1. 2.1 The Real Number Line 01 2 3 45 6 78 9 10 11 -3 -2 -4-5-6-7-8-9-10 Positive Numbers Origin Negative Numbers Graph and label 5.5, ½, –4.25, –9/4 Positive numbers:Ex: Negative numbers:Ex: Zero:Ex: Integers: Abbr: Ex: Real numbers: Abbr: Ex: Points to the right of zero Points to the left of zero Neither positive nor negative Negative and positive numbers & zero All integers and all numbers in between (fractions and decimals) Z R Objective: To be able to graph numbers on the number line and to find the opposite and absolute value of numbers.

2. II. Comparing Real Numbers We compare numbers in order by their location on the number line. Graph –4 and –5 on the number line. Then write two inequalities that compare the two numbers. Put –1, 4, –2, 1.5 in increasing order 01 2 3 45 6 78 9 10 11 -3 -2 -4-5-6-7-8-9-10 –4 > –5 or –5 < –4 01 2 3 45 6 78 9 10 11 -3 -2 -4-5-6-7-8-9-10 Since –5 is farther left, we say –2, –1, 1.5, 4 Left to right

3. Write the following set of numbers in increasing order: –2.3, –4.8, 6.1, 3.5, –2.15, 0.25, 6.02 II. Comparing Real Numbers –4.8, –2.3, –2.15, 0.25, 3.5, 6.02, 6.1 01 2 3 45 6 78 9 10 11 -3 -2 -4-5-6-7-8-9-10

4. III. Fraction Time!!! To convert a fraction to a decimal, Write each set of numbers in increasing order. a. b. YOU TRY a, c, and d! c. –3, -3.2, -3.15, -3.001, 3 d. Divide the numerator by the denominator

5. IV. Opposites Opposites: Name the opposite of the following numbers: a. 10b. -½ c. 4.5d. 0 01 2 3 45 6 78 9 10 11 -3 -2 -4-5-6-7-8-9-10 8 units away from origin Two points (numbers) that are the same distance from the origin but on opposite sides of the origin –10 1/2 –4.5 0

6. V. Absolute Value What is absolute value? –The distance a number is from. –Distance is ALWAYS! What does it look like? We say “the absolute value of x” Think: “How many units away from 5 to zero? Think: “How many units away from -5 to zero? Absolute value bars Find the absolute value of the following: 6 04 origin Non-negative

7. Tricky Case: How are these different from each other? From the ones on the previous slide? VI. Solving Absolute Value Equations Using Mental Math Think, “What number(s) is/are 3 units away from zero? So… How many answers can these have? –4 Ex. 3 or –3 7 or –7 No solution 0 Don’t confuse that “No solution” and “x = 0” are different!!!

8. Summary 1.Graph the real numbers on the number line. 2.Compare the real numbers (rewrite the real numbers in increasing/decreasing order). The number at the LEFT is smaller than the one at the RIGHT. 3.When converting a fraction to a decimal, just divide the numerator by the denominator. 4.Opposites are the two real numbers “mirror” each other. 5.Absolute value is the distance a number on the number line from the origin. Can you compare and order real numbers and find the opposite and absolute value of numbers??

9. Homework: 2.1: P 67 #’s 4 – 15, 28 – 48 (Even), 58 – 65, 83 – 85