Just the facts: Order of Operations and Properties of real ...

Just the facts: Order of Operations and Properties of real numbers A GEMS/ALEX Submission Submitted by: Elizabeth Thompson, PhD Summer, 2008 Important things to remember Parenthesis anything grouped including information above or below a fraction bar. Exponents anything in the same family as a power this includes radicals (square roots). Multiplication- this includes distributive property (discussed in detail later). Some items are grouped!!! Multiplication and Division are GROUPED from left to

right (like reading a book- do whichever comes first. Addition and Subtraction are also grouped from left to right, do whichever comes first in the problem. So really it looks like this.. Parenthesis Exponents Multiplication and Division In order from left to right Addition and Subtraction In order from left to right SAMPLE PROBLEM #1

3 16 4(3 1) 22 11 3 16 4(2) 22 11 Parenthesis Exponents 16 4(8) 22 11 4(8) 22 11 32 22 11 This one is tricky! Remember: Multiplication/Division are grouped from left to rightwhat comes 1st?

Division didnow do the multiplication (indicated by parenthesis) More division 32 2 Subtraction 30 SAMPLE PROBLEM 2 2 3(5) 65 3(2 3) 65

2 2 Exponents Parenthesis 75 65 10 3(25) 65 2 2 2

Remember the division symbol here is grouping everything on top, so work everything up there first.multiplication Subtraction Division because all the work is done above and below the line 5

Order of Operations-BASICS Think: PEMDAS Please Excuse My Dear Aunt Sally Parenthesis Exponents Multiplication Division Addition Subtraction

Take time to practice Assignment #1 (When all assigned problems are finished do for Homework as needed) Remember PEMDAS and Please Excuse My Dear Aunt Sally? Make up your own acronym for PEMDAS and post it on the class wiki. Write it on White Paper and Illustrate your acronym. Make sure it is school appropriate. Lesson Extension

Can you fill in the missing operations? 1. 2 - (3+5) + 4 = -2 2. 4 + 7 * 3 3 = 11 3. 5 * 3 + 5 2 = 10 Assignment #2 Create a Puzzle Greeting Fold a piece of paper (white or colored) like a greeting card. On the cover: Write an equation with missing operations (like the practice slide) In the middle: Write the equation with the correct operations On the back: Put your name as you would

find a companies name on the back of a greeting card. Part 2: Properties of Real Numbers (A listing) Associative Properties Commutative Properties Inverse Properties

Identity Properties Distributive Property All of these rules apply to Addition and Multiplication Associative Properties Associate = group It doesnt matter how you group (associate) addition or multiplicationthe answer will be the same! Rules: Samples: Associative Property of Addition

Associative Property of Addition (a+b)+c = a+(b+c) (1+2)+3 = 1+(2+3) Associative Property of Multiplication Associative Property of Multiplication (ab)c = a(bc) (2x3)4 = 2(3x4) Commutative Properties Commute = travel (move)

It doesnt matter how you swap addition or multiplication aroundthe answer will be the same! Rules: Samples: Commutative Property of Addition Commutative Property of Addition a+b = b+a 1+2 = 2+1 Commutative Property of Multiplication

Commutative Property of Multiplication ab = ba (2x3) = (3x2) Stop and think! Does the Associative Property hold true for Subtraction and Division? Is (5-2)-3 = 5-(2-3)? Is (6/3)-2 the same as 6/(3-2)? Does the Commutative Property hold true for Subtraction and Division?

Is 5-2 = 2-5? Is 6/3 the same as 3/6? Properties of real numbers are only for Addition and Multiplication Inverse Properties Think: Opposite What is the opposite (inverse) of addition? What is the opposite of multiplication? Rules: Inverse Property of Addition a+(-a) = 0

Subtraction (add the negative) Division (multiply by reciprocal) Samples: Inverse Property of Addition 3+(-3)=0 Inverse Property of Multiplication Inverse Property of Multiplication a(1/a) = 1 2(1/2)=1

Identity Properties What can you add to a number & get the same number back? 0 (zero) What can you multiply a number by and get the number back? 1 (one) Rules: Identity Property of Addition a+0 = a Samples: Identity Property of Addition 3+0=3 Identity Property of Multiplication

Identity Property of Multiplication a(1) = a 2(1)=2 Distributive Property If something is sitting just outside a set of parenthesis, you can distribute it through the parenthesis with multiplication and remove the parenthesis. Rule: a(b+c) = ab+bc Samples: 4(3+2)=4(3)+4(2)=12+8=20

2(x+3) = 2x + 6 -(3+x) = -3 - x Take time to practice Homework Log on to class wiki / discussion thread Follow the directions given: Give an example of each of the properties discussed in class, do not duplicate a previous entry.