1. 1.1 – Real Numbers, Number Operations

2. Most things in math and life we work with are real numbers
We can divide real numbers into two categories;
Rational
Irrational

3. Rational vs. Irrational
Rational = a number that may be written as a ratio of integers AND decimals that terminate or repeat
Types of Rational Numbers
1) Integers (no decimals, positive and negatives); -27, 3, 0, 45
2) Whole Numbers (no decimals, only zero and positives); 0, 1, 2,…, 100

4. Irrational
Irrational = cannot be written as ratio of integers AND decimals that terminate/repeat
Most common irrational number?
Others; √2, √14

5. Real Numbers on Number Line
Recall from Algebra 1, we can represent the real numbers and their values using a number line
On a number line, we use “0” as a place marker; negatives to the left, positives to the right

6. Example. Plot the following numbers on a number line.
-2/5, 5, 10, 0, -2

7. Comparing Real Numbers
With real numbers, we can compare their values using inequality symbols
Read an inequality like you read a book; left to right
< = less than
> = greater than
≥ = greater than OR equal to
≤ = less than OR equal to

8. Example. Compare the following pairs of numbers using one of the four inequality symbols
D) 0, 50

9. Example. Graph the following numbers on a number line, then put them in order from least to greatest.
-6, 3, -3, 4, -14, 0, 9

10. Addition and Multiplication Properties
With the real numbers, we have several properties for addition and multiplication
You use these all the time, but probably forgot their “technical” names

11. Addition Commutative Associative Identity Inverse a + (-a) = 0
a + b = b + a
Associative
(a + b) + c = a + (b + c)
Identity
a + 0 = a, 0 + a = a
Inverse
a + (-a) = 0
Key Words; addition, sum

12. Multiplication Commutative Associative Identity a(1) = a Inverse
ab = ba
Associative
(ab)c = a(bc)
Identity
a(1) = a
Inverse
a(1/a) = 1 (a cannot = 0)
Key words; product

13. Subtraction/Division
Subtraction is just like adding; just add the opposite
a – b = a + (-b)
Key words; difference
Division is multiplication by the reciprocal
a/b = a(1/b)
Key words; quotient

14. Example. Identify the following properties
B) 3 x 1 = 3
C) = 4
D) (6 x 3) x 9 = 6 x (3 x 9)
E) 4(9 + 2) = 4x9 + 4x2

15. Example. Perform the operation to answer the question.
What is the sum of 4 and 21?
What is the product of 10 and -6?
What is the quotient of 7 and 1?

16. Assignment
Pg. 6
#4-7, 15-19, odd, 39-41, odd, 51-53