Equivalent ratios worksheet with problems to solve by filling in missing numbers to create equivalent ratios.

Let's solve each of these equivalent ratio problems step by step. The goal is to fill in the blank so that the two ratios are equivalent, meaning they represent the same relationship.

We use the idea that if:

$$
a : b = c : d
$$

Then:

$$
\frac{a}{b} = \frac{c}{d}
$$

Cross-multiplying gives:

$$
a \cdot d = b \cdot c
$$

We'll apply this method to each problem.

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1. $ \_ : 9 = 10 : 45 $

Let the missing number be $ x $.
So:
$$
x : 9 = 10 : 45 \Rightarrow \frac{x}{9} = \frac{10}{45}
$$

Simplify $ \frac{10}{45} = \frac{2}{9} $, so:
$$
\frac{x}{9} = \frac{2}{9} \Rightarrow x = 2
$$

✔ Answer: 2

---

2. $ \_ : 8 = 16 : 32 $

Let $ x $ be missing:
$$
\frac{x}{8} = \frac{16}{32} = \frac{1}{2}
\Rightarrow x = 8 \times \frac{1}{2} = 4
$$

✔ Answer: 4

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3. $ \_ : 3 = 40 : 15 $

$$
\frac{x}{3} = \frac{40}{15} = \frac{8}{3}
\Rightarrow x = 3 \times \frac{8}{3} = 8
$$

✔ Answer: 8

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4. $ 8 : 2 = \_ : 6 $

$$
\frac{8}{2} = \frac{x}{6} \Rightarrow 4 = \frac{x}{6} \Rightarrow x = 24
$$

✔ Answer: 24

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5. $ 9 : \_ = 18 : 14 $

Let $ x $ be missing:
$$
\frac{9}{x} = \frac{18}{14} = \frac{9}{7}
\Rightarrow \frac{9}{x} = \frac{9}{7} \Rightarrow x = 7
$$

✔ Answer: 7

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6. $ 3 : \_ = 9 : 6 $

$$
\frac{3}{x} = \frac{9}{6} = \frac{3}{2}
\Rightarrow \frac{3}{x} = \frac{3}{2} \Rightarrow x = 2
$$

✔ Answer: 2

---

7. $ \_ : 7 = 45 : 35 $

$$
\frac{x}{7} = \frac{45}{35} = \frac{9}{7}
\Rightarrow x = 7 \times \frac{9}{7} = 9
$$

✔ Answer: 9

---

8. $ 3 : 2 = 9 : \_ $

$$
\frac{3}{2} = \frac{9}{x} \Rightarrow 3x = 18 \Rightarrow x = 6
$$

✔ Answer: 6

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9. $ 6 : 5 = \_ : 15 $

$$
\frac{6}{5} = \frac{x}{15} \Rightarrow x = \frac{6 \times 15}{5} = 18
$$

✔ Answer: 18

---

10. $ 6 : \_ = 30 : 30 $

$$
\frac{6}{x} = \frac{30}{30} = 1 \Rightarrow x = 6
$$

✔ Answer: 6

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11. $ 6 : 4 = 18 : \_ $

$$
\frac{6}{4} = \frac{18}{x} \Rightarrow \frac{3}{2} = \frac{18}{x} \Rightarrow 3x = 36 \Rightarrow x = 12
$$

✔ Answer: 12

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12. $ 6 : 8 = \_ : 16 $

$$
\frac{6}{8} = \frac{x}{16} \Rightarrow \frac{3}{4} = \frac{x}{16} \Rightarrow x = 12
$$

✔ Answer: 12

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13. $ 2 : 8 = \_ : 40 $

$$
\frac{2}{8} = \frac{x}{40} \Rightarrow \frac{1}{4} = \frac{x}{40} \Rightarrow x = 10
$$

✔ Answer: 10

---

14. $ 5 : \_ = 10 : 18 $

$$
\frac{5}{x} = \frac{10}{18} = \frac{5}{9}
\Rightarrow \frac{5}{x} = \frac{5}{9} \Rightarrow x = 9
$$

✔ Answer: 9

---

15. $ 6 : 8 = \_ : 16 $

Same as #12:
$$
\frac{6}{8} = \frac{x}{16} \Rightarrow x = 12
$$

✔ Answer: 12

---

16. $ 6 : \_ = 24 : 28 $

$$
\frac{6}{x} = \frac{24}{28} = \frac{6}{7}
\Rightarrow \frac{6}{x} = \frac{6}{7} \Rightarrow x = 7
$$

✔ Answer: 7

---

17. $ 3 : 9 = \_ : 36 $

$$
\frac{3}{9} = \frac{x}{36} \Rightarrow \frac{1}{3} = \frac{x}{36} \Rightarrow x = 12
$$

✔ Answer: 12

---

18. $ 6 : 9 = 12 : \_ $

$$
\frac{6}{9} = \frac{12}{x} \Rightarrow \frac{2}{3} = \frac{12}{x} \Rightarrow 2x = 36 \Rightarrow x = 18
$$

✔ Answer: 18

---

19. $ 9 : 3 = \_ : 15 $

$$
\frac{9}{3} = \frac{x}{15} \Rightarrow 3 = \frac{x}{15} \Rightarrow x = 45
$$

✔ Answer: 45

---

20. $ 4 : \_ = 20 : 25 $

$$
\frac{4}{x} = \frac{20}{25} = \frac{4}{5}
\Rightarrow \frac{4}{x} = \frac{4}{5} \Rightarrow x = 5
$$

✔ Answer: 5

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✔ Final Answers (in order):

1. 2
2. 4
3. 8
4. 24
5. 7
6. 2
7. 9
8. 6
9. 18
10. 6
11. 12
12. 12
13. 10
14. 9
15. 12
16. 7
17. 12
18. 18
19. 45
20. 5

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