lecture pemdas&expression

8/3/2019 Lecture PEMDAS&Expression

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UPWARD BOUND

MATH COURSE - ALGEBRA 26/27/11

Instructor: Rachel Hammond, M.S.


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Lecture Outline

oCourse Syllabus

oWhat Do You Know?

o

Algebra 2 Basicso Real Numbers

o Order of Operations

o Evaluating and Simplifying Expressions


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Syllabus Topic Outline

oOrder of Operations Evaluating Expressions

oSolving Linear Equations (1 & 2 systems)

o

Graphing Linear EquationsoExponents

oQuadratic Equations

o Logarithmic FunctionsoMatrices

o Intro to Other Topics


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What Do You Know?

oBy Raising Your HandWho

o Has taken Algebra 2?

o

Has taken Algebra 1?oKnows what a Matrix is?

oKnows what m stands for in the equation

of a line (y = mx + b)?o Can solve the following problem for x:

3x= 9


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Todays Topic Outline

oReal Numbers

oOrder of Operations

o

Evaluating and Simplifying Expressions


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Real Numbers

oWhat is a Real Number?

o All numbers on a number line (positive,negative, fractions, square roots,

o

Graph and write the following numbers inincreasing order: 100, ,8, 16

5


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Real Numbers

o Graph and write the following numbers in increasingorder:

o Increasing Order:

o Graph:

100, ,8, 16

5

1016,0, ,8

5


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Real Numbers

o Terms:

o Additive Inverse

o

Reciprocal

oProperties:

o Additive & Multiplicative Inverse/Identityo Distributive

o Associative (Addition and Multiplication)

o Commutative


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Real Numbers - Terms

oAdditive Inverse

The opposite, or additive inverse, ofany number a is -a

oReciprocal

The reciprocal, or multiplicativeinverse, of any nonzero number is 1a


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Real Numbers - Properties

oAdditive Inverse Property

oMultiplicative Inverse Property

7 7 0

When added, they equal 0

18 18

When multipled, they equal 1


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oCommutative Property

o

Distributive Property

5 3 3 5

5 3 3 5Changing order does not matter

5 10 2 5 10 5 2 50 10 60

5 10 2 5 10 5 2 50 10 40


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oAssociative Property of Addition

o

Associative Property of Multiplication

5 7 3 5 7 3

Doesn't matter where are

6 4 5 6 4 5

Doesn't matter where are


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Properties of Real Numbers

o I will NOT ask you:

oWhat does the Distributive Property State?

o I will ask you:

oEvaluate the following:

3(2 + 5) 3 2 + 3 5*According to the Distributive Property


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Expressions - Vocab

oAn algebraic expression is a mathematicalstatement involving numbers and/or variables:

3x, 2y, 3x + 2y

oA variable is a letter that is used to representone or more numbers: x, y, z, i

oA coefficient is the number multiplied by avariable in a term: In 3x, 3 is the coefficient. In

x, 1 is the coefficient.


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Expressions - Vocab

oExponents

o An exponent is the number or variable thatrepresents the number of times the base isused as a factor.

o The base of an exponent is the number orvariable that is used as a factor in repeated

multiplication.

24 16

4 = Base2 = Exponent

Result = 16 (aka Power)


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Expressions - Vocab

oWhen evaluating expressions, you combinethe LIKE TERMS.

o Terms are the parts that are added in anexpression. They are separated by operators:3x + 4x - 2y

oLike terms are expressions that have thesame variable part: 3x and 4x are like terms.


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Evaluating Expressions

oAny number used to replace a variable is avalue of the variable:

Let x = 2

oWhen the variables in an algebraicexpression are replaced by numbers, theresult is called the value of the expression:

What is the value of 3x?


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Basically.

oSimplify and Evaluate Expressions by:

o Combining Like Terms

o

Replacing a Variable With a Numbero Stick to the Properties of Real Numbers

(Distributive, Associative, Commutative, andInverses)

oDont Forget PEMDAS!!!!


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PEMDAS!!?

oPEMDAS = The order of performingoperations, when evaluating expressions:

Please Excuse My Dear Aunt Sally

( )Exponents

Multiply/Divide L to R

Add/Subtract L to R


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PEMDAS

oEvaluate the Expression: 22 3 18 3 7

2 2 4

22 3 18 3 7 first!

22 3 18 3 7 2 3 18 9 7

2 3 18 9 7 2 3 2 7

2 3 2 7 2 5 7 2 2


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Your Turn

oEvaluate the Expressions:

2

3

2

2

2

1. 1 3 4

2. 14 12 3

3. 2

4. 5 2 4

5. 36 3 1

6. 2


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Simplifying By Combining Like Terms

Simplify 6 4x y x y

6 6 4 4 Distributive Propertyx y x y

6 4 6 4 Group Like Termsx x y y

2 2 Combine Like Termsx y


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Your Turn

oSimplify Each Expression:

2 2

2 2

1. 7 9 5

2. 2 5 4

3. 6 4 15

4. 7 2 3 9 4 5

x x

n n n n

x x x x

x y y x


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Evaluating and SimplifyingExpressions

oWhats the difference?

Evaluate:

Simplify:

2

2 3 18 3 7 4

6 4 2 2x y x y x y


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Summary

o Today

o Course Syllabus email me withquestions/concerns.

o Real Numbers

o Order of Operations

o

Evaluating and Simplifying ExpressionsoNext Step

o Practice, Practice, Practice!


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Next Time

oReview (teeny tiny)

oSolving Equations (1,2 steps)

o

Word Problems

lecture pemdas&expression

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