac{2}{10}$$
5. $$\frac{5}{9}$$
6. $$\frac{0}{2} = 0$$
7. $$\frac{3}{12}$$
8. $$\frac{3}{8}$$
9. $$\frac{5}{10} = \frac{1}{2}$$
10. $$\frac{3}{25}$$
11. $$\frac{2}{6} = \frac{1}{3}$$
12. $$\frac{1}{3}$$
13. $$\frac{4}{14} = \frac{2}{7}$$
14. $$\frac{2}{6} = \frac{1}{3}$$
15. $$0$$
16. $$\frac{1}{15}$$
17. $$\frac{1}{10}$$
18. $$\frac{1}{7}$$
19. $$\frac{5}{20} = \frac{1}{4}$$
20. $$\frac{3}{18} = \frac{1}{6}$$

Medium Level Answers

21. $$\frac{1}{5}$$
22. $$\frac{1}{4}$$
23. $$\frac{1}{2}$$
24. $$\frac{5}{8}$$
25. $$\frac{3}{10}$$
26. $$\frac{1}{6}$$
27. $$\frac{7}{20}$$
28. $$\frac{5}{12}$$
29. $$\frac{2}{9}$$
30. $$\frac{3}{8}$$
31. $$\frac{7}{12}$$
32. $$\frac{5}{7}$$
33. $$\frac{6}{15} = \frac{2}{5}$$
34. $$\frac{6}{10} = \frac{3}{5}$$
35. $$\frac{7}{30}$$
36. $$\frac{1}{5}$$
37. $$\frac{8}{15}$$
38. $$\frac{1}{12}$$
39. $$\frac{3}{12} = \frac{1}{4}$$
40. $$\frac{3}{12} = \frac{1}{4}$$

Hard Level Answers

41. $$\frac{7}{18}$$
42. $$\frac{1}{2}$$
43. $$\frac{5}{15} = \frac{1}{3}$$
44. $$\frac{11}{20}$$
45. $$\frac{2}{15}$$
46. $$\frac{5}{14}$$
47. $$\frac{1}{8}$$
48. $$\frac{1}{4}$$
49. $$\frac{11}{15}$$
50. $$\frac{2}{9}$$
51. $$\frac{7}{18}$$
52. $$\frac{5}{16}$$
53. $$\frac{1}{4}$$
54. $$\frac{10}{21}$$
55. $$\frac{5}{24}$$
56. $$\frac{12}{20} = \frac{3}{5}$$
57. $$\frac{5}{11}$$
58. $$\frac{3}{7}$$
59. $$\frac{7}{30}$$
60. $$\frac{1}{4}$$

That’s all for today, Year 6! Keep practicing subtracting fractions, and you’ll get even better at it. If you have any questions, don’t hesitate to ask!