Just the facts: Order of Operations and

Properties of real numbers

A GEMS/ALEX SubmissionSubmitted by: Elizabeth Thompson, PhD

Summer, 2008

Important things toImportant things to rememberremember• 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…..So really it looks like this…..

• PParenthesis

• EExponents

• MMultiplication and DDivision

• AAddition and SSubtraction

In order from left to right

In order from left to right

SAMPLE PROBLEM #1SAMPLE PROBLEM #1

1122)13(416 3

1122)8(416

1122)2(416 3

1122)8(4 112232

23230

Parenthesis

Exponents

This one is tricky!

Remember: Multiplication/Division are grouped from left to right…what comes 1st?

Division did…now do the multiplication (indicated by parenthesis)

More division

Subtraction

SAMPLE PROBLEM

2

65)32(3 2

2

65)5(3 2

2

65)25(3 2

6575 2

10 5Subtraction

Exponents

Remember the division symbol here is grouping everything on top, so work everything up there first….multiplication

Parenthesis

Division – because all the work is done above and below the line

Order of Operations-BASICSOrder of Operations-BASICSThink: PEMDAS Think: PEMDAS

Please Excuse My Dear Aunt Sally

• PParenthesis

• EExponents

• MMultiplication

• DDivision

• AAddition

• SSubtraction

Take time to practice

Assignment #1Assignment #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 ExtensionLesson 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 #2Assignment #2Create a Puzzle GreetingCreate 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: Part 2: Properties of Real NumbersProperties of Real Numbers

(A listing)(A listing)

• Associative PropertiesAssociative Properties

• Commutative PropertiesCommutative Properties

• Inverse PropertiesInverse Properties

• Identity PropertiesIdentity Properties

• Distributive PropertyDistributive PropertyAll of these rules apply to Addition and Multiplication

Associative PropertiesAssociative PropertiesAssociate = 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 It doesn’t matter how you group (associate) addition or multiplication…the answer will be the same!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 PropertiesCommutative PropertiesCommute = 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 It doesn’t matter how you swap addition or multiplication around…the answer will be the same!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!

• 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 = 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)? 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 PropertiesInverse PropertiesThink: OppositeThink: 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 (inverse) of addition?

What is the opposite of multiplication?What is the opposite of multiplication?

Subtraction (add the negative)Subtraction (add the negative)

Division (multiply by reciprocal)Division (multiply by reciprocal)

Identity PropertiesIdentity 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 add to a number & get the same number back?

What can you multiply a number by and get the number back?What can you multiply a number by and get the number back?

0 (zero)0 (zero)

1 (one)1 (one)

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

remove the parenthesis.remove the parenthesis.

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.