Equivalent Fractions Worksheet - Free Printable

To solve the problems on the "Equivalent Fractions Sheet 4," we need to find the missing numbers in each fraction so that the fractions remain equivalent. The key principle is that multiplying or dividing both the numerator and the denominator of a fraction by the same number results in an equivalent fraction.

Let's solve each problem step by step:

---

Problem 1:

$$
\frac{2}{3} = \frac{\_\_}{9}
$$
- The denominator changes from 3 to 9. To find the multiplier:
$$
9 \div 3 = 3
$$
- Multiply the numerator by the same number (3):
$$
2 \times 3 = 6
$$
- So, the equivalent fraction is:
$$
\frac{2}{3} = \frac{6}{9}
$$

---

Problem 2:

$$
\frac{2}{5} = \frac{\_\_}{15}
$$
- The denominator changes from 5 to 15. To find the multiplier:
$$
15 \div 5 = 3
$$
- Multiply the numerator by the same number (3):
$$
2 \times 3 = 6
$$
- So, the equivalent fraction is:
$$
\frac{2}{5} = \frac{6}{15}
$$

---

Problem 3:

$$
\frac{1}{7} = \frac{\_\_}{14}
$$
- The denominator changes from 7 to 14. To find the multiplier:
$$
14 \div 7 = 2
$$
- Multiply the numerator by the same number (2):
$$
1 \times 2 = 2
$$
- So, the equivalent fraction is:
$$
\frac{1}{7} = \frac{2}{14}
$$

---

Problem 4:

$$
\frac{3}{3} = \frac{\_\_}{9}
$$
- The denominator changes from 3 to 9. To find the multiplier:
$$
9 \div 3 = 3
$$
- Multiply the numerator by the same number (3):
$$
3 \times 3 = 9
$$
- So, the equivalent fraction is:
$$
\frac{3}{3} = \frac{9}{9}
$$

---

Problem 5:

$$
\frac{3}{4} = \frac{9}{\_\_}
$$
- The numerator changes from 3 to 9. To find the multiplier:
$$
9 \div 3 = 3
$$
- Multiply the denominator by the same number (3):
$$
4 \times 3 = 12
$$
- So, the equivalent fraction is:
$$
\frac{3}{4} = \frac{9}{12}
$$

---

Problem 6:

$$
\frac{1}{2} = \frac{6}{\_\_}
$$
- The numerator changes from 1 to 6. To find the multiplier:
$$
6 \div 1 = 6
$$
- Multiply the denominator by the same number (6):
$$
2 \times 6 = 12
$$
- So, the equivalent fraction is:
$$
\frac{1}{2} = \frac{6}{12}
$$

---

Problem 7:

$$
\frac{5}{6} = \frac{\_\_}{18}
$$
- The denominator changes from 6 to 18. To find the multiplier:
$$
18 \div 6 = 3
$$
- Multiply the numerator by the same number (3):
$$
5 \times 3 = 15
$$
- So, the equivalent fraction is:
$$
\frac{5}{6} = \frac{15}{18}
$$

---

Problem 8:

$$
\frac{1}{5} = \frac{3}{\_\_}
$$
- The numerator changes from 1 to 3. To find the multiplier:
$$
3 \div 1 = 3
$$
- Multiply the denominator by the same number (3):
$$
5 \times 3 = 15
$$
- So, the equivalent fraction is:
$$
\frac{1}{5} = \frac{3}{15}
$$

---

Problem 9:

$$
\frac{2}{9} = \frac{\_\_}{18}
$$
- The denominator changes from 9 to 18. To find the multiplier:
$$
18 \div 9 = 2
$$
- Multiply the numerator by the same number (2):
$$
2 \times 2 = 4
$$
- So, the equivalent fraction is:
$$
\frac{2}{9} = \frac{4}{18}
$$

---

Problem 10:

$$
\frac{3}{5} = \frac{\_\_}{20}
$$
- The denominator changes from 5 to 20. To find the multiplier:
$$
20 \div 5 = 4
$$
- Multiply the numerator by the same number (4):
$$
3 \times 4 = 12
$$
- So, the equivalent fraction is:
$$
\frac{3}{5} = \frac{12}{20}
$$

---

Problem 11:

$$
\frac{2}{6} = \frac{6}{\_\_}
$$
- The numerator changes from 2 to 6. To find the multiplier:
$$
6 \div 2 = 3
$$
- Multiply the denominator by the same number (3):
$$
6 \times 3 = 18
$$
- So, the equivalent fraction is:
$$
\frac{2}{6} = \frac{6}{18}
$$

---

Problem 12:

$$
\frac{3}{7} = \frac{9}{\_\_}
$$
- The numerator changes from 3 to 9. To find the multiplier:
$$
9 \div 3 = 3
$$
- Multiply the denominator by the same number (3):
$$
7 \times 3 = 21
$$
- So, the equivalent fraction is:
$$
\frac{3}{7} = \frac{9}{21}
$$

---

Problem 13:

$$
\frac{4}{12} = \frac{\_\_}{3}
$$
- The denominator changes from 12 to 3. To find the divisor:
$$
12 \div 3 = 4
$$
- Divide the numerator by the same number (4):
$$
4 \div 4 = 1
$$
- So, the equivalent fraction is:
$$
\frac{4}{12} = \frac{1}{3}
$$

---

Problem 14:

$$
\frac{4}{6} = \frac{\_\_}{3}
$$
- The denominator changes from 6 to 3. To find the divisor:
$$
6 \div 3 = 2
$$
- Divide the numerator by the same number (2):
$$
4 \div 2 = 2
$$
- So, the equivalent fraction is:
$$
\frac{4}{6} = \frac{2}{3}
$$

---

Problem 15:

$$
\frac{3}{6} = \frac{1}{\_\_}
$$
- The numerator changes from 3 to 1. To find the divisor:
$$
3 \div 1 = 3
$$
- Divide the denominator by the same number (3):
$$
6 \div 3 = 2
$$
- So, the equivalent fraction is:
$$
\frac{3}{6} = \frac{1}{2}
$$

---

Problem 16:

$$
\frac{9}{12} = \frac{\_\_}{4}
$$
- The denominator changes from 12 to 4. To find the divisor:
$$
12 \div 4 = 3
$$
- Divide the numerator by the same number (3):
$$
9 \div 3 = 3
$$
- So, the equivalent fraction is:
$$
\frac{9}{12} = \frac{3}{4}
$$

---

Problem 17:

$$
\frac{4}{10} = \frac{\_\_}{5}
$$
- The denominator changes from 10 to 5. To find the divisor:
$$
10 \div 5 = 2
$$
- Divide the numerator by the same number (2):
$$
4 \div 2 = 2
$$
- So, the equivalent fraction is:
$$
\frac{4}{10} = \frac{2}{5}
$$

---

Problem 18:

$$
\frac{5}{10} = \frac{\_\_}{2}
$$
- The denominator changes from 10 to 2. To find the divisor:
$$
10 \div 2 = 5
$$
- Divide the numerator by the same number (5):
$$
5 \div 5 = 1
$$
- So, the equivalent fraction is:
$$
\frac{5}{10} = \frac{1}{2}
$$

---

Problem 19:

$$
\frac{4}{16} = \frac{1}{\_\_}
$$
- The numerator changes from 4 to 1. To find the divisor:
$$
4 \div 1 = 4
$$
- Divide the denominator by the same number (4):
$$
16 \div 4 = 4
$$
- So, the equivalent fraction is:
$$
\frac{4}{16} = \frac{1}{4}
$$

---

Problem 20:

$$
\frac{8}{8} = \frac{\_\_}{2}
$$
- The denominator changes from 8 to 2. To find the divisor:
$$
8 \div 2 = 4
$$
- Divide the numerator by the same number (4):
$$
8 \div 4 = 2
$$
- So, the equivalent fraction is:
$$
\frac{8}{8} = \frac{2}{2}
$$

---

Problem 21:

$$
\frac{8}{10} = \frac{4}{\_\_}
$$
- The numerator changes from 8 to 4. To find the divisor:
$$
8 \div 4 = 2
$$
- Divide the denominator by the same number (2):
$$
10 \div 2 = 5
$$
- So, the equivalent fraction is:
$$
\frac{8}{10} = \frac{4}{5}
$$

---

Problem 22:

$$
\frac{2}{\_\_} = \frac{8}{12}
$$
- Simplify the fraction $\frac{8}{12}$:
$$
\frac{8 \div 4}{12 \div 4} = \frac{2}{3}
$$
- So, the equivalent fraction is:
$$
\frac{2}{3} = \frac{8}{12}
$$

---

Problem 23:

$$
\frac{1}{\_\_} = \frac{5}{15}
$$
- Simplify the fraction $\frac{5}{15}$:
$$
\frac{5 \div 5}{15 \div 5} = \frac{1}{3}
$$
- So, the equivalent fraction is:
$$
\frac{1}{3} = \frac{5}{15}
$$

---

Problem 24:

$$
\frac{1}{\_\_} = \frac{3}{21}
$$
- Simplify the fraction $\frac{3}{21}$:
$$
\frac{3 \div 3}{21 \div 3} = \frac{1}{7}
$$
- So, the equivalent fraction is:
$$
\frac{1}{7} = \frac{3}{21}
$$

---

Problem 25:

$$
\frac{2}{\_\_} = \frac{4}{18}
$$
- Simplify the fraction $\frac{4}{18}$:
$$
\frac{4 \div 2}{18 \div 2} = \frac{2}{9}
$$
- So, the equivalent fraction is:
$$
\frac{2}{9} = \frac{4}{18}
$$

---

Problem 26:

$$
\frac{3}{\_\_} = \frac{9}{15}
$$
- Simplify the fraction $\frac{9}{15}$:
$$
\frac{9 \div 3}{15 \div 3} = \frac{3}{5}
$$
- So, the equivalent fraction is:
$$
\frac{3}{5} = \frac{9}{15}
$$

---

Problem 27:

$$
\frac{5}{9} = \frac{15}{\_\_}
$$
- The numerator changes from 5 to 15. To find the multiplier:
$$
15 \div 5 = 3
$$
- Multiply the denominator by the same number (3):
$$
9 \times 3 = 27
$$
- So, the equivalent fraction is:
$$
\frac{5}{9} = \frac{15}{27}
$$

---

Problem 28:

$$
\frac{4}{\_\_} = \frac{16}{20}
$$
- Simplify the fraction $\frac{16}{20}$:
$$
\frac{16 \div 4}{20 \div 4} = \frac{4}{5}
$$
- So, the equivalent fraction is:
$$
\frac{4}{5} = \frac{16}{20}
$$

---

Problem 29:

$$
\frac{3}{10} = \frac{12}{\_\_}
$$
- The numerator changes from 3 to 12. To find the multiplier:
$$
12 \div 3 = 4
$$
- Multiply the denominator by the same number (4):
$$
10 \times 4 = 40
$$
- So, the equivalent fraction is:
$$
\frac{3}{10} = \frac{12}{40}
$$

---

Problem 30:

$$
\frac{\_\_}{9} = \frac{8}{36}
$$
- Simplify the fraction $\frac{8}{36}$:
$$
\frac{8 \div 4}{36 \div 4} = \frac{2}{9}
$$
- So, the equivalent fraction is:
$$
\frac{2}{9} = \frac{8}{36}
$$

---

Problem 31:

$$
\frac{5}{7} = \frac{\_\_}{35}
$$
- The denominator changes from 7 to 35. To find the multiplier:
$$
35 \div 7 = 5
$$
- Multiply the numerator by the same number (5):
$$
5 \times 5 = 25
$$
- So, the equivalent fraction is:
$$
\frac{5}{7} = \frac{25}{35}
$$

---

Problem 32:

$$
\frac{6}{11} = \frac{18}{\_\_}
$$
- The numerator changes from 6 to 18. To find the multiplier:
$$
18 \div 6 = 3
$$
- Multiply the denominator by the same number (3):
$$
11 \times 3 = 33
$$
- So, the equivalent fraction is:
$$
\frac{6}{11} = \frac{18}{33}
$$

---

Final Answer:

$$
\boxed{
\begin{array}{ll}
1) \frac{2}{3} = \frac{6}{9} & 2) \frac{2}{5} = \frac{6}{15} \\
3) \frac{1}{7} = \frac{2}{14} & 4) \frac{3}{3} = \frac{9}{9} \\
5) \frac{3}{4} = \frac{9}{12} & 6) \frac{1}{2} = \frac{6}{12} \\
7) \frac{5}{6} = \frac{15}{18} & 8) \frac{1}{5} = \frac{3}{15} \\
9) \frac{2}{9} = \frac{4}{18} & 10) \frac{3}{5} = \frac{12}{20} \\
11) \frac{2}{6} = \frac{6}{18} & 12) \frac{3}{7} = \frac{9}{21} \\
13) \frac{4}{12} = \frac{1}{3} & 14) \frac{4}{6} = \frac{2}{3} \\
15) \frac{3}{6} = \frac{1}{2} & 16) \frac{9}{12} = \frac{3}{4} \\
17) \frac{4}{10} = \frac{2}{5} & 18) \frac{5}{10} = \frac{1}{2} \\
19) \frac{4}{16} = \frac{1}{4} & 20) \frac{8}{8} = \frac{2}{2} \\
21) \frac{8}{10} = \frac{4}{5} & 22) \frac{2}{3} = \frac{8}{12} \\
23) \frac{1}{3} = \frac{5}{15} & 24) \frac{1}{7} = \frac{3}{21} \\
25) \frac{2}{9} = \frac{4}{18} & 26) \frac{3}{5} = \frac{9}{15} \\
27) \frac{5}{9} = \frac{15}{27} & 28) \frac{4}{5} = \frac{16}{20} \\
29) \frac{3}{10} = \frac{12}{40} & 30) \frac{2}{9} = \frac{8}{36} \\
31) \frac{5}{7} = \frac{25}{35} & 32) \frac{6}{11} = \frac{18}{33} \\
\end{array}
}
$$