1. Chapter 2 – Properties of Real Numbers 2.1 – The Real Number Line

2. Today we will be: Today we will be: Graphing and comparing real numbers using the number line Graphing and comparing real numbers using the number line Finding the opposite and absolute value of a number in a real-life application Finding the opposite and absolute value of a number in a real-life application

3. 2.1 – The Real Number Line The numbers in this book are real numbers. They can be pictured on the real number line. The point labeled 0 is the origin. Points to the left of zero are negative numbers. Points to the right of zero are positive numbers.

4. 2.1 – The Real Number Line The scale marks represent integers. The real number line has points that represent fractions and decimals as well. The point that corresponds to a number is the graph. Drawing the point is called graphing the number or plotting the point.

5. 2.1 – The Real Number Line Example 1 Graph the numbers -1 ¾ and 2.7.

6. 2.1 – The Real Number Line Example 2 Write two inequalities that compare – ½ and – 3/2.

7. 2.1 – The Real Number Line Example 3 Write the following numbers in increasing order: -1.5, 1/3, -3, 2.5, 0, -1

8. 2.1 – The Real Number Line Two points that are the same distance from the origin but on opposite sides of the origin are opposites.

9. 2.1 – The Real Number Line Example 4 The numbers ½ and – ½ are opposites because each is ½ unit from the origin.

10. 2.1 – The Real Number Line The expression -3 can be stated as “negative 3” or “the opposite of 3”. Do not assume that –a is a negative number. If a = -2, then –a = -(-2) = 2

11. 2.1 – The Real Number Line The absolute value of a real number is the distance between the origin and the point representing the real number. The symbol | a | represents the absolute value of a number a.

12. 2.1 – The Real Number Line THE ABSOLUTE VALUE OF A NUMBER If a is a positive number, then | a | = a | 3 | = 3 If a is zero, then | a | = 0 | 0 | = 0 If a is a negative number, then | a | = -a | -3 | = 3

13. 2.1 – The Real Number Line Example 5 Evaluate the expression | ½ | | -1.6 | - | 3 |

14. 2.1 – The Real Number Line Example 6 Use mental math to solve. | x | = 4.3 | x | = ¾

15. 2.1 – The Real Number Line Velocity shows both speed and direction (up is positive; down is negative). Speed is the absolute value of velocity.

16. 2.1 – The Real Number Line Example 7 An object is dropped towards Earth’s surface. It falls at a rate of 32 ft/sec (if air resistance is ignored). What are the object’s speed and velocity?

17. 2.1 – The Real Number Line Example 8 Decide whether the statement is true or false. If it is false, give a counterexample. The expression | a | is ALWAYS positive. The absolute value of a number is ALWAYS greater than the number. The symbol –a is SOMETIMES equal to | a |.

18. 2.1 – The Real Number Line HOMEWORK Page 67 #18 – 64 even