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

9. the temperature of 5 degrees below zero as -5 ºC. Verticalnumber line

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