Equivalent Fractions (B) | Fun and Engaging 4th Grade PDF Worksheets - Free Printable

To solve the problem of finding equivalent fractions, we need to understand that equivalent fractions are fractions that represent the same value but are expressed with different numerators and denominators. This is achieved by multiplying or dividing both the numerator and the denominator by the same non-zero number.

Let's solve each section step by step.

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Section A: Fill in the blanks to create equivalent fractions.

#### 1. $\frac{1}{2} = \frac{6}{\square}$
- To find the missing denominator, notice that the numerator $1$ is multiplied by $6$. Therefore, the denominator $2$ must also be multiplied by $6$.
- $2 \times 6 = 12$.
- So, $\frac{1}{2} = \frac{6}{12}$.

#### 2. $\frac{1}{3} = \frac{\square}{7}$
- Here, the denominator $3$ is multiplied by $\frac{7}{3}$ to get $7$. Therefore, the numerator $1$ must also be multiplied by $\frac{7}{3}$.
- $1 \times \frac{7}{3} = \frac{7}{3}$.
- So, $\frac{1}{3} = \frac{7}{21}$.

#### 3. $\frac{1}{6} = \frac{9}{\square}$
- The numerator $1$ is multiplied by $9$. Therefore, the denominator $6$ must also be multiplied by $9$.
- $6 \times 9 = 54$.
- So, $\frac{1}{6} = \frac{9}{54}$.

#### 4. $\frac{1}{7} = \frac{\square}{14}$
- The denominator $7$ is multiplied by $2$ to get $14$. Therefore, the numerator $1$ must also be multiplied by $2$.
- $1 \times 2 = 2$.
- So, $\frac{1}{7} = \frac{2}{14}$.

#### 5. $\frac{1}{9} = \frac{5}{\square}$
- The numerator $1$ is multiplied by $5$. Therefore, the denominator $9$ must also be multiplied by $5$.
- $9 \times 5 = 45$.
- So, $\frac{1}{9} = \frac{5}{45}$.

#### 6. $\frac{1}{8} = \frac{4}{\square}$
- The numerator $1$ is multiplied by $4$. Therefore, the denominator $8$ must also be multiplied by $4$.
- $8 \times 4 = 32$.
- So, $\frac{1}{8} = \frac{4}{32}$.

#### 7. $\frac{1}{12} = \frac{3}{\square}$
- The numerator $1$ is multiplied by $3$. Therefore, the denominator $12$ must also be multiplied by $3$.
- $12 \times 3 = 36$.
- So, $\frac{1}{12} = \frac{3}{36}$.

#### 8. $\frac{1}{8} = \frac{\square}{32}$
- The denominator $8$ is multiplied by $4$ to get $32$. Therefore, the numerator $1$ must also be multiplied by $4$.
- $1 \times 4 = 4$.
- So, $\frac{1}{8} = \frac{4}{32}$.

#### 9. $\frac{1}{5} = \frac{9}{\square}$
- The numerator $1$ is multiplied by $9$. Therefore, the denominator $5$ must also be multiplied by $9$.
- $5 \times 9 = 45$.
- So, $\frac{1}{5} = \frac{9}{45}$.

#### 10. $\frac{1}{11} = \frac{4}{\square}$
- The numerator $1$ is multiplied by $4$. Therefore, the denominator $11$ must also be multiplied by $4$.
- $11 \times 4 = 44$.
- So, $\frac{1}{11} = \frac{4}{44}$.

#### 11. $\frac{1}{6} = \frac{12}{\square}$
- The numerator $1$ is multiplied by $12$. Therefore, the denominator $6$ must also be multiplied by $12$.
- $6 \times 12 = 72$.
- So, $\frac{1}{6} = \frac{12}{72}$.

#### 12. $\frac{1}{7} = \frac{\square}{49}$
- The denominator $7$ is multiplied by $7$ to get $49$. Therefore, the numerator $1$ must also be multiplied by $7$.
- $1 \times 7 = 7$.
- So, $\frac{1}{7} = \frac{7}{49}$.

#### 13. $\frac{1}{8} = \frac{3}{\square}$
- The numerator $1$ is multiplied by $3$. Therefore, the denominator $8$ must also be multiplied by $3$.
- $8 \times 3 = 24$.
- So, $\frac{1}{8} = \frac{3}{24}$.

#### 14. $\frac{1}{6} = \frac{7}{\square}$
- The numerator $1$ is multiplied by $7$. Therefore, the denominator $6$ must also be multiplied by $7$.
- $6 \times 7 = 42$.
- So, $\frac{1}{6} = \frac{7}{42}$.

#### 15. $\frac{1}{12} = \frac{10}{\square}$
- The numerator $1$ is multiplied by $10$. Therefore, the denominator $12$ must also be multiplied by $10$.
- $12 \times 10 = 120$.
- So, $\frac{1}{12} = \frac{10}{120}$.

#### 16. $\frac{1}{9} = \frac{\square}{63}$
- The denominator $9$ is multiplied by $7$ to get $63$. Therefore, the numerator $1$ must also be multiplied by $7$.
- $1 \times 7 = 7$.
- So, $\frac{1}{9} = \frac{7}{63}$.

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Section B: Fill in the blanks to create equivalent fractions.

#### 1. $\frac{2}{3} = \frac{4}{\square}$
- The numerator $2$ is multiplied by $2$. Therefore, the denominator $3$ must also be multiplied by $2$.
- $3 \times 2 = 6$.
- So, $\frac{2}{3} = \frac{4}{6}$.

#### 2. $\frac{4}{5} = \frac{12}{\square}$
- The numerator $4$ is multiplied by $3$. Therefore, the denominator $5$ must also be multiplied by $3$.
- $5 \times 3 = 15$.
- So, $\frac{4}{5} = \frac{12}{15}$.

#### 3. $\frac{3}{4} = \frac{21}{\square}$
- The numerator $3$ is multiplied by $7$. Therefore, the denominator $4$ must also be multiplied by $7$.
- $4 \times 7 = 28$.
- So, $\frac{3}{4} = \frac{21}{28}$.

#### 4. $\frac{2}{5} = \frac{10}{\square}$
- The numerator $2$ is multiplied by $5$. Therefore, the denominator $5$ must also be multiplied by $5$.
- $5 \times 5 = 25$.
- So, $\frac{2}{5} = \frac{10}{25}$.

#### 5. $\frac{2}{9} = \frac{16}{\square}$
- The numerator $2$ is multiplied by $8$. Therefore, the denominator $9$ must also be multiplied by $8$.
- $9 \times 8 = 72$.
- So, $\frac{2}{9} = \frac{16}{72}$.

#### 6. $\frac{9}{10} = \frac{18}{\square}$
- The numerator $9$ is multiplied by $2$. Therefore, the denominator $10$ must also be multiplied by $2$.
- $10 \times 2 = 20$.
- So, $\frac{9}{10} = \frac{18}{20}$.

#### 7. $\frac{4}{7} = \frac{16}{\square}$
- The numerator $4$ is multiplied by $4$. Therefore, the denominator $7$ must also be multiplied by $4$.
- $7 \times 4 = 28$.
- So, $\frac{4}{7} = \frac{16}{28}$.

#### 8. $\frac{3}{11} = \frac{27}{\square}$
- The numerator $3$ is multiplied by $9$. Therefore, the denominator $11$ must also be multiplied by $9$.
- $11 \times 9 = 99$.
- So, $\frac{3}{11} = \frac{27}{99}$.

#### 9. $\frac{7}{8} = \frac{\square}{56}$
- The denominator $8$ is multiplied by $7$ to get $56$. Therefore, the numerator $7$ must also be multiplied by $7$.
- $7 \times 7 = 49$.
- So, $\frac{7}{8} = \frac{49}{56}$.

#### 10. $\frac{2}{3} = \frac{\square}{36}$
- The denominator $3$ is multiplied by $12$ to get $36$. Therefore, the numerator $2$ must also be multiplied by $12$.
- $2 \times 12 = 24$.
- So, $\frac{2}{3} = \frac{24}{36}$.

#### 11. $\frac{5}{6} = \frac{\square}{48}$
- The denominator $6$ is multiplied by $8$ to get $48$. Therefore, the numerator $5$ must also be multiplied by $8$.
- $5 \times 8 = 40$.
- So, $\frac{5}{6} = \frac{40}{48}$.

#### 12. $\frac{3}{7} = \frac{\square}{84}$
- The denominator $7$ is multiplied by $12$ to get $84$. Therefore, the numerator $3$ must also be multiplied by $12$.
- $3 \times 12 = 36$.
- So, $\frac{3}{7} = \frac{36}{84}$.

#### 13. $\frac{1}{20} = \frac{\square}{160}$
- The denominator $20$ is multiplied by $8$ to get $160$. Therefore, the numerator $1$ must also be multiplied by $8$.
- $1 \times 8 = 8$.
- So, $\frac{1}{20} = \frac{8}{160}$.

#### 14. $\frac{3}{50} = \frac{\square}{150}$
- The denominator $50$ is multiplied by $3$ to get $150$. Therefore, the numerator $3$ must also be multiplied by $3$.
- $3 \times 3 = 9$.
- So, $\frac{3}{50} = \frac{9}{150}$.

#### 15. $\frac{11}{30} = \frac{\square}{120}$
- The denominator $30$ is multiplied by $4$ to get $120$. Therefore, the numerator $11$ must also be multiplied by $4$.
- $11 \times 4 = 44$.
- So, $\frac{11}{30} = \frac{44}{120}$.

#### 16. $\frac{9}{25} = \frac{\square}{100}$
- The denominator $25$ is multiplied by $4$ to get $100$. Therefore, the numerator $9$ must also be multiplied by $4$.
- $9 \times 4 = 36$.
- So, $\frac{9}{25} = \frac{36}{100}$.

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Section C: Fill in the blanks to create equivalent fractions.

#### 1. $\frac{2}{3} = \frac{\square}{9} = \frac{12}{\square} = \frac{\square}{21}$
- For $\frac{2}{3} = \frac{\square}{9}$:
- The denominator $3$ is multiplied by $3$ to get $9$. Therefore, the numerator $2$ must also be multiplied by $3$.
- $2 \times 3 = 6$.
- So, $\frac{2}{3} = \frac{6}{9}$.

- For $\frac{2}{3} = \frac{12}{\square}$:
- The numerator $2$ is multiplied by $6$. Therefore, the denominator $3$ must also be multiplied by $6$.
- $3 \times 6 = 18$.
- So, $\frac{2}{3} = \frac{12}{18}$.

- For $\frac{2}{3} = \frac{\square}{21}$:
- The denominator $3$ is multiplied by $7$ to get $21$. Therefore, the numerator $2$ must also be multiplied by $7$.
- $2 \times 7 = 14$.
- So, $\frac{2}{3} = \frac{14}{21}$.

#### 2. $\frac{3}{5} = \frac{\square}{25} = \frac{36}{\square} = \frac{24}{\square}$
- For $\frac{3}{5} = \frac{\square}{25}$:
- The denominator $5$ is multiplied by $5$ to get $25$. Therefore, the numerator $3$ must also be multiplied by $5$.
- $3 \times 5 = 15$.
- So, $\frac{3}{5} = \frac{15}{25}$.

- For $\frac{3}{5} = \frac{36}{\square}$:
- The numerator $3$ is multiplied by $12$. Therefore, the denominator $5$ must also be multiplied by $12$.
- $5 \times 12 = 60$.
- So, $\frac{3}{5} = \frac{36}{60}$.

- For $\frac{3}{5} = \frac{24}{\square}$:
- The numerator $3$ is multiplied by $8$. Therefore, the denominator $5$ must also be multiplied by $8$.
- $5 \times 8 = 40$.
- So, $\frac{3}{5} = \frac{24}{40}$.

#### 3. $\frac{6}{7} = \frac{\square}{14} = \frac{36}{\square} = \frac{\square}{56}$
- For $\frac{6}{7} = \frac{\square}{14}$:
- The denominator $7$ is multiplied by $2$ to get $14$. Therefore, the numerator $6$ must also be multiplied by $2$.
- $6 \times 2 = 12$.
- So, $\frac{6}{7} = \frac{12}{14}$.

- For $\frac{6}{7} = \frac{36}{\square}$:
- The numerator $6$ is multiplied by $6$. Therefore, the denominator $7$ must also be multiplied by $6$.
- $7 \times 6 = 42$.
- So, $\frac{6}{7} = \frac{36}{42}$.

- For $\frac{6}{7} = \frac{\square}{56}$:
- The denominator $7$ is multiplied by $8$ to get $56$. Therefore, the numerator $6$ must also be multiplied by $8$.
- $6 \times 8 = 48$.
- So, $\frac{6}{7} = \frac{48}{56}$.

#### 4. $\frac{11}{20} = \frac{\square}{40} = \frac{66}{\square} = \frac{132}{\square}$
- For $\frac{11}{20} = \frac{\square}{40}$:
- The denominator $20$ is multiplied by $2$ to get $40$. Therefore, the numerator $11$ must also be multiplied by $2$.
- $11 \times 2 = 22$.
- So, $\frac{11}{20} = \frac{22}{40}$.

- For $\frac{11}{20} = \frac{66}{\square}$:
- The numerator $11$ is multiplied by $6$. Therefore, the denominator $20$ must also be multiplied by $6$.
- $20 \times 6 = 120$.
- So, $\frac{11}{20} = \frac{66}{120}$.

- For $\frac{11}{20} = \frac{132}{\square}$:
- The numerator $11$ is multiplied by $12$. Therefore, the denominator $20$ must also be multiplied by $12$.
- $20 \times 12 = 240$.
- So, $\frac{11}{20} = \frac{132}{240}$.

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Final Answer:

\[
\boxed{
\begin{array}{l}
\text{Section A:} \\
\frac{1}{2} = \frac{6}{12}, \quad \frac{1}{3} = \frac{7}{21}, \quad \frac{1}{6} = \frac{9}{54}, \quad \frac{1}{7} = \frac{2}{14}, \\
\frac{1}{9} = \frac{5}{45}, \quad \frac{1}{8} = \frac{4}{32}, \quad \frac{1}{12} = \frac{3}{36}, \quad \frac{1}{8} = \frac{4}{32}, \\
\frac{1}{5} = \frac{9}{45}, \quad \frac{1}{11} = \frac{4}{44}, \quad \frac{1}{6} = \frac{12}{72}, \quad \frac{1}{7} = \frac{7}{49}, \\
\frac{1}{8} = \frac{3}{24}, \quad \frac{1}{6} = \frac{7}{42}, \quad \frac{1}{12} = \frac{10}{120}, \quad \frac{1}{9} = \frac{7}{63}. \\
\\
\text{Section B:} \\
\frac{2}{3} = \frac{4}{6}, \quad \frac{4}{5} = \frac{12}{15}, \quad \frac{3}{4} = \frac{21}{28}, \quad \frac{2}{5} = \frac{10}{25}, \\
\frac{2}{9} = \frac{16}{72}, \quad \frac{9}{10} = \frac{18}{20}, \quad \frac{4}{7} = \frac{16}{28}, \quad \frac{3}{11} = \frac{27}{99}, \\
\frac{7}{8} = \frac{49}{56}, \quad \frac{2}{3} = \frac{24}{36}, \quad \frac{5}{6} = \frac{40}{48}, \quad \frac{3}{7} = \frac{36}{84}, \\
\frac{1}{20} = \frac{8}{160}, \quad \frac{3}{50} = \frac{9}{150}, \quad \frac{11}{30} = \frac{44}{120}, \quad \frac{9}{25} = \frac{36}{100}. \\
\\
\text{Section C:} \\
\frac{2}{3} = \frac{6}{9} = \frac{12}{18} = \frac{14}{21}, \\
\frac{3}{5} = \frac{15}{25} = \frac{36}{60} = \frac{24}{40}, \\
\frac{6}{7} = \frac{12}{14} = \frac{36}{42} = \frac{48}{56}, \\
\frac{11}{20} = \frac{22}{40} = \frac{66}{120} = \frac{132}{240}.
\end{array}
}
\]