Just the facts: Order of Operations and

Properties of real numbers

A GEMS/ALEX SubmissionSubmitted 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 • Addition and Subtraction

In order from left to right

In order from left to right

SAMPLE 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-BASICSThink: 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 #2Create 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 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 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 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 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)-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 PropertiesThink: 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

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

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