Lesson2
- 1. Chapter I Real Numbers Lesson 2 Number Theory
- 2. If the name MALOU is written continously without gap, what is the 2013th letter?
- 3. Division of Real Numbers Rational Numbers Irrational Numbers Fractions Decimals Integers Non-Terminating / Whole Non-Repeating Counting Nos. Nos. Decimals Nos. that can be expressed as fraction whose denominator is not zero. Nos. that are not rational or cannot be expressed in the fraction form.
- 4. Answer the following When is a number considered rational? If the number can be expressed in the form a/b, where b ≠ 0. When is it considered irrational? If the number can not be expressed in the form a/b, where b ≠ 0.
- 5. What is the opposite of prime numbers? Ans. composite numbers Show that 12 is even. To show that a number is even, show that the number is divisible by 2 by expressing it in the form 2n. Answer: 12 is even because it can be written as 2(6).
- 6. Prove that 8 is rational. 8 is rational because it can be written 8 in the form . 1 Is 0.75 rational? Prove or disprove. 0.75 is rational since it can be written as fraction form 3 . 4
- 7. Whole Numbers Whole Numbers {0, 1, 2, 3,4, 5,6……..} Natural or Counting Nos. {1, 2, 3,4 ,5, ………} Set of Even Nos. – {2, 4, 6, 8,10……} Set of Odd Nos. – {1, 3, 5, 7,9,…….} Set of Prime Nos. – {2, 3, 5, 7, 11……} When is a number considered prime? A no. is prime if it has only two factors, 1 and the number itself.
- 8. To show that a number is even: Express the number in the form 2n or show that 2 is a factor of the number. Show that 18 is an even no. 18 = 2(9) hence, 18 is even.
- 9. Show that 27 is an odd number. To show that a number is odd, express the number in the form (even+1) or (2n+1) or (2n – 1). 27 is odd since 27 = 2(13) + 1 or = 2(14) – 1 List all prime numbers from 1 to 100. 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
- 10. Factors and Multiples If a, b and c are real numbers and 1. a x b = c, then a and b are factors of c. Example: 3 x 2 = 6 hence, 3 and 2 are factors of 6. Also, 2. If a x b = c, then, c is a multiple of a and b . Hence, 6 is a multiple of 2 and 3.
- 11. 1. 2. 3. 4. Answer the following Is 8 a factor of 4? Why / Why not? What are factors of 4? Is 5 a multiple of 10? Why/Why not? When will you say that a number is a multiple of 10? 5. Give the smallest common multiple of 3 and 4? 6. List all factors of 18. 7. Show that 38 is an even number. 8. Enumerate the prime numbers between 40 and 60. 9. Show that 0.25 is a rational number. 10. When is a number divisible by 9?
- 12. 11. Mike said, 91 is a prime number. Do you agree? Explain. 12. Every decimal number is rational number. True or false. Explain. 13. Explain the difference between rational and irrational, prime and composite and GCF and LCM of numbers. 14. How many numbers less than 50 are divisible by 3 or 4?
- 13. 15. What is the smallest positive number greater than 1 that will give a remainder of 1 when divided by 2, 3, 4, 5, 6, 7, 8, and 9? 16. Red lights flash every 5 seconds, green every 4 sec, blue and yellow every 3 sec. If the lights flash together at 6pm, when will they flash again together?
- 14. There are 100 students and 100 lockers along the hallway. All lockers are closed. The first student goes to every locker and opens all. The second student goes to every second locker and closes the locker. The third student goes to every third locker and opens it if it is close or closes it if it is open. The fourth student goes to every fourth locker and again closes it if open or open it if close. The pattern continuous with the fifth, sixth, etc. student. After all 100 students have gone through the lockers, how many lockers are left open?