Math worksheet with fraction and proportion problems to solve, featuring a fun nose and cactus theme.

To find the missing numbers, we need to solve each proportion. A proportion means two ratios are equal. We can solve them by finding the multiplier (what you multiply by to get from one number to the other) or by cross-multiplying.

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

1. $\frac{5}{6} = \frac{10}{\square}$
* Look at the top numbers: $5 \times 2 = 10$.
* Do the same to the bottom: $6 \times 2 = 12$.
* Missing number: 12 (Letter C)

2. $\frac{3}{\square} = \frac{9}{21}$
* Look at the top numbers: $3 \times 3 = 9$.
* So, the bottom number times 3 must be 21. Since $7 \times 3 = 21$, the missing number is 7.
* Missing number: 7 (Letter T)

3. $\frac{7}{8} = \frac{\square}{32}$
* Look at the bottom numbers: $8 \times 4 = 32$.
* Do the same to the top: $7 \times 4 = 28$.
* Missing number: 28 (Letter R)

4. $1 : 9 = \square : 45$
* Look at the second numbers: $9 \times 5 = 45$.
* Do the same to the first: $1 \times 5 = 5$.
* Missing number: 5 (Letter S)

5. $\square : 12 = 6 : 36$
* Look at the second numbers: $12 \times 3 = 36$.
* So the first number times 3 must be 6. Since $2 \times 3 = 6$, the missing number is 2.
* Missing number: 2 (Letter E)

6. $4 : \square = 6 : 9$
* Look at the first numbers: $4 \times 1.5 = 6$ (or simplify $6:9$ to $2:3$, then $4:6$). Let's use cross multiplication: $4 \times 9 = 36$. Then $36 \div 6 = 6$.
* Missing number: 6 (Letter N)

7. $9 \text{ to } \square = 54 \text{ to } 24$
* Look at the first numbers: $9 \times 6 = 54$.
* Do the same to the second: $\square \times 6 = 24$. Since $4 \times 6 = 24$, the missing number is 4.
* Missing number: 4 (Letter A)

8. $14 \text{ to } \square = 56 \text{ to } 12$
* Look at the first numbers: $14 \times 4 = 56$.
* Do the same to the second: $\square \times 4 = 12$. Since $3 \times 4 = 12$, the missing number is 3.
* Missing number: 3 (Letter L)

9. $5 \text{ to } 2 = \square \text{ to } 6$
* Look at the second numbers: $2 \times 3 = 6$.
* Do the same to the first: $5 \times 3 = 15$.
* Missing number: 15 (Letter M)

10. $\frac{\square}{3} = \frac{40}{15}$
* Look at the bottom numbers: $3 \times 5 = 15$.
* Do the same to the top: $\square \times 5 = 40$. Since $8 \times 5 = 40$, the missing number is 8.
* Missing number: 8 (Letter B)

11. $\frac{10}{11} = \frac{50}{\square}$
* Look at the top numbers: $10 \times 5 = 50$.
* Do the same to the bottom: $11 \times 5 = 55$.
* Missing number: 55 (Letter Y)

12. $\frac{1}{\square} = \frac{7}{70}$
* Look at the top numbers: $1 \times 7 = 7$.
* Do the same to the bottom: $\square \times 7 = 70$. Since $10 \times 7 = 70$, the missing number is 10.
* Missing number: 10 (Letter H)

13. $13 : 14 = \square : 70$
* Look at the second numbers: $14 \times 5 = 70$.
* Do the same to the first: $13 \times 5 = 65$.
* Missing number: 65 (Letter I)

14. $12 : \square = 4 : 10$
* Cross multiply: $12 \times 10 = 120$.
* Divide by the known inner number: $120 \div 4 = 30$.
* Missing number: 30 (Letter O)

15. $44 : 99 = 4 : \square$
* Look at the first numbers: $44 \div 11 = 4$.
* Do the same to the second: $99 \div 11 = 9$.
* Missing number: 9 (Letter D)

16. $\square \text{ to } 4 = 77 \text{ to } 28$
* Look at the second numbers: $4 \times 7 = 28$.
* Do the same to the first: $\square \times 7 = 77$. Since $11 \times 7 = 77$, the missing number is 11.
* Missing number: 11 (Letter P)

17. $26 \text{ to } 8 = \square \text{ to } 4$
* Look at the second numbers: $8 \div 2 = 4$.
* Do the same to the first: $26 \div 2 = 13$.
* Missing number: 13 (Letter U)

18. $17 \text{ to } \square = 34 \text{ to } 2$
* Look at the first numbers: $17 \times 2 = 34$.
* Do the same to the second: $\square \times 2 = 2$. The missing number is 1.
* Missing number: 1 (Letter W)

19. $\frac{81}{\square} = \frac{27}{24}$
* Look at the top numbers: $81 \div 3 = 27$.
* Do the same to the bottom: $\square \div 3 = 24$. So, $24 \times 3 = 72$.
* Missing number: 72 (Letter K)

20. $11 : 17 = 33 : \square$
* Look at the first numbers: $11 \times 3 = 33$.
* Do the same to the second: $17 \times 3 = 51$.
* Missing number: 51 (Letter G)

21. $3 \text{ to } \square = 4 \text{ to } 48$
* Look at the first numbers: $3 \times ? = 4$ (This is tricky with whole numbers). Let's look at the relationship differently.
* $4 \times 12 = 48$. So multiply the first part by 12? No, proportions work across.
* Let's cross multiply: $3 \times 48 = 144$.
* Divide by the outer number 4: $144 \div 4 = 36$.
* Missing number: 36 (Letter F)

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Matching Answers to Letters:

Now we match the problem numbers to the letters based on the answers we found:

* Problem 1: Answer 12 -> C
* Problem 2: Answer 7 -> T
* Problem 3: Answer 28 -> R
* Problem 4: Answer 5 -> S
* Problem 5: Answer 2 -> E
* Problem 6: Answer 6 -> N
* Problem 7: Answer 4 -> A
* Problem 8: Answer 3 -> L
* Problem 9: Answer 15 -> M
* Problem 10: Answer 8 -> B
* Problem 11: Answer 55 -> Y
* Problem 12: Answer 10 -> H
* Problem 13: Answer 65 -> I
* Problem 14: Answer 30 -> O
* Problem 15: Answer 9 -> D
* Problem 16: Answer 11 -> P
* Problem 17: Answer 13 -> U
* Problem 18: Answer 1 -> W
* Problem 19: Answer 72 -> K
* Problem 20: Answer 51 -> G
* Problem 21: Answer 36 -> F

Filling in the Riddle Boxes:

The boxes at the bottom correspond to the problem numbers in order (1 through 21).

1. C
2. T
3. R
4. S
5. E
6. N
7. A
8. L
9. M
10. B
11. Y
12. H
13. I
14. O
15. D
16. P
17. U
18. W
19. K
20. G
21. F

Reading the letters in order: C T R S E N A L M B Y H I O D P U W K G F

Wait, let me re-read the riddle instruction. "Record the corresponding letter of the correct answer in the rectangles at the bottom to answer the riddle."

Let's look at the Legend again to ensure I didn't swap anything.
Legend:
3=C, 13=T, 9=R, 4=S, 30=E, 65=N
28=A, 7=L, 2=M, 36=B, 51=Y, 6=I
11=D, 1=P, 72=O, 12=H, 5=W, 55=G
55 is listed twice in my legend reading? Let me check the image carefully.
Ah, looking at the legend box:
Row 1: 3=C