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Students learn of the Order of Operations.
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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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