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.

Order of Operations 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?

Order of Operations 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)

Order of Operations 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)

Numerical expressions often contain more than one operation.

Order of Operations 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)

Numerical expressions often contain more than one operation.

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

Order of Operations Order of Operations

Cost = $4.95 + $0.99(117 – 100)

Order of Operations Order of Operations

Cost = $4.95 + $0.99(117 – 100)

This rule is called the _________________order of operations

Order of Operations Order of Operations

Step 1: Evaluate expressions inside grouping symbols.

Cost = $4.95 + $0.99(117 – 100)

This rule is called the _________________order of operations

Order of Operations Order of Operations

Step 1: Evaluate expressions inside grouping symbols.

Cost = $4.95 + $0.99(117 – 100)

This rule is called the _________________order of operations

Cost = $4.95 + $0.99(17)

Order of Operations Order of Operations

Step 1: Evaluate expressions inside grouping symbols.

Cost = $4.95 + $0.99(117 – 100)

This rule is called the _________________order of operations

Cost = $4.95 + $0.99(17)

Order of Operations Order of Operations

Step 2: Evaluate all powers.

Step 1: Evaluate expressions inside grouping symbols.

Cost = $4.95 + $0.99(117 – 100)

This rule is called the _________________order of operations

Cost = $4.95 + $0.99(17)

Step 2: Evaluate all powers.

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

Order of Operations Order of Operations

Step 1: Evaluate expressions inside grouping symbols.

Cost = $4.95 + $0.99(117 – 100)

This rule is called the _________________order of operations

Cost = $4.95 + $0.99(17)

Step 2: Evaluate all powers.

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

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

Order of Operations Order of Operations

Step 1: Evaluate expressions inside grouping symbols.

Cost = $4.95 + $0.99(117 – 100)

This rule is called the _________________order of operations

Cost = $4.95 + $0.99(17)

Step 2: Evaluate all powers.

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

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

Cost = $4.95 + $16.83

Order of Operations Order of Operations

Step 1: Evaluate expressions inside grouping symbols.

Cost = $4.95 + $0.99(117 – 100)

This rule is called the _________________order of operations

Cost = $4.95 + $0.99(17)

Step 2: Evaluate all powers.

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

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

Cost = $4.95 + $16.83

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

Order of Operations Order of Operations

Step 1: Evaluate expressions inside grouping symbols.

Cost = $4.95 + $0.99(117 – 100)

This rule is called the _________________order of operations

Cost = $4.95 + $0.99(17)

Step 2: Evaluate all powers.

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

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

Cost = $4.95 + $16.83

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

Cost = $21.78

Order of Operations Order of Operations

Some students remember the order by using the following mnemonic:

PEMDAS

lease

xcuse

y

ear

unt

ally

(parentheses / grouping symbols)

(exponents)

(multiplication)

(division)

(addition)

(subtraction)

Order of Operations Order of Operations

Some students remember the order by using the following mnemonic:

PEMDAS

lease

xcuse

y

ear

unt

ally

(parentheses / grouping symbols)

(exponents)

(multiplication)

(division)

(addition)

(subtraction)

Evaluate each expression:

Order of Operations Order of Operations

Some students remember the order by using the following mnemonic:

PEMDAS

lease

xcuse

y

ear

unt

ally

(parentheses / grouping symbols)

(exponents)

(multiplication)

(division)

(addition)

(subtraction)

Evaluate each expression:

3 + 2 • 3 + 5

Order of Operations Order of Operations

Some students remember the order by using the following mnemonic:

PEMDAS

lease

xcuse

y

ear

unt

ally

(parentheses / grouping symbols)

(exponents)

(multiplication)

(division)

(addition)

(subtraction)

Evaluate each expression:

3 + 2 • 3 + 5

3 + 2 • 3 + 5 = 3 + 2 • 3 + 5

Order of Operations Order of Operations

Some students remember the order by using the following mnemonic:

PEMDAS

lease

xcuse

y

ear

unt

ally

(parentheses / grouping symbols)

(exponents)

(multiplication)

(division)

(addition)

(subtraction)

Evaluate each expression:

3 + 2 • 3 + 5

3 + 2 • 3 + 5 = 3 + 2 • 3 + 5

= 3 + 6 + 5

Order of Operations Order of Operations

Some students remember the order by using the following mnemonic:

PEMDAS

lease

xcuse

y

ear

unt

ally

(parentheses / grouping symbols)

(exponents)

(multiplication)

(division)

(addition)

(subtraction)

Evaluate each expression:

3 + 2 • 3 + 5

3 + 2 • 3 + 5 = 3 + 2 • 3 + 5

= 3 + 6 + 5

= 9 + 5

Order of Operations Order of Operations

Some students remember the order by using the following mnemonic:

PEMDAS

lease

xcuse

y

ear

unt

ally

(parentheses / grouping symbols)

(exponents)

(multiplication)

(division)

(addition)

(subtraction)

Evaluate each expression:

3 + 2 • 3 + 5

3 + 2 • 3 + 5 = 3 + 2 • 3 + 5

= 3 + 6 + 5

= 9 + 5

= 14

Order of Operations Order of Operations

Some students remember the order by using the following mnemonic:

PEMDAS

lease

xcuse

y

ear

unt

ally

(parentheses / grouping symbols)

(exponents)

(multiplication)

(division)

(addition)

(subtraction)

Evaluate each expression:

3 + 2 • 3 + 5

3 + 2 • 3 + 5 = 3 + 2 • 3 + 5

= 3 + 6 + 5

= 9 + 5

= 14

15 ÷ 3 • 5 – 42

Order of Operations Order of Operations

Some students remember the order by using the following mnemonic:

PEMDAS

lease

xcuse

y

ear

unt

ally

(parentheses / grouping symbols)

(exponents)

(multiplication)

(division)

(addition)

(subtraction)

Evaluate each expression:

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

Order of Operations Order of Operations

Some students remember the order by using the following mnemonic:

PEMDAS

lease

xcuse

y

ear

unt

ally

(parentheses / grouping symbols)

(exponents)

(multiplication)

(division)

(addition)

(subtraction)

Evaluate each expression:

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

Order of Operations Order of Operations

Some students remember the order by using the following mnemonic:

PEMDAS

lease

xcuse

y

ear

unt

ally

(parentheses / grouping symbols)

(exponents)

(multiplication)

(division)

(addition)

(subtraction)

Evaluate each expression:

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

Order of Operations Order of Operations

Some students remember the order by using the following mnemonic:

PEMDAS

lease

xcuse

y

ear

unt

ally

(parentheses / grouping symbols)

(exponents)

(multiplication)

(division)

(addition)

(subtraction)

Evaluate each expression:

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

Order of Operations Order of Operations

PEMDAS

lease

xcuse

y

ear

unt

ally

Evaluate each expression:

Order of Operations Order of Operations

PEMDAS

lease

xcuse

y

ear

unt

ally

Evaluate each expression:

2(5) + 3(4 + 3)

Order of Operations Order of Operations

PEMDAS

lease

xcuse

y

ear

unt

ally

Evaluate each expression:

2(5) + 3(4 + 3)

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

Order of Operations Order of Operations

PEMDAS

lease

xcuse

y

ear

unt

ally

Evaluate each expression:

2(5) + 3(4 + 3)

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

= 10 + 21

Order of Operations Order of Operations

PEMDAS

lease

xcuse

y

ear

unt

ally

Evaluate each expression:

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.

Order of Operations Order of Operations

PEMDAS

lease

xcuse

y

ear

unt

ally

Evaluate each expression:

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.

2[5 + (30 ÷ 6)2]

Order of Operations Order of Operations

PEMDAS

lease

xcuse

y

ear

unt

ally

Evaluate each expression:

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.

2[5 + (30 ÷ 6)2]

2[5 + (30 ÷ 6)2] = 2[5 + (5)2]

Order of Operations Order of Operations

PEMDAS

lease

xcuse

y

ear

unt

ally

Evaluate each expression:

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.

2[5 + (30 ÷ 6)2]

2[5 + (30 ÷ 6)2] = 2[5 + (5)2]

= 2[5 + 25]

Order of Operations Order of Operations

PEMDAS

lease

xcuse

y

ear

unt

ally

Evaluate each expression:

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.

2[5 + (30 ÷ 6)2]

2[5 + (30 ÷ 6)2] = 2[5 + (5)2]

= 2[5 + 25]

= 2[30]

Order of Operations Order of Operations

PEMDAS

lease

xcuse

y

ear

unt

ally

Evaluate each expression:

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.

2[5 + (30 ÷ 6)2]

2[5 + (30 ÷ 6)2] = 2[5 + (5)2]

= 2[5 + 25]

= 2[30]

= 60

Order of Operations Order of Operations

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.

Order of Operations Order of Operations

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.

43

462

2

Order of Operations Order of Operations

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.

43

462

2

49

166

43

462

2

Order of Operations Order of Operations

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.

43

462

2

49

166

43

462

2

or 36

22

Order of Operations Order of Operations

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.

43

462

2

49

166

43

462

2

or 36

22

18

11

Order of Operations Order of Operations

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

Order of Operations Order of Operations

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

Algebraic expressions can be evaluated when _______________________________.

Evaluate: a2 – (b2 – 4c)

Order of Operations Order of Operations

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

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

Evaluate: a2 – (b2 – 4c)

Order of Operations Order of Operations

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

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

Order of Operations Order of Operations

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

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

First, replace the variables with their values.

Evaluate: a2 – (b2 – 4c)

Order of Operations Order of Operations

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

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

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

First, replace the variables with their values.

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

a2 – (b2 – 4c) = 72 – (33 – 4•5)

Order of Operations Order of Operations

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

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

First, replace the variables with their values.

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

a2 – (b2 – 4c) = 72 – (33 – 4•5)

Order of Operations Order of Operations

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

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

First, replace the variables with their values.

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

a2 – (b2 – 4c) = 72 – (33 – 4•5)

Order of Operations Order of Operations

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

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

First, replace the variables with their values.

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

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

Order of Operations Order of Operations

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

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

First, replace the variables with their values.

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

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

= 49 – (27 – 20)

Order of Operations Order of Operations

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

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

First, replace the variables with their values.

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

Order of Operations Order of Operations

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

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

First, replace the variables with their values.

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

= 42

Order of Operations Order of Operations

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

Order of Operations Order of Operations

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

Sample answer: 2 + 4 ÷ 3

Order of Operations Order of Operations

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?

Order of Operations Order of Operations

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?

( )

Order of Operations Order of Operations

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.

Order of Operations Order of Operations

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.

Order of Operations Order of Operations

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