Equivalent Ratios worksheet for math practice.

To solve the problem of finding equivalent ratios, we need to ensure that the ratios on both sides of the equation are equal. This involves scaling the given ratios by a common factor. Let's solve each part step by step.

Problem 1: \( \_\_ : 9 = 10 : 45 \)

1. Simplify the ratio \( 10 : 45 \):
\[
\frac{10}{45} = \frac{2}{9}
\]
2. The simplified form is \( 2 : 9 \). Therefore, the missing number is \( 2 \).

Answer: \( 2 \)

Problem 2: \( \_\_ : 8 = 16 : 32 \)

1. Simplify the ratio \( 16 : 32 \):
\[
\frac{16}{32} = \frac{1}{2}
\]
2. The simplified form is \( 1 : 2 \). To make the second term \( 8 \), we scale \( 1 : 2 \) by 4:
\[
1 \times 4 : 2 \times 4 = 4 : 8
\]
3. Therefore, the missing number is \( 4 \).

Answer: \( 4 \)

Problem 3: \( \_\_ : 3 = 40 : 15 \)

1. Simplify the ratio \( 40 : 15 \):
\[
\frac{40}{15} = \frac{8}{3}
\]
2. The simplified form is \( 8 : 3 \). Therefore, the missing number is \( 8 \).

Answer: \( 8 \)

Problem 4: \( 8 : 2 = \_\_ : 6 \)

1. Simplify the ratio \( 8 : 2 \):
\[
\frac{8}{2} = 4
\]
2. The simplified form is \( 4 : 1 \). To make the second term \( 6 \), we scale \( 4 : 1 \) by 6:
\[
4 \times 6 : 1 \times 6 = 24 : 6
\]
3. Therefore, the missing number is \( 24 \).

Answer: \( 24 \)

Problem 5: \( 9 : \_\_ = 18 : 14 \)

1. Simplify the ratio \( 18 : 14 \):
\[
\frac{18}{14} = \frac{9}{7}
\]
2. The simplified form is \( 9 : 7 \). Therefore, the missing number is \( 7 \).

Answer: \( 7 \)

Problem 6: \( 3 : \_\_ = 9 : 6 \)

1. Simplify the ratio \( 9 : 6 \):
\[
\frac{9}{6} = \frac{3}{2}
\]
2. The simplified form is \( 3 : 2 \). Therefore, the missing number is \( 2 \).

Answer: \( 2 \)

Problem 7: \( \_\_ : 7 = 45 : 35 \)

1. Simplify the ratio \( 45 : 35 \):
\[
\frac{45}{35} = \frac{9}{7}
\]
2. The simplified form is \( 9 : 7 \). Therefore, the missing number is \( 9 \).

Answer: \( 9 \)

Problem 8: \( 3 : 2 = 9 : \_\_ \)

1. Simplify the ratio \( 3 : 2 \):
\[
\frac{3}{2}
\]
2. To make the first term \( 9 \), we scale \( 3 : 2 \) by 3:
\[
3 \times 3 : 2 \times 3 = 9 : 6
\]
3. Therefore, the missing number is \( 6 \).

Answer: \( 6 \)

Problem 9: \( 6 : 5 = \_\_ : 15 \)

1. To make the second term \( 15 \), we scale \( 6 : 5 \) by 3:
\[
6 \times 3 : 5 \times 3 = 18 : 15
\]
2. Therefore, the missing number is \( 18 \).

Answer: \( 18 \)

Problem 10: \( 6 : \_\_ = 30 : 30 \)

1. Simplify the ratio \( 30 : 30 \):
\[
\frac{30}{30} = 1
\]
2. The simplified form is \( 1 : 1 \). To make the first term \( 6 \), we scale \( 1 : 1 \) by 6:
\[
1 \times 6 : 1 \times 6 = 6 : 6
\]
3. Therefore, the missing number is \( 6 \).

Answer: \( 6 \)

Problem 11: \( 6 : 4 = 18 : \_\_ \)

1. Simplify the ratio \( 6 : 4 \):
\[
\frac{6}{4} = \frac{3}{2}
\]
2. The simplified form is \( 3 : 2 \). To make the first term \( 18 \), we scale \( 3 : 2 \) by 6:
\[
3 \times 6 : 2 \times 6 = 18 : 12
\]
3. Therefore, the missing number is \( 12 \).

Answer: \( 12 \)

Problem 12: \( 6 : 8 = \_\_ : 16 \)

1. Simplify the ratio \( 6 : 8 \):
\[
\frac{6}{8} = \frac{3}{4}
\]
2. The simplified form is \( 3 : 4 \). To make the second term \( 16 \), we scale \( 3 : 4 \) by 4:
\[
3 \times 4 : 4 \times 4 = 12 : 16
\]
3. Therefore, the missing number is \( 12 \).

Answer: \( 12 \)

Problem 13: \( 2 : 8 = \_\_ : 40 \)

1. Simplify the ratio \( 2 : 8 \):
\[
\frac{2}{8} = \frac{1}{4}
\]
2. The simplified form is \( 1 : 4 \). To make the second term \( 40 \), we scale \( 1 : 4 \) by 10:
\[
1 \times 10 : 4 \times 10 = 10 : 40
\]
3. Therefore, the missing number is \( 10 \).

Answer: \( 10 \)

Problem 14: \( 5 : \_\_ = 10 : 18 \)

1. Simplify the ratio \( 10 : 18 \):
\[
\frac{10}{18} = \frac{5}{9}
\]
2. The simplified form is \( 5 : 9 \). Therefore, the missing number is \( 9 \).

Answer: \( 9 \)

Problem 15: \( 6 : 8 = \_\_ : 16 \)

1. Simplify the ratio \( 6 : 8 \):
\[
\frac{6}{8} = \frac{3}{4}
\]
2. The simplified form is \( 3 : 4 \). To make the second term \( 16 \), we scale \( 3 : 4 \) by 4:
\[
3 \times 4 : 4 \times 4 = 12 : 16
\]
3. Therefore, the missing number is \( 12 \).

Answer: \( 12 \)

Problem 16: \( 6 : \_\_ = 24 : 28 \)

1. Simplify the ratio \( 24 : 28 \):
\[
\frac{24}{28} = \frac{6}{7}
\]
2. The simplified form is \( 6 : 7 \). Therefore, the missing number is \( 7 \).

Answer: \( 7 \)

Problem 17: \( 3 : 9 = \_\_ : 36 \)

1. Simplify the ratio \( 3 : 9 \):
\[
\frac{3}{9} = \frac{1}{3}
\]
2. The simplified form is \( 1 : 3 \). To make the second term \( 36 \), we scale \( 1 : 3 \) by 12:
\[
1 \times 12 : 3 \times 12 = 12 : 36
\]
3. Therefore, the missing number is \( 12 \).

Answer: \( 12 \)

Problem 18: \( 6 : 9 = 12 : \_\_ \)

1. Simplify the ratio \( 6 : 9 \):
\[
\frac{6}{9} = \frac{2}{3}
\]
2. The simplified form is \( 2 : 3 \). To make the first term \( 12 \), we scale \( 2 : 3 \) by 6:
\[
2 \times 6 : 3 \times 6 = 12 : 18
\]
3. Therefore, the missing number is \( 18 \).

Answer: \( 18 \)

Problem 19: \( 9 : 3 = \_\_ : 15 \)

1. Simplify the ratio \( 9 : 3 \):
\[
\frac{9}{3} = 3
\]
2. The simplified form is \( 3 : 1 \). To make the second term \( 15 \), we scale \( 3 : 1 \) by 15:
\[
3 \times 15 : 1 \times 15 = 45 : 15
\]
3. Therefore, the missing number is \( 45 \).

Answer: \( 45 \)

Problem 20: \( 4 : \_\_ = 20 : 25 \)

1. Simplify the ratio \( 20 : 25 \):
\[
\frac{20}{25} = \frac{4}{5}
\]
2. The simplified form is \( 4 : 5 \). Therefore, the missing number is \( 5 \).

Answer: \( 5 \)

Final Answer:

\[
\boxed{2, 4, 8, 24, 7, 2, 9, 6, 18, 6, 12, 12, 10, 9, 12, 7, 12, 18, 45, 5}
\]