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DO NOW. Rational Rational Irrational Irrational Rational. College Lecture - Categories of Numbers. Lesson 1.5. COLLEGE LECTURE – PART I. Natural Numbers. {1, 2, 3, 4, 5 ….}. Real Numbers. Complex numbers. Natural Numbers. Whole Numbers. {0, 1, 2, 3, 4…..}. Real Numbers.

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  1. DO NOW • Rational • Rational • Irrational • Irrational • Rational

  2. College Lecture - Categories of Numbers Lesson 1.5

  3. COLLEGE LECTURE – PART I

  4. Natural Numbers {1, 2, 3, 4, 5 ….} Real Numbers Complex numbers

  5. Natural Numbers Whole Numbers {0, 1, 2, 3, 4…..} Real Numbers Complex numbers

  6. Natural Numbers Whole Numbers Integers {….-2, -1, 0, 1, 2 ….} Real Numbers Complex numbers

  7. Natural Numbers Whole Numbers Rational Numbers Integers The set of numbers in which the decimal terminates or repeats. Can be written as a ratio of two integers. ie 4.5, 3., Real Numbers Complex numbers

  8. Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Set of numbers in which the decimal does not terminate and does not repeat i.e. π, = 1.4142135… Real Numbers Complex numbers

  9. Other Types of Numbers

  10. INTERMISSION

  11. Quick Check Questions • Define: • Irrational number • Rational number • Integer • Natural number • Whole number • Even • Odd • Prime • Composite • Consecutive • Is 0 a prime or composite number? • Is 1 a prime or composite number?

  12. COLLEGE LECTURE – PART II

  13. Example #1 • The following are two rational numbers greater than 1 and less than 2. , 1.234 Give two more rational numbers greater than 1 and less than 2. Give reasons why your numbers are rational numbers

  14. Example #1 - Answer 1.5 between 1 and 2; terminating decimal equal to 1 ; can be written as a ratio of integers

  15. Example #2 • Look at the following expressions. Then choose the true statement. is any REAL number. Expression A: Expression B: • Expression A is greater. • Expression B is greater. • The two expressions are equal. • The relationship between expression A and B cannot be determined from the information given.

  16. Example #2 - Answer • Look at the following expressions. Then choose the true statement. is any REAL number. Expression A: Expression B: • Expression A is greater. • Expression B is greater. • The two expressions are equal. • The relationship between expression A and B cannot be determined from the information given. x = 2 B is greater Expression A: 2 Expression B: 2 2 = 4 x = A is greater Expression A: Expression B: = A and B are equal x = 0 Expression A: 0 Expression B: 0 0 = 0

  17. Example #3 The sum of three consecutive positive odd integers is 381. What is the greatest of these integers? + The sum of three consecutive positive odd integers is 381. What is the greatest of these integers? ?

  18. Example #3 - Answer 1 = x 3 = x + 2 5 = x + 4 x + (x+2) + (x+4) = 381 3x + 6 = 381 -6 -6 3x = 375 x = 125

  19. Example #3 - Answer 125 = x 127 = x + 2 129 = x + 4 125 + 127 + 129 = 381 381 = 381  The greatest integer is 129.

  20. END OF COLLEGE LECTURE

  21. Check for Understanding • Record key takeaways in summary section • Record questions in the cue column • Annotate or add to your notes Practice set – complete at least #1-6

  22. EXIT TICKET Question #3 • Use the following information: Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Write the set(s) to which each number belongs. • 4 • -2 • 6.5

  23. BACKUP

  24. Example #2 • In the statement below, is any REAL number. Determine if the statement below is always true, sometimes true, or never true. • Always true. • Sometimes true • Never true. • The answer cannot be determined from the information given.

  25. Example #3 • The sum of three consecutive positive odd integers is 381. What is the greatest of these integers? The greatest integer is

  26. Defend your answer! • The sum of three consecutive positive odd integers is 381. What is the greatest of these integers? The greatest integer is

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