Year 8 Maths: Equivalent Fractions

Equivalent fractions are different fractions that represent the same value or proportion of a whole. For example,

$$\frac{1}{2}$$ is equivalent to $$\frac{2}{4}$$ and $$\frac{3}{6}$$ because they all represent half of something. To find equivalent fractions, you multiply or divide both the numerator (the top number) and the denominator (the bottom number) by the same number. This keeps the value of the fraction the same, even though it looks different.

How to Find Equivalent Fractions

Method 1: Multiplying Both Numerator and Denominator by the Same Number

One way to create an equivalent fraction is to multiply both the numerator and the denominator by the same number.

Example

$$\frac{1}{3} \times \frac{2}{2} = \frac{2}{6}$$

In this example, multiplying both the numerator (1) and denominator (3) by 2 gives an equivalent fraction

$$\frac{2}{6}$$ .

Method 2: Dividing Both Numerator and Denominator by the Same Number

You can also simplify a fraction by dividing both the numerator and the denominator by the same number, as long as they have a common factor.

Example

$$\frac{4}{8} \div \frac{2}{2} = \frac{2}{4}$$

Here, dividing both the numerator (4) and denominator (8) by 2 gives the equivalent fraction

$$\frac{2}{4}$$ , which can be further simplified to $$\frac{1}{2}$$ .

Why Are Equivalent Fractions Important?

Understanding equivalent fractions helps in simplifying fractions, comparing fractions, and solving fraction-based problems. It also helps in adding, subtracting, multiplying, and dividing fractions by making it easier to work with common denominators.

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Practice Questions on Equivalent Fractions

Easy Level

1. Write two equivalent fractions for $$\frac{1}{2}$$ .
2. Write two equivalent fractions for $$\frac{3}{4}$$ .
3. Write two equivalent fractions for $$\frac{2}{3}$$ .
4. Write two equivalent fractions for $$\frac{5}{6}$$ .
5. Write two equivalent fractions for $$\frac{1}{3}$$ .
6. Write two equivalent fractions for $$\frac{4}{5}$$ .
7. Write two equivalent fractions for $$\frac{1}{4}$$ .
8. Write two equivalent fractions for $$\frac{2}{5}$$ .
9. Write two equivalent fractions for $$\frac{7}{8}$$ .
10. Write two equivalent fractions for $$\frac{3}{5}$$ .
11. Find the equivalent fraction of $$\frac{2}{6}$$ using the numerator 4.
12. Find the equivalent fraction of $$\frac{5}{7}$$ using the denominator 21.
13. Write an equivalent fraction for $$\frac{3}{6}$$ by simplifying it.
14. Write an equivalent fraction for $$\frac{9}{12}$$ by simplifying it.
15. Write two equivalent fractions for $$\frac{4}{6}$$ .
16. Find the equivalent fraction of $$\frac{1}{8}$$ using the numerator 2.
17. Find the equivalent fraction of $$\frac{3}{9}$$ using the denominator 18.
18. Write two equivalent fractions for $$\frac{2}{7}$$ .
19. Write two equivalent fractions for $$\frac{3}{8}$$ .
20. Write two equivalent fractions for $$\frac{6}{10}$$ .

Medium Level

1. Simplify the fraction $$\frac{8}{12}$$ .
2. Simplify the fraction $$\frac{10}{15}$$ .
3. Simplify the fraction $$\frac{18}{24}$$ .
4. Find the equivalent fraction of $$\frac{7}{9}$$ with the denominator 27.
5. Find the equivalent fraction of $$\frac{5}{8}$$ with the numerator 25.
6. Write two equivalent fractions for $$\frac{11}{15}$$ .
7. Find the equivalent fraction of $$\frac{6}{14}$$ using the denominator 28.
8. Simplify the fraction $$\frac{9}{18}$$ .
9. Write two equivalent fractions for $$\frac{7}{12}$$ .
10. Find the equivalent fraction of $$\frac{4}{9}$$ using the numerator 12.
11. Write an equivalent fraction for $$\frac{14}{28}$$ by simplifying it.
12. Write two equivalent fractions for $$\frac{5}{11}$$ .
13. Find the equivalent fraction of $$\frac{3}{7}$$ using the numerator 9.
14. Simplify the fraction $$\frac{16}{24}$$ .
15. Write two equivalent fractions for $$\frac{2}{9}$$ .
16. Simplify the fraction $$\frac{12}{20}$$ .
17. Find the equivalent fraction of $$\frac{7}{10}$$ using the denominator 30.
18. Write two equivalent fractions for $$\frac{9}{14}$$ .
19. Find the equivalent fraction of $$\frac{3}{8}$$ using the numerator 6.
20. Simplify the fraction $$\frac{15}{25}$$ .

Hard Level

1. Simplify the fraction $$\frac{24}{36}$$ .
2. Find the equivalent fraction of $$\frac{12}{15}$$ using the denominator 75.
3. Write two equivalent fractions for $$\frac{8}{9}$$ .
4. Find the equivalent fraction of $$\frac{25}{35}$$ using the numerator 50.
5. Simplify the fraction $$\frac{18}{27}$$ .
6. Write two equivalent fractions for $$\frac{9}{16}$$ .
7. Find the equivalent fraction of $$\frac{15}{24}$$ using the denominator 48.
8. Simplify the fraction $$\frac{28}{42}$$ .
9. Write two equivalent fractions for $$\frac{12}{20}$$ .
10. Simplify the fraction $$\frac{32}{48}$$ .
11. Find the equivalent fraction of $$\frac{5}{9}$$ using the numerator 10.
12. Simplify the fraction $$\frac{20}{30}$$ .
13. Write two equivalent fractions for $$\frac{14}{21}$$ .
14. Simplify the fraction $$\frac{36}{54}$$ .
15. Find the equivalent fraction of $$\frac{11}{22}$$ using the denominator 66.
16. Write two equivalent fractions for $$\frac{16}{25}$$ .
17. Simplify the fraction $$\frac{40}{60}$$ .
18. Find the equivalent fraction of $$\frac{6}{9}$$ using the numerator 12.
19. Write two equivalent fractions for $$\frac{18}{24}$$ .
20. Simplify the fraction $$\frac{50}{75}$$ .

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Answers and Explanations

Easy Level

1. $$\frac{1}{2} = \frac{2}{4} = \frac{3}{6}$$

• Multiply numerator and denominator by 2 and 3.

1. $$\frac{3}{4} = \frac{6}{8} = \frac{9}{12}$$

• Multiply numerator and denominator by 2 and 3.

1. $$\frac{2}{3} = \frac{4}{6} = \frac{6}{9}$$

• Multiply numerator and denominator by 2 and 3.

1. $$\frac{5}{6} = \frac{10}{12} = \frac{15}{18}$$

• Multiply numerator and denominator by 2 and 3.

1. $$\frac{1}{3} = \frac{2}{6} = \frac{3}{9}$$

• Multiply numerator and denominator by 2 and 3.

1. $$\frac{4}{5} = \frac{8}{10} = \frac{12}{15}$$

• Multiply numerator and denominator by 2 and 3.

1. $$\frac{1}{4} = \frac{2}{8} = \frac{3}{12}$$

• Multiply numerator and denominator by 2 and 3.

1. $$\frac{2}{5} = \frac{4}{10} = \frac{6}{15}$$

• Multiply numerator and denominator by 2 and 3.

1. $$\frac{7}{8} = \frac{14}{16} = \frac{21}{24}$$

• Multiply numerator and denominator by 2 and 3.

1. $$\frac{3}{5} = \frac{6}{10} = \frac{9}{15}$$
   • Multiply numerator and denominator by 2 and 3.
2. $$\frac{2}{6} = \frac{4}{12}$$
   • Multiply numerator and denominator by 2.
3. $$\frac{5}{7} = \frac{15}{21}$$
   • Multiply numerator and denominator by 3.
4. $$\frac{3}{6} = \frac{1}{2}$$
   • Simplified by dividing both numerator and denominator by 3.
5. $$ \frac{9}{12} = \frac{3}{4} $

$
– Simplified by dividing both numerator and denominator by 3.

15. $$\frac{4}{6} = \frac{2}{3} = \frac{8}{12}$$
    • Multiply or divide numerator and denominator by 2.
16. $$\frac{1}{8} = \frac{2}{16}$$
    • Multiply numerator and denominator by 2.
17. $$\frac{3}{9} = \frac{6}{18}$$
    • Multiply numerator and denominator by 2.
18. $$\frac{2}{7} = \frac{4}{14} = \frac{6}{21}$$
    • Multiply numerator and denominator by 2 and 3.
19. $$\frac{3}{8} = \frac{6}{16} = \frac{9}{24}$$
    • Multiply numerator and denominator by 2 and 3.
20. $$\frac{6}{10} = \frac{12}{20} = \frac{18}{30}$$
    • Multiply numerator and denominator by 2 and 3.

Medium Level

1. $$\frac{8}{12} = \frac{2}{3}$$

• Simplify by dividing both by 4.

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

• Simplify by dividing both by 5.

1. $$\frac{18}{24} = \frac{3}{4}$$

• Simplify by dividing both by 6.

1. $$\frac{7}{9} = \frac{21}{27}$$

• Multiply numerator and denominator by 3.

1. $$\frac{5}{8} = \frac{25}{40}$$

• Multiply numerator and denominator by 5.

1. $$\frac{11}{15} = \frac{22}{30} = \frac{33}{45}$$

• Multiply numerator and denominator by 2 and 3.

1. $$\frac{6}{14} = \frac{12}{28}$$

• Multiply numerator and denominator by 2.

1. $$\frac{9}{18} = \frac{1}{2}$$

• Simplify by dividing both by 9.

1. $$\frac{7}{12} = \frac{14}{24} = \frac{21}{36}$$

• Multiply numerator and denominator by 2 and 3.

1. $$\frac{4}{9} = \frac{12}{27}$$
   • Multiply numerator and denominator by 3.
2. $$\frac{14}{28} = \frac{1}{2}$$
   • Simplify by dividing both by 14.
3. $$\frac{5}{11} = \frac{10}{22} = \frac{15}{33}$$
   • Multiply numerator and denominator by 2 and 3.
4. $$\frac{3}{7} = \frac{9}{21}$$
   • Multiply numerator and denominator by 3.
5. $$\frac{16}{24} = \frac{2}{3}$$
   • Simplify by dividing both by 8.
6. $$\frac{2}{9} = \frac{4}{18} = \frac{6}{27}$$
   • Multiply numerator and denominator by 2 and 3.
7. $$\frac{12}{20} = \frac{3}{5}$$
   • Simplify by dividing both by 4.
8. $$\frac{7}{10} = \frac{21}{30}$$
   • Multiply numerator and denominator by 3.
9. $$\frac{9}{14} = \frac{18}{28} = \frac{27}{42}$$
   • Multiply numerator and denominator by 2 and 3.
10. $$\frac{3}{8} = \frac{6}{16}$$
    • Multiply numerator and denominator by 2.
11. $$\frac{15}{25} = \frac{3}{5}$$
    • Simplify by dividing both by 5.

Hard Level

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

• Simplify by dividing both by 12.

1. $$\frac{12}{15} = \frac{60}{75}$$

• Multiply numerator and denominator by 5.

1. $$\frac{8}{9} = \frac{16}{18} = \frac{24}{27}$$

• Multiply numerator and denominator by 2 and 3.

1. $$\frac{25}{35} = \frac{50}{70}$$

• Multiply numerator and denominator by 2.

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

• Simplify by dividing both by 9.

1. $$\frac{9}{16} = \frac{18}{32} = \frac{27}{48}$$

• Multiply numerator and denominator by 2 and 3.

1. $$\frac{15}{24} = \frac{30}{48}$$

• Multiply numerator and denominator by 2.

1. $$\frac{28}{42} = \frac{2}{3}$$

• Simplify by dividing both by 14.

1. $$\frac{12}{20} = \frac{24}{40} = \frac{36}{60}$$

• Multiply numerator and denominator by 2 and 3.

1. $$\frac{32}{48} = \frac{2}{3}$$
   • Simplify by dividing both by 16.
2. $$\frac{5}{9} = \frac{10}{18}$$
   • Multiply numerator and denominator by 2.
3. $$\frac{20}{30} = \frac{2}{3}$$
   • Simplify by dividing both by 10.
4. $$\frac{14}{21} = \frac{28}{42} = \frac{42}{63}$$
   • Multiply numerator and denominator by 2 and 3.
5. $$\frac{36}{54} = \frac{2}{3}$$
   • Simplify by dividing both by 18.
6. $$\frac{11}{22} = \frac{33}{66}$$
   • Multiply numerator and denominator by 3.
7. $$\frac{16}{25} = \frac{32}{50} = \frac{48}{75}$$
   • Multiply numerator and denominator by 2 and 3.
8. $$\frac{40}{60} = \frac{2}{3}$$
   • Simplify by dividing both by 20.
9. $$\frac{6}{9} = \frac{12}{18}$$
   • Multiply numerator and denominator by 2.
10. $$\frac{18}{24} = \frac{3}{4}$$
    • Simplify by dividing both by 6.
11. $$\frac{50}{75} = \frac{2}{3}$$
    • Simplify by dividing both by 25.

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These questions and answers should help students get a clear understanding of equivalent fractions, how to generate them, and how to simplify fractions to find equivalencies.