Year 8 Maths: Simplifying Fractions

Simplifying fractions is a fundamental skill in mathematics that involves reducing a fraction to its simplest form. A fraction is simplified when the numerator (the top number) and the denominator (the bottom number) have no common factors other than 1. This process makes fractions easier to work with in calculations and comparisons.

Understanding Simplifying Fractions

To simplify a fraction, follow these steps:

1. Find the Greatest Common Divisor (GCD): Determine the largest number that divides both the numerator and the denominator without leaving a remainder.
2. Divide Both Numerator and Denominator by the GCD: This will reduce the fraction to its simplest form.

Example

Simplify the fraction

1. The GCD of 8 and 12 is 4.
2. Divide both numerator and denominator by 4:
   $$\frac{8 \div 4}{12 \div 4} = \frac{2}{3}$$

So,

Practice Questions

Easy Level

1. Simplify $$\frac{2}{4}$$ .
2. Simplify $$\frac{6}{8}$$ .
3. Simplify $$\frac{10}{15}$$ .
4. Simplify $$\frac{9}{12}$$ .
5. Simplify $$\frac{14}{21}$$ .
6. Simplify $$\frac{5}{10}$$ .
7. Simplify $$\frac{16}{24}$$ .
8. Simplify $$\frac{18}{27}$$ .
9. Simplify $$\frac{12}{16}$$ .
10. Simplify $$\frac{20}{25}$$ .
11. Simplify $$\frac{4}{6}$$ .
12. Simplify $$\frac{7}{14}$$ .
13. Simplify $$\frac{15}{20}$$ .
14. Simplify $$\frac{21}{28}$$ .
15. Simplify $$\frac{8}{32}$$ .
16. Simplify $$\frac{3}{9}$$ .
17. Simplify $$\frac{10}{20}$$ .
18. Simplify $$\frac{5}{15}$$ .
19. Simplify $$\frac{14}{18}$$ .
20. Simplify $$\frac{6}{12}$$ .

Medium Level

1. Simplify $$\frac{24}{36}$$ .
2. Simplify $$\frac{30}{45}$$ .
3. Simplify $$\frac{48}{60}$$ .
4. Simplify $$\frac{50}{75}$$ .
5. Simplify $$\frac{35}{49}$$ .
6. Simplify $$\frac{40}{56}$$ .
7. Simplify $$\frac{27}{54}$$ .
8. Simplify $$\frac{33}{44}$$ .
9. Simplify $$\frac{42}{63}$$ .
10. Simplify $$\frac{28}{35}$$ .
11. Simplify $$\frac{36}{48}$$ .
12. Simplify $$\frac{45}{60}$$ .
13. Simplify $$\frac{32}{40}$$ .
14. Simplify $$\frac{39}{52}$$ .
15. Simplify $$\frac{25}{50}$$ .
16. Simplify $$\frac{18}{30}$$ .
17. Simplify $$\frac{22}{33}$$ .
18. Simplify $$\frac{16}{24}$$ .
19. Simplify $$\frac{20}{28}$$ .
20. Simplify $$\frac{14}{21}$$ .

Hard Level

1. Simplify $$\frac{84}{126}$$ .
2. Simplify $$\frac{90}{150}$$ .
3. Simplify $$\frac{120}{180}$$ .
4. Simplify $$\frac{156}{208}$$ .
5. Simplify $$\frac{99}{132}$$ .
6. Simplify $$\frac{144}{192}$$ .
7. Simplify $$\frac{210}{280}$$ .
8. Simplify $$\frac{175}{245}$$ .
9. Simplify $$\frac{198}{264}$$ .
10. Simplify $$\frac{225}{300}$$ .
11. Simplify $$\frac{160}{200}$$ .
12. Simplify $$\frac{189}{252}$$ .
13. Simplify $$\frac{132}{176}$$ .
14. Simplify $$\frac{165}{220}$$ .
15. Simplify $$\frac{144}{216}$$ .
16. Simplify $$\frac{180}{270}$$ .
17. Simplify $$\frac{210}{315}$$ .
18. Simplify $$\frac{234}{351}$$ .
19. Simplify $$\frac{288}{360}$$ .
20. Simplify $$\frac{120}{168}$$ .

Answers and Explanations

Easy Level

1. $$\frac{2}{4} = \frac{1}{2}$$

• GCD of 2 and 4 is 2. Divide both by 2.

1. $$\frac{6}{8} = \frac{3}{4}$$

• GCD of 6 and 8 is 2. Divide both by 2.

1. $$\frac{10}{15} = \frac{2}{3}$$

• GCD of 10 and 15 is 5. Divide both by 5.

1. $$\frac{9}{12} = \frac{3}{4}$$

• GCD of 9 and 12 is 3. Divide both by 3.

1. $$\frac{14}{21} = \frac{2}{3}$$

• GCD of 14 and 21 is 7. Divide both by 7.

1. $$\frac{5}{10} = \frac{1}{2}$$

• GCD of 5 and 10 is 5. Divide both by 5.

1. $$\frac{16}{24} = \frac{2}{3}$$

• GCD of 16 and 24 is 8. Divide both by 8.

1. $$\frac{18}{27} = \frac{2}{3}$$

• GCD of 18 and 27 is 9. Divide both by 9.

1. $$\frac{12}{16} = \frac{3}{4}$$

• GCD of 12 and 16 is 4. Divide both by 4.

1. $$\frac{20}{25} = \frac{4}{5}$$
   • GCD of 20 and 25 is 5. Divide both by 5.
2. $$\frac{4}{6} = \frac{2}{3}$$
   • GCD of 4 and 6 is 2. Divide both by 2.
3. $$\frac{7}{14} = \frac{1}{2}$$
   • GCD of 7 and 14 is 7. Divide both by 7.
4. $$\frac{15}{20} = \frac{3}{4}$$
   • GCD of 15 and 20 is 5. Divide both by 5.
5. $$\frac{21}{28} = \frac{3}{4}$$
   • GCD of 21 and 28 is 7. Divide both by 7.
6. $$\frac{8}{32} = \frac{1}{4}$$
   • GCD of 8 and 32 is 8. Divide both by 8.
7. $$\frac{3}{9} = \frac{1}{3}$$
   • GCD of 3 and 9 is 3. Divide both by 3.
8. $$\frac{10}{20} = \frac{1}{2}$$
   • GCD of 10 and 20 is 10. Divide both by 10.
9. $$\frac{5}{15} = \frac{1}{3}$$
   • GCD of 5 and 15 is 5. Divide both by 5.
10. $$\frac{14}{18} = \frac{7}{9}$$
    • GCD of 14 and 18 is 2. Divide both by 2.
11. $$\frac{6}{12} = \frac{1}{2}$$
    • GCD of 6 and 12 is 6. Divide both by 6.

Medium Level

1. $$\frac{24}{36} = \frac{2}{3}$$

• GCD is 12. Divide both by 12.

1. $$\frac{30}{45} = \frac{2}{3}$$

• GCD is 15. Divide both by 15.

1. $$\frac{48}{60} = \frac{4}{5}$$

• GCD is 12. Divide both by 12.

1. $$\frac{50}{75} = \frac{2}{3}$$

• GCD is 25. Divide both by 25.

1. $$\frac{35}{49} = \frac{5}{7}$$

• GCD is 7. Divide both by 7.

1. $$\frac{40}{56} = \frac{5}{7}$$

• GCD is 8. Divide both by 8.

1. $$\frac{27}{54} = \frac{1}{2}$$

• GCD is 27. Divide both by 27.

1. $$\frac{33}{44} = \frac{3}{4}$$

• GCD is 11. Divide both by 11.

1. $$\frac{42}{63} = \frac{2}{3}$$

• GCD is 21. Divide both by 21.

1. $$\frac{28}{35} = \frac{4}{5}$$
   • GCD is 7. Divide both by 7.
2. $$\frac{36}{48} = \frac{3}{4}$$
   • GCD is 12. Divide both by 12.
3. $$\frac{45}{60} = \frac{3}{4}$$
   • GCD is 15. Divide both by 15.
4. $$\frac{32}{40} = \frac{4}{5}$$
   • GCD is 8. Divide both by 8.
5. $$\frac{39}{52} = \frac{3}{4}$$
   • GCD is 13. Divide both by 13.
6. $$\frac{25}{50} = \frac{1}{2}$$
   • GCD is 25. Divide both by 25.
7. $$\frac{18}{30} = \frac{3}{5}$$
   • GCD is 6. Divide both by 6.
8. $$\frac{22}{33} = \frac{2}{3}$$
   • GCD is 11. Divide both by 11.
9. $$\frac{16}{24} = \frac{2}{3}$$
   • GCD is 8. Divide both by 8.
10. $$\frac{20}{28} = \frac{5}{7}$$
    • GCD is 4. Divide both by 4.
11. $$\frac{14}{21} = \frac{2}{3}$$
    • GCD is 7. Divide both by 7.

Hard Level

1. $$\frac{84}{126} = \frac{2}{3}$$

• GCD is 42. Divide both by 42.

1. $$\frac{90}{150} = \frac{3}{5}$$

• GCD is 30. Divide both by 30.

1. $$\frac{120}{180} = \frac{2}{3}$$

• GCD is 60. Divide both by 60.

1. $$\frac{156}{208} = \frac{3}{4}$$

• GCD is 52. Divide both by 52.

1. $$\frac{99}{132} = \frac{3}{4}$$

• GCD is 33. Divide both by 33.

1. $$\frac{144}{192} = \frac{3}{4}$$

• GCD is 48. Divide both by 48.

1. $$\frac{210}{280} = \frac{3}{4}$$

• GCD is 70. Divide both by 70.

1. $$\frac{175}{245} = \frac{5}{7}$$

• GCD is 35. Divide both by 35.

1. $$\frac{198}{264} = \frac{3}{4}$$

• GCD is 66. Divide both by 66.

1. $$\frac{225}{300} = \frac{3}{4}$$
   • GCD is 75. Divide both by 75.
2. $$\frac{160}{200} = \frac{4}{5}$$
   • GCD is 40. Divide both by 40.
3. $$\frac{189}{252} = \frac{3}{4}$$
   • GCD is 63. Divide both by 63.
4. $$\frac{132}{176} = \frac{3}{4}$$
   • GCD is 44. Divide both by 44.
5. $$\frac{165}{220} = \frac{3}{4}$$
   • GCD is 55. Divide both by 55.
6. $$\frac{144}{216} = \frac{2}{3}$$
   • GCD is 72. Divide both by 72.
7. $$\frac{180}{270} = \frac{2}{3}$$
   • GCD is 90. Divide both by 90.
8. $$\frac{210}{315} = \frac{2}{3}$$
   • GCD is 105. Divide both by 105.
9. $$\frac{234}{351} = \frac{2}{3}$$
   • GCD is 117. Divide both by 117.
10. $$\frac{288}{360} = \frac{4}{5}$$
    • GCD is 72. Divide both by 72.
11. $$\frac{120}{168} = \frac{5}{7}$$
    • GCD is 24. Divide both by 24.