This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here are the solutions to the questions: PART B: Short Answer Questions 11. The smallest natural number is 1. 12. Is 0 a whole number? Yes. 13. One example of a negative integer is -1. (Other examples include -2, -5, etc.) 14. Is sqrt(9) a rational number? sqrt(9) = 3. Since 3 can be written as (3)/(1), it is a rational number. Yes. 15. One irrational number between 1 and 2 is sqrt(2). (Approximately 1.414) 16. The prime numbers less than 10 are 2, 3, 5, 7. 17. Is 49 a prime or composite number? 49 can be divided by 7 (49 = 7 × 7). Since it has factors other than 1 and itself, it is a composite number. Composite. 18. A prime number has exactly two factors (1 and itself). 19. The smallest multiple of 10 greater than 50 is 60. 20. A number that is a multiple of both 4 and 6 is 12. (Other examples include 24, 36, etc.) PART C: Calculations and Explanations 21. To list all the factors of 36, we find all pairs of numbers that multiply to 36: 1 × 36 = 36 2 × 18 = 36 3 × 12 = 36 4 × 9 = 36 6 × 6 = 36 The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. 22. To write the prime factorization of 180, we can use the division method: 180 ÷ 2 = 90 90 ÷ 2 = 45 45 ÷ 3 = 15 15 ÷ 3 = 5 5 ÷ 5 = 1 The prime factorization of 180 is 2 × 2 × 3 × 3 × 5. Using exponents, this is 2^2 × 3^2 × 5. 23. From the list: 4, 9, 11, 15, 23, 25, 29 a) Identify all prime numbers. Prime numbers are numbers greater than 1 that have only two factors: 1 and themselves. The prime numbers are 11, 23, 29. b) Identify all composite numbers. Composite numbers are numbers greater than 1 that have more than two factors. The composite numbers are 4, 9, 15, 25. 24. a) Explain why 0 is a rational number. Write it as a fraction p/q. A rational number is any number that can be expressed as a fraction (p)/(q), where p and q are integers and q is not zero. Zero can be written as (0)/(1) (or (0)/(2), (0)/(3), etc.), where 0 is an integer and 1 is a non-zero integer. Therefore, 0 is a rational number. As a fraction (p)/(q): (0)/(1). 25. a) What is the smallest positive number that is a multiple of both 8 and 12? This is the Least Common Multiple (LCM) of 8 and 12. The smallest positive number that is a multiple of both 8 and 12 is 24. b) Show how you found it (e.g., method used). Method: Listing multiples Multiples of 8: 8, 16, 24, 32, ... Multiples of 12: 12, 24, 36, ... The smallest common multiple is 24. That's 2 down. 3 left today — send the next one.