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  • 1. The Real Number System
  • 2. N : 1,2,3,….
    Z : …,-2,-1,0,1,2,..
    Q :
    Irational:
  • 3. Real Numbers
    Rational Numbers
    ¼ ⅓
    0.6
    - ⅔ √0.25
    Irrational
    Numbers
    π
    0.101001
    √2
    Integers
    - 4 -3
    -8
    Whole Numbers
    0
    Natural
    Numbers
    2
    5
  • 4. Concept Summary
  • 5. Operation of Integers
  • 6. Four Fundamental Operations
  • 7.
  • 8. 1.1
    Integers and Their Symbols
    A
    +5
    0
    -5
    +5
    -5
    0
    Positive and Negative Numbers
    The numbers 5 and -5 can be drawn on a vertical or a horizontal line as follows.
    thermometer
    Horizontal number line
    You may write:
    • the temperature of 5 degrees above zero as 5 ºC,
    • 9. the temperature of 5 degrees below zero as -5 ºC.
    Verticalnumber line
  • 10. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
    Positive integers
    Negative integers
    0 is neither positive nor negative
    A set of integers; ..., 3, 2, 1, 0, 1, 2, 3, ... , can be symbolized as Z.
    • The complete number line of integers can be drawn as follows.
    Natural numbers ( bilanganAsli ) : 1, 2, 3, 4, …Whole numbers ( bilanganCacah ) : 0, 1, 2, 3, 4, …Integers ( bilanganBulat ) : …, -2, -1, 0, 1, 2, …
  • 11. a. Determine all integers between 5 and 4.
    Example 1
    Solution:
    4, 3, 2, 1, 0, 1, 2, 3
    b. Write all even integers between 6 and 11.
    Solution:
    The even integers between 6 and 11 are 4, 2, 0, 2, 4, 6, 8, and 10
    c. Write all odd integers between 7 and 8.
    Solution:
    The odd integers between 7 and 8 are -5, -3, -1, 1 , 3 , 5, and 7
  • 12. B
    -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
    Comparing and Ordering Integers
    -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
    increase
    decrease
    What if we use a vertical number line?
    Change the sign  to <, >, or = on 4 7
    Solution:
    Example 2
    The number 4 is located on the right side of 7. Therefore, 4 > 7.
  • 13. Problem 1
    Arrange the following numbers from the least to the greatest.
    a. 5, 3, 6, 6, 2, 4, 1
    b. 9, 5, 6, 12, 17, 8, 14
    Problem 1
    Solution :
    a. -6, -3, -1, 2, 4, 5, 6
    b. -14, -12, -5, 6, 8, 9, 17
  • 14. In a mathematics test, the score for the right answer is 4, for the wrong answer is -1, and 0 for failing to answer.
    Complete the table below (use a spreadsheet, if possible) and then sort the students based on their scores from the highest to the lowest.
    Problem 2
    17
    20
    18
    30
    31
    32
    27
    25