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Let's work through the questions on the worksheet you provided. The topics cover reciprocals, prime numbers, and prime factorizations. I'll solve the questions from both sections.

### Reciprocals:
To find the reciprocal of a number, you simply flip the numerator and the denominator.

1. \( \frac{1}{100} \): The reciprocal is \( \frac{100}{1} = 100 \).
2. \( \frac{9}{10} \): The reciprocal is \( \frac{10}{9} \).
3. \( \frac{1}{8} \): The reciprocal is \( \frac{8}{1} = 8 \).
4. \( 25 \frac{1}{2} = \frac{51}{2} \): The reciprocal is \( \frac{2}{51} \).
5. \( \frac{9}{2} \): The reciprocal is \( \frac{2}{9} \).
6. \( -\frac{1}{4} \): The reciprocal is \( -4 \).
7. \( \frac{3}{7} \): The reciprocal is \( \frac{7}{3} \).
8. \( 9 \): The reciprocal is \( \frac{1}{9} \).
9. \( 14 \): The reciprocal is \( \frac{1}{14} \).
10. \( 0.5 \) (which is \( \frac{1}{2} \)): The reciprocal is \( 2 \).
11. \( 3x \): The reciprocal is \( \frac{1}{3x} \).
12. \( \frac{2x}{y} \): The reciprocal is \( \frac{y}{2x} \).

### Prime Numbers:
Prime numbers are numbers that only have two distinct divisors: 1 and themselves. Let's go through the options provided.

1. Which of the following are prime?
   - A. 9: Not prime (divisible by 3).
   - B. 10: Not prime (divisible by 2 and 5).
   - C. 11: **Prime**.

2. Which of the following are prime?
   - F. 24: Not prime (divisible by 2, 3, 4, etc.).
   - G. 29: **Prime**.
   - H. 33: Not prime (divisible by 3 and 11).

3. Which of the following are prime?
   - A. 2: **Prime** (smallest prime number).
   - B. 20: Not prime (divisible by 2, 4, 5).
   - C. 200: Not prime (divisible by 2, 4, 5, etc.).

4. Which of the following are prime?
   - F. 9: Not prime (divisible by 3).
   - G. 19: **Prime**.
   - H. 99: Not prime (divisible by 3 and 11).

### Prime Factorizations:
Prime factorization is the process of breaking down a number into its prime factors.

5. \( 99 = 3^2 \times 11 \)
6. \( 64 = 2^6 \)
7. \( 49 = 7^2 \)
8. \( 18 = 2 \times 3^2 \)
9. \( 200 = 2^3 \times 5^2 \)
10. \( 169 = 13^2 \)
11. \( 27 = 3^3 \)
12. \( 54 = 2 \times 3^3 \)
13. \( 144 = 2^4 \times 3^2 \)
14. \( 102 = 2 \times 3 \times 17 \)
15. \( 81 = 3^4 \)
16. \( 60 = 2^2 \times 3 \times 5 \)

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Would you like more detailed explanations for any specific part of the solution? Here are 5 related questions you might find useful:

1. How do you find the reciprocal of a mixed fraction?
2. What is the method for determining if a large number is prime?
3. How do you break down numbers into their prime factors?
4. Why is 1 not considered a prime number?
5. How do reciprocals apply in solving algebraic equations?

**Tip:** When dealing with large numbers, always check divisibility by small primes like 2, 3, 5, 7 first before proceeding to larger primes.

Math worksheet involving reciprocals, prime numbers, and prime factorizations.

Solve a math worksheet covering reciprocals, prime numbers, and prime factorizations with step-by-step solutions. Perfect for students in Grades 6-8, this worksheet provides a thorough understanding of these mathematical concepts.

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