Use integers and rational numbers

1. Use integers and rational numbers Section 2.1

2. Most Important Points • Number Classification system • Opposites • Absolute Value • Conditional Statements

3. The Concept • Today we’re going to discuss the nature of numbers • We’re first going to talk about how we can classify numbers • We’ll then take a look at how mathematicians classify numbers

4. Classify If you were going to classify numbers, how would you do it?

5. Mathematical Classification In mathematics we use this general system Real Numbers Rational Numbers Integers Irrational Numbers Whole Numbers Counting numbers

6. Bellwork Solution • What kind of number is shown below

7. Bellwork Solution • What kind of number is shown below

8. Bellwork Solution • What kind of number is shown below

9. Bellwork Solution • What kind of number is shown below

10. Bellwork Solution • What kind of number is shown below

11. The Number line To aid us in our look at opposites and absolute value, we must only look to the number line

12. Opposites • The opposite of a number is the number that is in the same position on the other side of 0 • e.g. The opposite of 4 is -4 Axis of symmetry Vertex

13. Bellwork Solution • Complete the statement using <, >, or = • 1.3 ____ 1.03

14. Bellwork Solution • Complete the statement using <, >, or = • 5/8______6/9

15. Bellwork Solution • Order from least to greatest: ½, .04, 3/7, .45

16. Bellwork Solution • A hobby store has balsa wood strips in three thicknesses (in inches): 3/16, 5/32 and 1/8. Which strip is the thickest?

17. ABS • Absolute Value • The measure of a distance a number is from 0 • Functionally, the positive value of the number • e.g. The absolute value of 8 is 8 • Denoted by bars on either side of a number Axis of symmetry Vertex

18. Example • Find the indicated value Axis of symmetry Vertex

19. Bellwork Solution • What is the opposite of the number below

20. Bellwork Solution • What is the opposite of the number below

21. Bellwork Solution • What is the absolute value of the number below

22. Bellwork Solution • What is the absolute value of the number below

23. Evaluate the expression when x=-9

24. Definition • Conditional Statement • Logical statement that uses a hypothesis and a conclusion • Most conditional statements follow an if-then format • The if part of the statement is the hypothesis and the then portion is the conclusion • Through these conditional statements we can assess validity (truthfulness) If you took good notes, then the test was easier Hypothesis Conclusion Axis of symmetry Vertex

25. Example • Assess the validity of the statement below • If a number is a rational number, then the number is an integer Axis of symmetry Vertex

26. On your own • Assess the validity of the statement • If a number is an integer, then the number is a rational number

27. On your own • Assess the validity of the statement • If a number is negative, then it is a whole number

28. Most Important Points • Number Classification system • Opposites • Absolute Value • Conditional Statements

29. Homework 2.1 • 1-4, 6-22 even, 23-34, 36-48 even, 53, 54