Equivalent Fractions Worksheet for practicing finding missing values in equivalent fraction equations.

To solve the problem of completing the equivalent fractions, we need to find the missing numerators or denominators in each fraction so that the fractions remain equivalent. This involves using the concept of multiplying or dividing both the numerator and the denominator by the same non-zero number.

Let's solve each problem step by step:

---

1) $\frac{5}{10} = \frac{\square}{90}$

- The original fraction is $\frac{5}{10}$.
- To find the missing numerator, we need to determine what number we multiply the denominator 10 by to get 90.
$$
90 \div 10 = 9
$$
- Now, multiply the numerator 5 by 9:
$$
5 \times 9 = 45
$$
- Therefore, the equivalent fraction is:
$$
\frac{5}{10} = \frac{45}{90}
$$

---

2) $\frac{2}{4} = \frac{\square}{20}$

- The original fraction is $\frac{2}{4}$.
- Simplify $\frac{2}{4}$ to its simplest form:
$$
\frac{2}{4} = \frac{1}{2}
$$
- To find the missing numerator, we need to determine what number we multiply the denominator 2 by to get 20.
$$
20 \div 2 = 10
$$
- Now, multiply the numerator 1 by 10:
$$
1 \times 10 = 10
$$
- Therefore, the equivalent fraction is:
$$
\frac{2}{4} = \frac{10}{20}
$$

---

3) $\frac{3}{7} = \frac{\square}{28}$

- The original fraction is $\frac{3}{7}$.
- To find the missing numerator, we need to determine what number we multiply the denominator 7 by to get 28.
$$
28 \div 7 = 4
$$
- Now, multiply the numerator 3 by 4:
$$
3 \times 4 = 12
$$
- Therefore, the equivalent fraction is:
$$
\frac{3}{7} = \frac{12}{28}
$$

---

4) $\frac{\square}{15} = \frac{8}{3}$

- The given fraction is $\frac{8}{3}$.
- To find the missing numerator, we need to determine what number we multiply the denominator 3 by to get 15.
$$
15 \div 3 = 5
$$
- Now, multiply the numerator 8 by 5:
$$
8 \times 5 = 40
$$
- Therefore, the equivalent fraction is:
$$
\frac{40}{15} = \frac{8}{3}
$$

---

5) $\frac{9}{2} = \frac{\square}{40}$

- The original fraction is $\frac{9}{2}$.
- To find the missing numerator, we need to determine what number we multiply the denominator 2 by to get 40.
$$
40 \div 2 = 20
$$
- Now, multiply the numerator 9 by 20:
$$
9 \times 20 = 180
$$
- Therefore, the equivalent fraction is:
$$
\frac{9}{2} = \frac{180}{40}
$$

---

6) $\frac{6}{\square} = \frac{30}{45}$

- The given fraction is $\frac{30}{45}$.
- Simplify $\frac{30}{45}$ to its simplest form:
$$
\frac{30}{45} = \frac{2}{3}
$$
- The original fraction is $\frac{6}{\square}$, which should be equivalent to $\frac{2}{3}$.
- To find the missing denominator, we need to determine what number we multiply the numerator 2 by to get 6.
$$
6 \div 2 = 3
$$
- Now, multiply the denominator 3 by 3:
$$
3 \times 3 = 9
$$
- Therefore, the equivalent fraction is:
$$
\frac{6}{9} = \frac{30}{45}
$$

---

7) $\frac{\square}{27} = \frac{7}{9}$

- The given fraction is $\frac{7}{9}$.
- To find the missing numerator, we need to determine what number we multiply the denominator 9 by to get 27.
$$
27 \div 9 = 3
$$
- Now, multiply the numerator 7 by 3:
$$
7 \times 3 = 21
$$
- Therefore, the equivalent fraction is:
$$
\frac{21}{27} = \frac{7}{9}
$$

---

8) $\frac{39}{12} = \frac{13}{\square}$

- The original fraction is $\frac{39}{12}$.
- Simplify $\frac{39}{12}$ to its simplest form:
$$
\frac{39}{12} = \frac{13}{4}
$$
- The given fraction is $\frac{13}{\square}$, which should be equivalent to $\frac{13}{4}$.
- Therefore, the missing denominator is:
$$
\frac{39}{12} = \frac{13}{4}
$$

---

9) $\frac{10}{3} = \frac{\square}{27}$

- The original fraction is $\frac{10}{3}$.
- To find the missing numerator, we need to determine what number we multiply the denominator 3 by to get 27.
$$
27 \div 3 = 9
$$
- Now, multiply the numerator 10 by 9:
$$
10 \times 9 = 90
$$
- Therefore, the equivalent fraction is:
$$
\frac{10}{3} = \frac{90}{27}
$$

---

10) $\frac{1}{6} = \frac{\square}{54}$

- The original fraction is $\frac{1}{6}$.
- To find the missing numerator, we need to determine what number we multiply the denominator 6 by to get 54.
$$
54 \div 6 = 9
$$
- Now, multiply the numerator 1 by 9:
$$
1 \times 9 = 9
$$
- Therefore, the equivalent fraction is:
$$
\frac{1}{6} = \frac{9}{54}
$$

---

11) $\frac{4}{4} = \frac{\square}{12}$

- The original fraction is $\frac{4}{4}$, which simplifies to 1.
- To find the missing numerator, we need to determine what number we multiply the denominator 4 by to get 12.
$$
12 \div 4 = 3
$$
- Now, multiply the numerator 4 by 3:
$$
4 \times 3 = 12
$$
- Therefore, the equivalent fraction is:
$$
\frac{4}{4} = \frac{12}{12}
$$

---

12) $\frac{1}{2} = \frac{5}{\square}$

- The original fraction is $\frac{1}{2}$.
- To find the missing denominator, we need to determine what number we multiply the numerator 1 by to get 5.
$$
5 \div 1 = 5
$$
- Now, multiply the denominator 2 by 5:
$$
2 \times 5 = 10
$$
- Therefore, the equivalent fraction is:
$$
\frac{1}{2} = \frac{5}{10}
$$

---

13) $\frac{4}{12} = \frac{\square}{6}$

- The original fraction is $\frac{4}{12}$.
- Simplify $\frac{4}{12}$ to its simplest form:
$$
\frac{4}{12} = \frac{1}{3}
$$
- To find the missing numerator, we need to determine what number we multiply the denominator 3 by to get 6.
$$
6 \div 3 = 2
$$
- Now, multiply the numerator 1 by 2:
$$
1 \times 2 = 2
$$
- Therefore, the equivalent fraction is:
$$
\frac{4}{12} = \frac{2}{6}
$$

---

14) $\frac{1}{4} = \frac{\square}{48}$

- The original fraction is $\frac{1}{4}$.
- To find the missing numerator, we need to determine what number we multiply the denominator 4 by to get 48.
$$
48 \div 4 = 12
$$
- Now, multiply the numerator 1 by 12:
$$
1 \times 12 = 12
$$
- Therefore, the equivalent fraction is:
$$
\frac{1}{4} = \frac{12}{48}
$$

---

15) $\frac{1}{7} = \frac{\square}{28}$

- The original fraction is $\frac{1}{7}$.
- To find the missing numerator, we need to determine what number we multiply the denominator 7 by to get 28.
$$
28 \div 7 = 4
$$
- Now, multiply the numerator 1 by 4:
$$
1 \times 4 = 4
$$
- Therefore, the equivalent fraction is:
$$
\frac{1}{7} = \frac{4}{28}
$$

---

Final Answers:

$$
\boxed{
\begin{aligned}
1) & \quad \frac{5}{10} = \frac{45}{90} \\
2) & \quad \frac{2}{4} = \frac{10}{20} \\
3) & \quad \frac{3}{7} = \frac{12}{28} \\
4) & \quad \frac{40}{15} = \frac{8}{3} \\
5) & \quad \frac{9}{2} = \frac{180}{40} \\
6) & \quad \frac{6}{9} = \frac{30}{45} \\
7) & \quad \frac{21}{27} = \frac{7}{9} \\
8) & \quad \frac{39}{12} = \frac{13}{4} \\
9) & \quad \frac{10}{3} = \frac{90}{27} \\
10) & \quad \frac{1}{6} = \frac{9}{54} \\
11) & \quad \frac{4}{4} = \frac{12}{12} \\
12) & \quad \frac{1}{2} = \frac{5}{10} \\
13) & \quad \frac{4}{12} = \frac{2}{6} \\
14) & \quad \frac{1}{4} = \frac{12}{48} \\
15) & \quad \frac{1}{7} = \frac{4}{28}
\end{aligned}
}
$$