Ratio Worksheets - Free Printable

To find the missing numbers in equivalent ratios, we need to make sure both sides of the equation represent the same relationship. We can do this by finding the "multiplier" (what number we multiply by) or by simplifying the ratio.

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

1) $12 : \underline{18} = 16 : 24$
Look at the right side: $16 : 24$. Both numbers can be divided by 8 to simplify to $2 : 3$.
Now look at the left side: $12 : ?$. To get from 2 to 12, we multiply by 6. So, we must also multiply 3 by 6.
$3 \times 6 = 18$.
Answer: 18

2) $18 : 10 = \underline{9} : 5$
Look at the second parts of the ratio: 10 and 5. To get from 10 to 5, we divide by 2.
So, we must divide the first part (18) by 2 as well.
$18 \div 2 = 9$.
Answer: 9

3) $6 : 7 = \underline{18} : 21$
Look at the second parts: 7 and 21. To get from 7 to 21, we multiply by 3.
So, we must multiply the first part (6) by 3.
$6 \times 3 = 18$.
Answer: 18

4) $7 : 1 = \underline{14} : 2$
Look at the second parts: 1 and 2. To get from 1 to 2, we multiply by 2.
So, we must multiply the first part (7) by 2.
$7 \times 2 = 14$.
Answer: 14

5) $8 : 3 = \underline{72} : 27$
Look at the second parts: 3 and 27. To get from 3 to 27, we multiply by 9.
So, we must multiply the first part (8) by 9.
$8 \times 9 = 72$.
Answer: 72

6) $\underline{24} : 32 = 21 : 28$
Let's simplify the right side ($21 : 28$). Both are divisible by 7.
$21 \div 7 = 3$ and $28 \div 7 = 4$. So the ratio is $3 : 4$.
Now look at the left side: $? : 32$. To get from 4 to 32, we multiply by 8.
So, we multiply 3 by 8.
$3 \times 8 = 24$.
Answer: 24

7) $\underline{10} : 40 = 6 : 24$
Simplify the right side ($6 : 24$). Divide both by 6 to get $1 : 4$.
Now look at the left side: $? : 40$. To get from 4 to 40, we multiply by 10.
So, we multiply 1 by 10.
$1 \times 10 = 10$.
Answer: 10

8) $15 : \underline{35} = 24 : 56$
Simplify the right side ($24 : 56$). Both are divisible by 8.
$24 \div 8 = 3$ and $56 \div 8 = 7$. So the ratio is $3 : 7$.
Now look at the left side: $15 : ?$. To get from 3 to 15, we multiply by 5.
So, we multiply 7 by 5.
$7 \times 5 = 35$.
Answer: 35

9) $\underline{4} : 5 = 16 : 20$
Simplify the right side ($16 : 20$). Divide both by 4 to get $4 : 5$.
The left side is already $? : 5$. Since the simplified ratio is $4 : 5$, the missing number is 4.
Alternatively: To get from 20 to 5, divide by 4. So divide 16 by 4.
$16 \div 4 = 4$.
Answer: 4

10) $16 : 32 = \underline{2} : 4$
Simplify the left side ($16 : 32$). Divide both by 16 to get $1 : 2$.
Now look at the right side: $? : 4$. To get from 2 to 4, multiply by 2.
So, multiply 1 by 2.
$1 \times 2 = 2$.
Answer: 2

11) $\underline{7} : 2 = 28 : 8$
Simplify the right side ($28 : 8$). Divide both by 4 to get $7 : 2$.
The left side is $? : 2$. It matches perfectly. The missing number is 7.
Alternatively: To get from 8 to 2, divide by 4. So divide 28 by 4.
$28 \div 4 = 7$.
Answer: 7

12) $7 : 56 = \underline{9} : 72$
Simplify the left side ($7 : 56$). Divide both by 7 to get $1 : 8$.
Now look at the right side: $? : 72$. To get from 8 to 72, multiply by 9.
So, multiply 1 by 9.
$1 \times 9 = 9$.
Answer: 9

13) $8 : 32 = 1 : \underline{4}$
Simplify the left side ($8 : 32$). Divide both by 8 to get $1 : 4$.
The right side is $1 : ?$. The missing number is 4.
Answer: 4

14) $5 : 3 = 45 : \underline{27}$
Look at the first parts: 5 and 45. To get from 5 to 45, multiply by 9.
So, multiply the second part (3) by 9.
$3 \times 9 = 27$.
Answer: 27

15) $\underline{32} : 20 = 8 : 5$
Look at the second parts: 20 and 5. To get from 5 to 20, multiply by 4.
So, multiply the first part (8) by 4.
$8 \times 4 = 32$.
Answer: 32

16) $6 : \underline{18} = 2 : 6$
Simplify the right side ($2 : 6$). Divide both by 2 to get $1 : 3$.
Now look at the left side: $6 : ?$. To get from 1 to 6, multiply by 6.
So, multiply 3 by 6.
$3 \times 6 = 18$.
Answer: 18

17) $8 : 24 = 1 : \underline{3}$
Simplify the left side ($8 : 24$). Divide both by 8 to get $1 : 3$.
The right side is $1 : ?$. The missing number is 3.
Answer: 3

18) $3 : 6 = \underline{15} : 30$
Simplify the left side ($3 : 6$). Divide both by 3 to get $1 : 2$.
Now look at the right side: $? : 30$. To get from 2 to 30, multiply by 15.
So, multiply 1 by 15.
$1 \times 15 = 15$.
Answer: 15

19) $\underline{18} : 15 = 6 : 5$
Look at the second parts: 15 and 5. To get from 5 to 15, multiply by 3.
So, multiply the first part (6) by 3.
$6 \times 3 = 18$.
Answer: 18

20) $72 : \underline{81} = 16 : 18$
Simplify the right side ($16 : 18$). Divide both by 2 to get $8 : 9$.
Now look at the left side: $72 : ?$. To get from 8 to 72, multiply by 9.
So, multiply 9 by 9.
$9 \times 9 = 81$.
Answer: 81

Final Answer:
1. 18
2. 9
3. 18
4. 14
5. 72
6. 24
7. 10
8. 35
9. 4
10. 2
11. 7
12. 9
13. 4
14. 27
15. 32
16. 18
17. 3
18. 15
19. 18
20. 81