Important things to remember Brackets – anything grouped… including information above or below a fraction bar. Indices (Exponents) – anything in the same family as a ‘power’… this includes radicals (square roots). 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….. :

So really it looks like this….. B rackets I ndices D ivision and M ultiplication A ddition and S ubtraction In order from left to right In order from left to right

SAMPLE PROBLEM #1:

SAMPLE PROBLEM #1 Brackets Indices This one is tricky! Remember: Multiplication/Division are grouped from left to right…what comes 1 st ? Division did…now do the multiplication (indicated by parenthesis) More division Subtraction

SAMPLE PROBLEM:

SAMPLE PROBLEM Subtraction Indices Remember the division symbol here is grouping everything on top, so work everything up there first….multiplication Brackets Division – because all the work is done above and below the line

Order of Operations-BASICS Think: BIDMAS :

Order of Operations-BASICS Think: BIDMAS B rakets I ndices D ivision M ultiplication A ddition S ubtraction

Take time to practice:

Take time to practice

Lesson Extension:

Lesson Extension Can you fill in the missing operations? 2 - (3+5) + 4 = -2 4 + 7 * 3 ÷ 3 = 11 5 * 3 + 5 ÷ 2 = 10

Assignment #2 Create a Puzzle Greeting:

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):

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 :

Associative Properties Associate = group Rules: Associative Property of Addition (a+b)+c = a+(b+c) Associative Property of Multiplication (ab)c = a(bc) It doesn’t matter how you group (associate) addition or multiplication…the answer will be the same! Samples: Associative Property of Addition (1+2)+3 = 1+(2+3) Associative Property of Multiplication (2x3)4 = 2(3x4)

Commutative Properties Commute = travel (move) :

Commutative Properties Commute = travel (move) Rules: Commutative Property of Addition a+b = b+a Commutative Property of Multiplication ab = ba It doesn’t matter how you swap addition or multiplication around…the answer will be the same! Samples: Commutative Property of Addition 1+2 = 2+1 Commutative Property of Multiplication (2x3) = (3x2)

Stop and think!:

Stop and think! Does the Associative Property hold true for Subtraction and Division? Does the Commutative Property hold true for Subtraction and Division? Is 5-2 = 2-5? Is 6/3 the same as 3/6? Is (5-2)-3 = 5-(2-3)? Is (6/3)-2 the same as 6/(3-2)? Properties of real numbers are only for Addition and Multiplication

Inverse Properties Think: Opposite :

Inverse Properties Think: Opposite Rules: Inverse Property of Addition a+(-a) = 0 Inverse Property of Multiplication a(1/a) = 1 Samples: Inverse Property of Addition 3+(-3)=0 Inverse Property of Multiplication 2(1/2)=1 What is the opposite (inverse) of addition? What is the opposite of multiplication? Subtraction (add the negative) Division (multiply by reciprocal)

Identity Properties :

Identity Properties Rules: Identity Property of Addition a+0 = a Identity Property of Multiplication a(1) = a Samples: Identity Property of Addition 3+0=3 Identity Property of Multiplication 2(1)=2 What can you add to a number & get the same number back? What can you multiply a number by and get the number back? 0 (zero) 1 (one)

Distributive Property:

Distributive Property 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 If something is sitting just outside a set of parenthesis, you can distribute it through the parenthesis with multiplication and remove the parenthesis.

Take time to practice:

Take time to practice

Homework:

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.

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