1. Order of Operations & Real Numbers
Wednesday, August 11th

2. Order of Operation

3. Order of Operation PEMDAS Parenthesis Exponents
Multiplication & Division
Addition & Subtraction

4. Example 2 * (3+2) 2 – 4 2 * (5) 2 – 4 Parenthesis First
2 * (3+2) 2 – 4
2 * (5) 2 – 4 Parenthesis First
2 * 25– 4 Exponents
Multiplication
46 Subtraction

5. Try One….
[ 3 * 4 + (2+ 4)2 ] / 8
* ( ) are parenthesis that are done before [ ]
* Answer = 6

6. Real Numbers

7. Real Numbers There are two types of Real numbers: Rational Numbers:
can be expressed as a ratio m/n, where m and n are integers and n is not zero. The decimal form of a rational number is either terminating or repeating decimal.
Irrational Numbers:
The decimal form of an irrational number neither terminates nor repeats.

8. Rational Numbers
Rational Numbers include:
1.9 -3

9. Rational Numbers Subsets/ categories of Rational numbers include:
Integers: Positive, Negative & Zero
…, -3, -2, -1, 0, 1, 2, 3,…
Whole numbers: Include Zero
0, 1, 2, 3, 4…
Natural numbers: Counting Numbers
1, 2, 3, 4, 5,…

10. Irrational Numbers Examples of Irrational numbers include: 0.010010001pi

11. Real Number Properties
Associative:
The addition or multiplication of a set of numbers is the same regardless of how the numbers are grouped.
Addition: (3 + 4) + 5 = 3 + (4 + 5)
Multiplication: (3 * 4) * 5 = 3 * (4 * 5)
Commutative:
The word “commute” means “exchange” or “swap over”. Commutative property states that numbers can be added or multiplied in any order.
Addition: =
Multiplication: 3 * 4 * 5 = 4 * 5 * 3

12. Properties Continued Identity Inverse
Additive Identity: the sum of zero and any number or variable is the number or variable itself.
4 + 0 = 4
Multiplicative Identity: the product of 1 and any number or variable is the number or variable itself.
9 * 1 = 9
Inverse
Addition: A positive number & that number negative will equal zero.
4 + (-4) = 0
Multiplication: A number times its reciprocal will equal one.
4 * (1/4) = 1

13. Last Property Distributive Property:
computation depends on multiplying through a parentheses
3 * ( 4 + 5) = (3 * 4) + (3 * 5)
8 * ( a + b) = 8a + 8b

14. Output/ HW What questions did you come up with during the lesson?
Show step by step (Order of Operations):
( 8 / 2) + 4 * 32
/ 3 * 3
23 – 4 / 4 * 7
CONTINUED….

15. Output/ HW Cont. Classify the following types of numbers: 9283…. ….