order of operations (algebra1 1_2)

1) order of operations

Order of Operations Order of Operations

Evaluate numerical expressions by using the order of operations. Evaluate algebraic expressions by using the order of operations.

Internet service costs $4.95 per month which includes 100 hours.Additional time costs $0.99 per hour.



Nicole used her internet connection for 117 hours this past month.Write an expression describing her cost for the month?




Cost = $4.95 + $0.99(117 – 100)




Cost = $4.95 + $0.99(117 – 100)

Numerical expressions often contain more than one operation.




Cost = $4.95 + $0.99(117 – 100)

Numerical expressions often contain more than one operation.

A rule is needed to let you know which operation to perform first.


Cost = $4.95 + $0.99(117 – 100)


Cost = $4.95 + $0.99(117 – 100)

This rule is called the _________________order of operations


Step 1: Evaluate expressions inside grouping symbols.

Cost = $4.95 + $0.99(117 – 100)




Cost = $4.95 + $0.99(117 – 100)


Cost = $4.95 + $0.99(17)



Cost = $4.95 + $0.99(117 – 100)


Cost = $4.95 + $0.99(17)


Step 2: Evaluate all powers.


Cost = $4.95 + $0.99(117 – 100)


Cost = $4.95 + $0.99(17)


Cost = $4.95 + $0.99(17) there are no powers to evaluate



Cost = $4.95 + $0.99(117 – 100)


Cost = $4.95 + $0.99(17)



Step 3: Do all multiplication and / or division from left to right.



Cost = $4.95 + $0.99(117 – 100)


Cost = $4.95 + $0.99(17)




Cost = $4.95 + $16.83



Cost = $4.95 + $0.99(117 – 100)


Cost = $4.95 + $0.99(17)




Cost = $4.95 + $16.83

Step 4: Do all addition and / or subtraction from left to right.



Cost = $4.95 + $0.99(117 – 100)


Cost = $4.95 + $0.99(17)




Cost = $4.95 + $16.83

Step 4: Do all addition and / or subtraction from left to right.

Cost = $21.78


Some students remember the order by using the following mnemonic:

PEMDAS

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(parentheses / grouping symbols)

(exponents)

(multiplication)

(division)

(addition)

(subtraction)



PEMDAS

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(exponents)

(multiplication)

(division)

(addition)

(subtraction)

Evaluate each expression:



PEMDAS

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(exponents)

(multiplication)

(division)

(addition)

(subtraction)


3 + 2 • 3 + 5



PEMDAS

lease

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(exponents)

(multiplication)

(division)

(addition)

(subtraction)


3 + 2 • 3 + 5

3 + 2 • 3 + 5 = 3 + 2 • 3 + 5



PEMDAS

lease

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(exponents)

(multiplication)

(division)

(addition)

(subtraction)


3 + 2 • 3 + 5

3 + 2 • 3 + 5 = 3 + 2 • 3 + 5

= 3 + 6 + 5



PEMDAS

lease

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(exponents)

(multiplication)

(division)

(addition)

(subtraction)


3 + 2 • 3 + 5

3 + 2 • 3 + 5 = 3 + 2 • 3 + 5

= 3 + 6 + 5

= 9 + 5



PEMDAS

lease

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y

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(exponents)

(multiplication)

(division)

(addition)

(subtraction)


3 + 2 • 3 + 5

3 + 2 • 3 + 5 = 3 + 2 • 3 + 5

= 3 + 6 + 5

= 9 + 5

= 14



PEMDAS

lease

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y

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(exponents)

(multiplication)

(division)

(addition)

(subtraction)


3 + 2 • 3 + 5

3 + 2 • 3 + 5 = 3 + 2 • 3 + 5

= 3 + 6 + 5

= 9 + 5

= 14

15 ÷ 3 • 5 – 42



PEMDAS

lease

xcuse

y

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unt

ally


(exponents)

(multiplication)

(division)

(addition)

(subtraction)


3 + 2 • 3 + 5

3 + 2 • 3 + 5 = 3 + 2 • 3 + 5

= 3 + 6 + 5

= 9 + 5

= 14

15 ÷ 3 • 5 – 42

15 ÷ 3 • 5 – 42 = 15 ÷ 3 • 5 – 16



PEMDAS

lease

xcuse

y

ear

unt

ally


(exponents)

(multiplication)

(division)

(addition)

(subtraction)


3 + 2 • 3 + 5

3 + 2 • 3 + 5 = 3 + 2 • 3 + 5

= 3 + 6 + 5

= 9 + 5

= 14

15 ÷ 3 • 5 – 42

15 ÷ 3 • 5 – 42 = 15 ÷ 3 • 5 – 16

= 5 • 5 – 16



PEMDAS

lease

xcuse

y

ear

unt

ally


(exponents)

(multiplication)

(division)

(addition)

(subtraction)


3 + 2 • 3 + 5

3 + 2 • 3 + 5 = 3 + 2 • 3 + 5

= 3 + 6 + 5

= 9 + 5

= 14

15 ÷ 3 • 5 – 42

15 ÷ 3 • 5 – 42 = 15 ÷ 3 • 5 – 16

= 5 • 5 – 16

= 25 – 16



PEMDAS

lease

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(exponents)

(multiplication)

(division)

(addition)

(subtraction)


3 + 2 • 3 + 5

3 + 2 • 3 + 5 = 3 + 2 • 3 + 5

= 3 + 6 + 5

= 9 + 5

= 14

15 ÷ 3 • 5 – 42

15 ÷ 3 • 5 – 42 = 15 ÷ 3 • 5 – 16

= 5 • 5 – 16

= 25 – 16

= 9


PEMDAS

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PEMDAS

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2(5) + 3(4 + 3)


PEMDAS

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2(5) + 3(4 + 3)

2(5) + 3(4 + 3) = 2(5) + 3(7)


PEMDAS

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2(5) + 3(4 + 3)

2(5) + 3(4 + 3) = 2(5) + 3(7)

= 10 + 21


PEMDAS

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2(5) + 3(4 + 3)

2(5) + 3(4 + 3) = 2(5) + 3(7)

= 10 + 21

= 31

When more than one grouping symbol is used, start evaluating within theinnermost grouping symbol.


PEMDAS

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2(5) + 3(4 + 3)

2(5) + 3(4 + 3) = 2(5) + 3(7)

= 10 + 21

= 31


2[5 + (30 ÷ 6)2]


PEMDAS

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2(5) + 3(4 + 3)

2(5) + 3(4 + 3) = 2(5) + 3(7)

= 10 + 21

= 31


2[5 + (30 ÷ 6)2]

2[5 + (30 ÷ 6)2] = 2[5 + (5)2]


PEMDAS

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2(5) + 3(4 + 3)

2(5) + 3(4 + 3) = 2(5) + 3(7)

= 10 + 21

= 31


2[5 + (30 ÷ 6)2]

2[5 + (30 ÷ 6)2] = 2[5 + (5)2]

= 2[5 + 25]


PEMDAS

lease

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2(5) + 3(4 + 3)

2(5) + 3(4 + 3) = 2(5) + 3(7)

= 10 + 21

= 31


2[5 + (30 ÷ 6)2]

2[5 + (30 ÷ 6)2] = 2[5 + (5)2]

= 2[5 + 25]

= 2[30]


PEMDAS

lease

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y

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2(5) + 3(4 + 3)

2(5) + 3(4 + 3) = 2(5) + 3(7)

= 10 + 21

= 31


2[5 + (30 ÷ 6)2]

2[5 + (30 ÷ 6)2] = 2[5 + (5)2]

= 2[5 + 25]

= 2[30]

= 60


PEMDAS

Evaluate the expression:

A fraction bar is another type of grouping symbol.

It indicates that the numerator and denominator should each be treatedas a single value.


PEMDAS




43

462

2


PEMDAS




43

462

2

49

166

43

462

2


PEMDAS




43

462

2

49

166

43

462

2

or 36

22


PEMDAS




43

462

2

49

166

43

462

2

or 36

22

18

11


Like numerical expressions, algebraic expressions often contain more than one operation.



Algebraic expressions can be evaluated when _______________________________.

Evaluate: a2 – (b2 – 4c)



Algebraic expressions can be evaluated when _______________________________.the value of the variables are known





Evaluate: a2 – (b2 – 4c) if a = 7, b = 3, and c = 5




First, replace the variables with their values.



if a = 7, b = 3, and c = 5





a2 – (b2 – 4c) = 72 – (33 – 4•5)






a2 – (b2 – 4c) = 72 – (33 – 4•5) Then, find the value of the numerical expression using the order of operations.







= 49 – (27 – 20)







= 49 – (27 – 20)

= 49 – ( 7)







= 49 – (27 – 20)

= 49 – ( 7)

= 42


Write an expression involving division in which the first step in evaluating theexpression is addition.



Sample answer: 2 + 4 ÷ 3




How can you “force” the addition to be done before the division?




How can you “force” the addition to be done before the division?

( )


Finding error(s) in your calculations is a skill that you must develop.

3[4 + (27 ÷ 3)]2 = 3(4 + 92)

= 3(4 + 81)

= 3(85)

= 255

3[4 + (27 ÷ 3)]2 = 3(4 + 9)2

= 3(13)2

= 3(169)

= 507

Determine which calculation is incorrect and identify the error.


Finding error(s) in your calculations is a skill that you must develop.

3[4 + (27 ÷ 3)]2 = 3(4 + 92)

= 3(4 + 81)

= 3(85)

= 255

3[4 + (27 ÷ 3)]2 = 3(4 + 9)2

= 3(13)2

= 3(169)

= 507

Determine which calculation is incorrect and identify the error.

Incorrect quantity raised to the second power.

The exponent is outsidethe grouping symbol.


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