Math worksheet for creating equivalent ratios with 20 problems to solve.

To solve these problems, we need to find the missing number that makes the two ratios equal. We can do this by looking at the relationship between the numbers we already know.

Here is the step-by-step solution for each problem:

1) 72 : 64 = 9 : \_\_
- Look at the first numbers: $72 \div 8 = 9$.
- Do the same to the second number: $64 \div 8 = 8$.
- Answer: 8

2) 2 : 6 = 14 : \_\_
- Look at the first numbers: $2 \times 7 = 14$.
- Do the same to the second number: $6 \times 7 = 42$.
- Answer: 42

3) \_\_ : 7 = 8 : 14
- Look at the second numbers: $14 \div 2 = 7$.
- Do the same to the first number: $8 \div 2 = 4$.
- Answer: 4

4) 32 : \_\_ = 12 : 24
- Look at the first numbers: $32 \div 12$ is tricky, so let's look at the right side. $12 \times 2 = 24$.
- So, multiply the left first number by 2? No, let's simplify the right side first. $12:24$ simplifies to $1:2$.
- So, $32 : \_\_$ must be equivalent to $1 : 2$.
- $32 \times 2 = 64$.
- Answer: 64

5) \_\_ : 12 = 7 : 14
- Look at the right side: $14 \div 2 = 7$ (going backwards) or $7 \times 2 = 14$.
- Since $14$ is double $7$, then $12$ must be double the missing number.
- $12 \div 2 = 6$.
- Answer: 6

6) 30 : 36 = 5 : \_\_
- Look at the first numbers: $30 \div 6 = 5$.
- Do the same to the second number: $36 \div 6 = 6$.
- Answer: 6

7) \_\_ : 6 = 4 : 3
- Look at the second numbers: $3 \times 2 = 6$.
- Do the same to the first number: $4 \times 2 = 8$.
- Answer: 8

8) 1 : 2 = \_\_ : 4
- Look at the second numbers: $2 \times 2 = 4$.
- Do the same to the first number: $1 \times 2 = 2$.
- Answer: 2

9) 4 : 2 = 20 : \_\_
- Look at the first numbers: $4 \times 5 = 20$.
- Do the same to the second number: $2 \times 5 = 10$.
- Answer: 10

10) 6 : \_\_ = 12 : 18
- Look at the first numbers: $6 \times 2 = 12$.
- So the missing number times 2 must equal 18.
- $18 \div 2 = 9$.
- Answer: 9

11) 63 : \_\_ = 7 : 2
- Look at the first numbers: $63 \div 9 = 7$.
- Do the same to the second number on the right? No, we divide the left side to get the right side.
- So we divide the missing number by 9 to get 2. That means the missing number is $2 \times 9$.
- $2 \times 9 = 18$.
- Answer: 18

12) \_\_ : 5 = 18 : 30
- Look at the second numbers: $30 \div 6 = 5$.
- Do the same to the first number: $18 \div 6 = 3$.
- Answer: 3

13) 18 : 27 = 16 : \_\_
- Simplify the left side: Both divide by 9. $18 \div 9 = 2$, $27 \div 9 = 3$. So ratio is $2:3$.
- Now we have $2 : 3 = 16 : \_\_$.
- $2 \times 8 = 16$.
- $3 \times 8 = 24$.
- Answer: 24

14) 6 : \_\_ = 9 : 12
- Simplify the right side: Both divide by 3. $9 \div 3 = 3$, $12 \div 3 = 4$. Ratio is $3:4$.
- Now we have $6 : \_\_ = 3 : 4$.
- $3 \times 2 = 6$.
- $4 \times 2 = 8$.
- Answer: 8

15) 15 : 3 = \_\_ : 1
- Look at the second numbers: $3 \div 3 = 1$.
- Do the same to the first number: $15 \div 3 = 5$.
- Answer: 5

16) \_\_ : 4 = 30 : 24
- Simplify the right side: Both divide by 6. $30 \div 6 = 5$, $24 \div 6 = 4$. Ratio is $5:4$.
- The left side is already over 4. So the top number is 5.
- Answer: 5

17) \_\_ : 14 = 1 : 2
- Look at the second numbers: $2 \times 7 = 14$.
- Do the same to the first number: $1 \times 7 = 7$.
- Answer: 7

18) 6 : \_\_ = 54 : 27
- Simplify the right side: $54 \div 27 = 2$. So the ratio is $2:1$.
- Left side is $6 : \_\_$. If the ratio is $2:1$, then $6 \div 2 = 3$.
- Alternatively: $54 \div 9 = 6$. So $27 \div 9 = 3$.
- Answer: 3

19) 12 : 15 = \_\_ : 45
- Look at the second numbers: $15 \times 3 = 45$.
- Do the same to the first number: $12 \times 3 = 36$.
- Answer: 36

20) 6 : 2 = \_\_ : 18
- Look at the second numbers: $2 \times 9 = 18$.
- Do the same to the first number: $6 \times 9 = 54$.
- Answer: 54

Final Answer:
1. 8
2. 42
3. 4
4. 64
5. 6
6. 6
7. 8
8. 2
9. 10
10. 9
11. 18
12. 3
13. 24
14. 8
15. 5
16. 5
17. 7
18. 3
19. 36
20. 54