Order of Operations & Real Numbers Wednesday, August 11th

Order of Operation

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

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 50-4 Multiplication 46 Subtraction

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

Real Numbers

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.

Rational Numbers Rational Numbers include: 1.9 -3

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,…

Irrational Numbers Examples of Irrational numbers include: 0.010010001 pi

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: 3 + 4 + 5 = 4 + 5 + 3 Multiplication: 3 * 4 * 5 = 4 * 5 * 3

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

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

Output/ HW What questions did you come up with during the lesson? Show step by step (Order of Operations): ( 8 / 2) + 4 * 32 6 + 7 - 9 / 3 * 3 23 – 4 / 4 * 7 CONTINUED….

Output/ HW Cont. Classify the following types of numbers: 9283 4.66666666666666…. 564.6417621….