Year 5 Maths: Simplifying Fractions

What is a Fraction?

A fraction is a way to show parts of a whole. It has two parts: the numerator (the top number) and the denominator (the bottom number). For example, in the fraction

$$\frac{3}{4}$$ , 3 is the numerator, and 4 is the denominator. This means we have 3 parts out of 4 total parts.

What Does It Mean to Simplify a Fraction?

Simplifying a fraction means making it as simple as possible. This means finding an equivalent fraction that has the smallest possible numbers while still representing the same amount.

For example, the fraction

$$\frac{4}{8}$$ can be simplified because both 4 and 8 can be divided by the same number.

How to Simplify a Fraction: Step-by-Step

1. Find the Greatest Common Factor (GCF): This is the largest number that can divide both the numerator and the denominator without leaving a remainder.
2. Divide the Numerator and Denominator by the GCF: This gives you the simplified fraction.

Example

Let’s simplify the fraction

$$\frac{6}{9}$$ .

1. Find the GCF: The factors of 6 are 1, 2, 3, and 6. The factors of 9 are 1, 3, and 9. The greatest common factor is 3.
2. Divide:
   • Divide the numerator: $$6 ÷ 3 = 2$$
   • Divide the denominator: $$9 ÷ 3 = 3$$

So,

$$\frac{6}{9}$$ simplifies to $$\frac{2}{3}$$ .

Key Rules for Simplifying Fractions

• Always look for the GCF first.
• Remember, you can only divide both the numerator and the denominator by the same number.
• If the numerator is smaller than the denominator, the fraction is already in its simplest form.

Tips and Tricks

• If you can’t find the GCF quickly, you can list the factors of both numbers and find the largest one.
• Use prime factorization to break each number down into its prime factors, which can make finding the GCF easier.

Questions for Practice

Easy Level (1-20)

1. Simplify $$\frac{2}{4}$$
2. Simplify $$\frac{3}{6}$$
3. Simplify $$\frac{5}{10}$$
4. Simplify $$\frac{8}{12}$$
5. Simplify $$\frac{1}{2}$$
6. Simplify $$\frac{6}{8}$$
7. Simplify $$\frac{4}{16}$$
8. Simplify $$\frac{9}{12}$$
9. Simplify $$\frac{10}{20}$$
10. Simplify $$\frac{14}{28}$$
11. Simplify $$\frac{12}{16}$$
12. Simplify $$\frac{15}{30}$$
13. Simplify $$\frac{2}{10}$$
14. Simplify $$\frac{7}{14}$$
15. Simplify $$\frac{3}{9}$$
16. Simplify $$\frac{5}{15}$$
17. Simplify $$\frac{4}{8}$$
18. Simplify $$\frac{16}{20}$$
19. Simplify $$\frac{18}{24}$$
20. Simplify $$\frac{6}{12}$$

Medium Level (21-40)

21. Simplify $$\frac{9}{15}$$
22. Simplify $$\frac{10}{25}$$
23. Simplify $$\frac{21}{28}$$
24. Simplify $$\frac{12}{30}$$
25. Simplify $$\frac{16}{24}$$
26. Simplify $$\frac{22}{33}$$
27. Simplify $$\frac{30}{45}$$
28. Simplify $$\frac{14}{21}$$
29. Simplify $$\frac{27}{36}$$
30. Simplify $$\frac{8}{18}$$
31. Simplify $$\frac{20}{30}$$
32. Simplify $$\frac{35}{50}$$
33. Simplify $$\frac{48}{60}$$
34. Simplify $$\frac{25}{100}$$
35. Simplify $$\frac{49}{56}$$
36. Simplify $$\frac{40}{60}$$
37. Simplify $$\frac{44}{88}$$
38. Simplify $$\frac{14}{42}$$
39. Simplify $$\frac{36}{48}$$
40. Simplify $$\frac{54}{72}$$

Hard Level (41-60)

41. Simplify $$\frac{18}{54}$$
42. Simplify $$\frac{32}{48}$$
43. Simplify $$\frac{45}{75}$$
44. Simplify $$\frac{80}{100}$$
45. Simplify $$\frac{100}{250}$$
46. Simplify $$\frac{63}{81}$$
47. Simplify $$\frac{99}{132}$$
48. Simplify $$\frac{56}{98}$$
49. Simplify $$\frac{88}{110}$$
50. Simplify $$\frac{30}{60}$$
51. Simplify $$\frac{72}{96}$$
52. Simplify $$\frac{28}{42}$$
53. Simplify $$\frac{16}{64}$$
54. Simplify $$\frac{40}{80}$$
55. Simplify $$\frac{88}{176}$$
56. Simplify $$\frac{27}{81}$$
57. Simplify $$\frac{50}{200}$$
58. Simplify $$\frac{72}{144}$$
59. Simplify $$\frac{36}{54}$$
60. Simplify $$\frac{18}{90}$$

Answers and Explanations

Easy Level Answers

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

Medium Level Answers

21. $$\frac{3}{5}$$ (GCF is 3)
22. $$\frac{2}{5}$$ (GCF is 5)
23. $$\frac{3}{4}$$ (GCF is 7)
24. $$\frac{2}{5}$$ (GCF is 6)
25. $$\frac{2}{3}$$ (GCF is 8)
26. $$\frac{2}{3}$$ (GCF is 11)
27. $$\frac{2}{3}$$ (GCF is 15)
28. $$\frac{2}{3}$$ (GCF is 7)
29. $$\frac{3}{4}$$ (GCF is 9)
30. $$\frac{4}{9}$$ (GCF is 2)
31. $$\frac{2}{3}$$ (GCF is 10)
32. $$\frac{7}{10}$$ (GCF is 5)
33. $$\frac{4}{5}$$ (GCF is 12)
34. $$\frac{1}{4}$$ (GCF is 25)
35. $$\frac{7}{8}$$ (GCF is 7)
36. $$\frac{2}{3}$$ (GCF is 20)
37. $$\frac{1}{2}$$ (GCF is 44)
38. $$\frac{1}{3}$$ (GCF is 14)
39. $$\frac{3}{4}$$ (GCF is 12)
40. $$\frac{3}{4}$$ (GCF is 18)

Hard Level Answers

41. $$\frac{1}{3}$$ (GCF is 18)
42. $$\frac{2}{3}$$ (GCF is 16)
43. $$\frac{3}{5}$$ (GCF is 15)
44. $$\frac{4}{5}$$ (GCF is 20)
45. $$\frac{2}{5}$$ (GCF is 50)
46. $$\frac{7}{9}$$ (GCF is 9)
47. $$\frac{3}{4}$$ (GCF is 33)
48. $$\frac{4}{7}$$ (GCF is 14)
49. $$\frac{8}{11}$$ (GCF is 8)
50. $$\frac{1}{2}$$ (GCF is 30)
51. $$\frac{3}{4}$$ (GCF is 72)
52. $$\frac{2}{3}$$ (GCF is 14)
53. $$\frac{1}{4}$$ (GCF is 16)
54. $$\frac{1}{2}$$ (GCF is 40)
55. $$\frac{1}{2}$$ (GCF is 88)
56. $$\frac{1}{3}$$ (GCF is 27)
57. $$\frac{1}{4}$$ (GCF is 50)
58. $$\frac{1}{2}$$ (GCF is 72)
59. $$\frac{2}{3}$$ (GCF is 18)
60. $$\frac{1}{5}$$ (GCF is 18)

Feel free to practice simplifying fractions with these questions, and remember to look for the GCF to help you simplify!