Equivalent fractions worksheet for students to practice finding missing values in fraction pairs.

To solve the problem of finding equivalent fractions, we need to ensure that the fractions on both sides of the equation are equal. This involves either simplifying or scaling up the fractions by multiplying or dividing the numerator and denominator by the same number. Let's solve each problem step by step.

---

Problem 1:

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

- Simplify the fraction on the right:
$$
\frac{2}{8} = \frac{2 \div 2}{8 \div 2} = \frac{1}{4}
$$
- Now, we have:
$$
\frac{\square}{4} = \frac{1}{4}
$$
- The numerators must be equal, so:
$$
\square = 1
$$

Answer:
$$
\boxed{1}
$$

---

Problem 2:

$$
\frac{1}{\square} = \frac{3}{9}
$$

- Simplify the fraction on the right:
$$
\frac{3}{9} = \frac{3 \div 3}{9 \div 3} = \frac{1}{3}
$$
- Now, we have:
$$
\frac{1}{\square} = \frac{1}{3}
$$
- The denominators must be equal, so:
$$
\square = 3
$$

Answer:
$$
\boxed{3}
$$

---

Problem 3:

$$
\frac{2}{3} = \frac{\square}{9}
$$

- To find the missing numerator, scale up the fraction $\frac{2}{3}$ to have a denominator of 9:
$$
\frac{2}{3} = \frac{2 \times 3}{3 \times 3} = \frac{6}{9}
$$
- Now, we have:
$$
\frac{2}{3} = \frac{6}{9}
$$
- Therefore:
$$
\square = 6
$$

Answer:
$$
\boxed{6}
$$

---

Problem 4:

$$
\frac{1}{3} = \frac{\square}{15}
$$

- To find the missing numerator, scale up the fraction $\frac{1}{3}$ to have a denominator of 15:
$$
\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}
$$
- Now, we have:
$$
\frac{1}{3} = \frac{5}{15}
$$
- Therefore:
$$
\square = 5
$$

Answer:
$$
\boxed{5}
$$

---

Problem 5:

$$
\frac{1}{\square} = \frac{10}{20}
$$

- Simplify the fraction on the right:
$$
\frac{10}{20} = \frac{10 \div 10}{20 \div 10} = \frac{1}{2}
$$
- Now, we have:
$$
\frac{1}{\square} = \frac{1}{2}
$$
- The denominators must be equal, so:
$$
\square = 2
$$

Answer:
$$
\boxed{2}
$$

---

Problem 6:

$$
\frac{2}{\square} = \frac{14}{21}
$$

- Simplify the fraction on the right:
$$
\frac{14}{21} = \frac{14 \div 7}{21 \div 7} = \frac{2}{3}
$$
- Now, we have:
$$
\frac{2}{\square} = \frac{2}{3}
$$
- The denominators must be equal, so:
$$
\square = 3
$$

Answer:
$$
\boxed{3}
$$

---

Problem 7:

$$
\frac{1}{\square} = \frac{11}{66}
$$

- Simplify the fraction on the right:
$$
\frac{11}{66} = \frac{11 \div 11}{66 \div 11} = \frac{1}{6}
$$
- Now, we have:
$$
\frac{1}{\square} = \frac{1}{6}
$$
- The denominators must be equal, so:
$$
\square = 6
$$

Answer:
$$
\boxed{6}
$$

---

Problem 8:

$$
\frac{3}{4} = \frac{\square}{24}
$$

- To find the missing numerator, scale up the fraction $\frac{3}{4}$ to have a denominator of 24:
$$
\frac{3}{4} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24}
$$
- Now, we have:
$$
\frac{3}{4} = \frac{18}{24}
$$
- Therefore:
$$
\square = 18
$$

Answer:
$$
\boxed{18}
$$

---

Problem 9:

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

- To find the missing denominator, scale up the fraction $\frac{1}{5}$ to have a numerator of 2:
$$
\frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10}
$$
- Now, we have:
$$
\frac{1}{5} = \frac{2}{10}
$$
- Therefore:
$$
\square = 10
$$

Answer:
$$
\boxed{10}
$$

---

Problem 10:

$$
\frac{1}{\square} = \frac{2}{16}
$$

- Simplify the fraction on the right:
$$
\frac{2}{16} = \frac{2 \div 2}{16 \div 2} = \frac{1}{8}
$$
- Now, we have:
$$
\frac{1}{\square} = \frac{1}{8}
$$
- The denominators must be equal, so:
$$
\square = 8
$$

Answer:
$$
\boxed{8}
$$

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Final Answers:

1. $\boxed{1}$
2. $\boxed{3}$
3. $\boxed{6}$
4. $\boxed{5}$
5. $\boxed{2}$
6. $\boxed{3}$
7. $\boxed{6}$
8. $\boxed{18}$
9. $\boxed{10}$
10. $\boxed{8}$

$$
\boxed{1, 3, 6, 5, 2, 3, 6, 18, 10, 8}
$$