Equivalent Fractions Worksheets - 15 Worksheets Library - Free Printable

To solve the problem of finding equivalent fractions, we need to use the concept that equivalent fractions have 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 part step by step:

---

1) $\frac{2}{5} = \frac{\square}{10} = \frac{\square}{15}$

- To find the missing numerator for $\frac{\square}{10}$:
- The denominator $5$ is multiplied by $2$ to get $10$. So, multiply the numerator $2$ by $2$:
$$
\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}
$$
- To find the missing numerator for $\frac{\square}{15}$:
- The denominator $5$ is multiplied by $3$ to get $15$. So, multiply the numerator $2$ by $3$:
$$
\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}
$$

Answer:
$$
\frac{2}{5} = \frac{4}{10} = \frac{6}{15}
$$

---

2) $\frac{3}{5} = \frac{\square}{15} = \frac{\square}{25}$

- To find the missing numerator for $\frac{\square}{15}$:
- The denominator $5$ is multiplied by $3$ to get $15$. So, multiply the numerator $3$ by $3$:
$$
\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}
$$
- To find the missing numerator for $\frac{\square}{25}$:
- The denominator $5$ is multiplied by $5$ to get $25$. So, multiply the numerator $3$ by $5$:
$$
\frac{3}{5} = \frac{3 \times 5}{5 \times 5} = \frac{15}{25}
$$

Answer:
$$
\frac{3}{5} = \frac{9}{15} = \frac{15}{25}
$$

---

3) $\frac{5}{9} = \frac{\square}{18} = \frac{\square}{45}$

- To find the missing numerator for $\frac{\square}{18}$:
- The denominator $9$ is multiplied by $2$ to get $18$. So, multiply the numerator $5$ by $2$:
$$
\frac{5}{9} = \frac{5 \times 2}{9 \times 2} = \frac{10}{18}
$$
- To find the missing numerator for $\frac{\square}{45}$:
- The denominator $9$ is multiplied by $5$ to get $45$. So, multiply the numerator $5$ by $5$:
$$
\frac{5}{9} = \frac{5 \times 5}{9 \times 5} = \frac{25}{45}
$$

Answer:
$$
\frac{5}{9} = \frac{10}{18} = \frac{25}{45}
$$

---

4) $\frac{1}{6} = \frac{\square}{24} = \frac{\square}{30}$

- To find the missing numerator for $\frac{\square}{24}$:
- The denominator $6$ is multiplied by $4$ to get $24$. So, multiply the numerator $1$ by $4$:
$$
\frac{1}{6} = \frac{1 \times 4}{6 \times 4} = \frac{4}{24}
$$
- To find the missing numerator for $\frac{\square}{30}$:
- The denominator $6$ is multiplied by $5$ to get $30$. So, multiply the numerator $1$ by $5$:
$$
\frac{1}{6} = \frac{1 \times 5}{6 \times 5} = \frac{5}{30}
$$

Answer:
$$
\frac{1}{6} = \frac{4}{24} = \frac{5}{30}
$$

---

5) $\frac{4}{9} = \frac{\square}{18} = \frac{\square}{27}$

- To find the missing numerator for $\frac{\square}{18}$:
- The denominator $9$ is multiplied by $2$ to get $18$. So, multiply the numerator $4$ by $2$:
$$
\frac{4}{9} = \frac{4 \times 2}{9 \times 2} = \frac{8}{18}
$$
- To find the missing numerator for $\frac{\square}{27}$:
- The denominator $9$ is multiplied by $3$ to get $27$. So, multiply the numerator $4$ by $3$:
$$
\frac{4}{9} = \frac{4 \times 3}{9 \times 3} = \frac{12}{27}
$$

Answer:
$$
\frac{4}{9} = \frac{8}{18} = \frac{12}{27}
$$

---

6) $\frac{1}{4} = \frac{\square}{24} = \frac{\square}{40}$

- To find the missing numerator for $\frac{\square}{24}$:
- The denominator $4$ is multiplied by $6$ to get $24$. So, multiply the numerator $1$ by $6$:
$$
\frac{1}{4} = \frac{1 \times 6}{4 \times 6} = \frac{6}{24}
$$
- To find the missing numerator for $\frac{\square}{40}$:
- The denominator $4$ is multiplied by $10$ to get $40$. So, multiply the numerator $1$ by $10$:
$$
\frac{1}{4} = \frac{1 \times 10}{4 \times 10} = \frac{10}{40}
$$

Answer:
$$
\frac{1}{4} = \frac{6}{24} = \frac{10}{40}
$$

---

7) $\frac{2}{3} = \frac{\square}{6} = \frac{\square}{15}$

- To find the missing numerator for $\frac{\square}{6}$:
- The denominator $3$ is multiplied by $2$ to get $6$. So, multiply the numerator $2$ by $2$:
$$
\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}
$$
- To find the missing numerator for $\frac{\square}{15}$:
- The denominator $3$ is multiplied by $5$ to get $15$. So, multiply the numerator $2$ by $5$:
$$
\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}
$$

Answer:
$$
\frac{2}{3} = \frac{4}{6} = \frac{10}{15}
$$

---

8) $\frac{2}{7} = \frac{\square}{21} = \frac{\square}{35}$

- To find the missing numerator for $\frac{\square}{21}$:
- The denominator $7$ is multiplied by $3$ to get $21$. So, multiply the numerator $2$ by $3$:
$$
\frac{2}{7} = \frac{2 \times 3}{7 \times 3} = \frac{6}{21}
$$
- To find the missing numerator for $\frac{\square}{35}$:
- The denominator $7$ is multiplied by $5$ to get $35$. So, multiply the numerator $2$ by $5$:
$$
\frac{2}{7} = \frac{2 \times 5}{7 \times 5} = \frac{10}{35}
$$

Answer:
$$
\frac{2}{7} = \frac{6}{21} = \frac{10}{35}
$$

---

9) $\frac{5}{12} = \frac{\square}{36} = \frac{\square}{60}$

- To find the missing numerator for $\frac{\square}{36}$:
- The denominator $12$ is multiplied by $3$ to get $36$. So, multiply the numerator $5$ by $3$:
$$
\frac{5}{12} = \frac{5 \times 3}{12 \times 3} = \frac{15}{36}
$$
- To find the missing numerator for $\frac{\square}{60}$:
- The denominator $12$ is multiplied by $5$ to get $60$. So, multiply the numerator $5$ by $5$:
$$
\frac{5}{12} = \frac{5 \times 5}{12 \times 5} = \frac{25}{60}
$$

Answer:
$$
\frac{5}{12} = \frac{15}{36} = \frac{25}{60}
$$

---

10) $\frac{6}{11} = \frac{\square}{22} = \frac{\square}{33}$

- To find the missing numerator for $\frac{\square}{22}$:
- The denominator $11$ is multiplied by $2$ to get $22$. So, multiply the numerator $6$ by $2$:
$$
\frac{6}{11} = \frac{6 \times 2}{11 \times 2} = \frac{12}{22}
$$
- To find the missing numerator for $\frac{\square}{33}$:
- The denominator $11$ is multiplied by $3$ to get $33$. So, multiply the numerator $6$ by $3$:
$$
\frac{6}{11} = \frac{6 \times 3}{11 \times 3} = \frac{18}{33}
$$

Answer:
$$
\frac{6}{11} = \frac{12}{22} = \frac{18}{33}
$$

---

11) $\frac{4}{15} = \frac{\square}{60} = \frac{\square}{90}$

- To find the missing numerator for $\frac{\square}{60}$:
- The denominator $15$ is multiplied by $4$ to get $60$. So, multiply the numerator $4$ by $4$:
$$
\frac{4}{15} = \frac{4 \times 4}{15 \times 4} = \frac{16}{60}
$$
- To find the missing numerator for $\frac{\square}{90}$:
- The denominator $15$ is multiplied by $6$ to get $90$. So, multiply the numerator $4$ by $6$:
$$
\frac{4}{15} = \frac{4 \times 6}{15 \times 6} = \frac{24}{90}
$$

Answer:
$$
\frac{4}{15} = \frac{16}{60} = \frac{24}{90}
$$

---

12) $\frac{3}{10} = \frac{\square}{20} = \frac{\square}{30}$

- To find the missing numerator for $\frac{\square}{20}$:
- The denominator $10$ is multiplied by $2$ to get $20$. So, multiply the numerator $3$ by $2$:
$$
\frac{3}{10} = \frac{3 \times 2}{10 \times 2} = \frac{6}{20}
$$
- To find the missing numerator for $\frac{\square}{30}$:
- The denominator $10$ is multiplied by $3$ to get $30$. So, multiply the numerator $3$ by $3$:
$$
\frac{3}{10} = \frac{3 \times 3}{10 \times 3} = \frac{9}{30}
$$

Answer:
$$
\frac{3}{10} = \frac{6}{20} = \frac{9}{30}
$$

---

Final Answer:

$$
\boxed{
\begin{aligned}
1) & \quad \frac{2}{5} = \frac{4}{10} = \frac{6}{15} \\
2) & \quad \frac{3}{5} = \frac{9}{15} = \frac{15}{25} \\
3) & \quad \frac{5}{9} = \frac{10}{18} = \frac{25}{45} \\
4) & \quad \frac{1}{6} = \frac{4}{24} = \frac{5}{30} \\
5) & \quad \frac{4}{9} = \frac{8}{18} = \frac{12}{27} \\
6) & \quad \frac{1}{4} = \frac{6}{24} = \frac{10}{40} \\
7) & \quad \frac{2}{3} = \frac{4}{6} = \frac{10}{15} \\
8) & \quad \frac{2}{7} = \frac{6}{21} = \frac{10}{35} \\
9) & \quad \frac{5}{12} = \frac{15}{36} = \frac{25}{60} \\
10) & \quad \frac{6}{11} = \frac{12}{22} = \frac{18}{33} \\
11) & \quad \frac{4}{15} = \frac{16}{60} = \frac{24}{90} \\
12) & \quad \frac{3}{10} = \frac{6}{20} = \frac{9}{30}
\end{aligned}
}
$$