2. The Real Numbers and Absolute Value Section 2.1

3. Essential Question What are the classifications of real numbers? How can you compare real number? Real numbers Integers Whole numbers Absolute value Rational Irrational

4. All numbers found on the number line. Real Numbers

5. Branching Real Numbers Real Numbers Rational Irrational Now let’s break these subsets down further!

6. Rational Numbers A rational number… is a real number that can be written as a ratio (fraction) of two integers. written in decimal form is terminating (ends) or repeating (same pattern of numbers).

7. Integers Integers are rational numbers because they can be written as fraction with 1 as the denominator. *Remember* Rational numbers can be written as a ratio (or in other words, a fraction)

8. What are integers? Integers are the whole numbers and their opposites. Examples of integers are 6 -12 0 186 -934 What do you notice about these integers?

9. Whole Numbers All positive numbers that are counting numbers plus zero. How can you remember that zero goes with whole numbers? Examples: 0, 1, 2, 3, 4, 5 …

10. Natural Numbers All of your counting numbers What numbers do you count with?

11. Kinds of Numbers 0 natural numbers 0 whole numbers 0 integers

12. Irrational Numbers An irrational number is a number that cannot be written as a ratio (fraction) of two integers. written as decimals are non-terminating (never end!) and non-repeating (no pattern).

13. Sets of Numbers Reals RationalsIrrationals - any number that can be written as a fraction., 7, -0. 4 Fractions/Decimals Integers, -0. 32, - 2. 1 … -3, -2, -1, 0, 1, 2, 3... Negative IntegersWholes … -3, -2, -10, 1, 2, 3... Zero 0 Naturals 1, 2, 3... - non-terminating and non-repeating decimals

14. This is a Venn Diagram that displays the following sets of numbers: Naturals, Wholes, Integers, Rationals, Irrationals, and Reals. Naturals 1, 2, 3... Wholes 0 Integers -3 -19 Rationals -2. 65 Irrationals Reals Sets of Numbers

15. Practice Integer, Rational or Irrational? 479251031218116 How did the astronaut feel about going to Mars?

16. #1 What kind of number is -5?

17. #1#2 integer, rational What kind of number is 42? What kind of number is -5?

18. #3#2 What kind of number is -4.5669? What kind of number is 42? natural, whole, integer, rational

19. #4#3 rational Give an example of a positive integer. What kind of number is -4.5669?

20. #5#4 Give an example of a negative natural number. Give an example of a positive integer.

21. #6#5 Give an example of a negative natural number. Give an example of a whole number that isn’t positive.

22. #7#6 Give an example of a whole number that isn’t positive. What kind of number is most useful to describe: your shoe size

23. #8#7 rational What kind of number is most useful to describe: your shoe size What kind of number is most useful to describe: the temperature in a news report

24. #9#8 integers What kind of number is most useful to describe: the temperature in a news report What kind of number is most useful to describe: the number of siblings a person has

25. #10#9 whole What kind of number is most useful to describe: the number of siblings a person has True or false: Every rational number is also an integer. If false, give a counterexample.

26. #11#10 True or false: Every rational number is also an integer. If false, give a counterexample. True or false: Every whole number is also a natural number. If false, give a counterexample. false

27. #12#11 True or false: Every whole number is also a natural number. If false, give a counterexample. True or false: Every natural number is also a rational number. If false, give a counterexample. false

28. #13#12 True or false: Every natural number is also a rational number. If false, give a counterexample. True or false: Every negative number is also an integer. If false, give a counterexample. true

29. #13 True or false: Every negative number is also an integer. If false, give a counterexample. True or False ?

30. Practice:Identify each of the following as Integer( I ) Whole ( W ) Rational ( R ) Irrational ( IR ) 1.-3 2.125 3.2 ¾ 4.0.9871523.... 5.- ¼ 6..9¯ 7.0.125 8.0

31. Ordering Numbers Symbols < Less than 45 < 87 > Greater than -4 > -7 ≤ Less than or equal 5 ≤ 11 or 12 ≤ 12 ≥ Greater than or equal -12 ≥ - 15 or 45 ≥ 45 = equals

32. 2.Kinds of Numbers 012345678-8-7-6-5-4-3-2-9 8-6 >

33. 2.Kinds of Numbers 012345678-8-7-6-5-4-3-2-9 -77 <

34. #14 -7 10 <

35. #15#14 -7 10-5 + 10 10 - 5 <

36. #16#15 -5 + 10 10 - 510 2 2 2 4 2 =

37. #16 10 2 2 2 4 2 >

38. Absolute Value The positive distance a number is from zero. 1. | 0 | 2. | -9 + 4 | 3. | 12 – 7 | 4. - | 15 – 5 | 5. | -2 | | 3 | 6. - ( - 23 ) 7. - ( 34 – 12 )8. - | - (-3 ) |

39. #17 6

40. #18#17 6

41. #19#18 -3

42. #20#19 -20

43. #21#20 -48

44. #21 1

45. 8.Homework Practice Challenge Simplify:

46. Examples 1. 5 -7 2.-2.3 2 3 10 3. -21 - 45

47. Examples 1. 5 -7 2.-2.3 2 3 10 3. -21 - 45 4. 4 12 7 21

48. Practice Textbook page 58 to 59 28 to 31 all 40 to 47 all 49 to 60 all Moodle: Math starter Page 59 numbers 61 to 64 all Moodle Worksheet 2.1