2.6 Order of Operations

Simplify. 1. 2. 3.

4. 5. 6.

7.

8.

9.

10.

11.

12.

Evaluate each expression for x = −3, y = 6, and z = −1 13. 14. 15.

16.

17.

18.

Mini-Lecture 2.6 Order of Operations

Learning Objectives:

1. Simplify expressions by using the order of operations.

2. Evaluate an algebraic expression.

Examples:

1. Simplify.

a) b) 2 5 6! " ! 2 5(5 8)! ! ! c) 2( 5)(7 3) 7! ! !

d) 80 e) f) ( 8) 15# ! ! 33 8(2! ) $ %28 2 7 2 3! ! "

g) h) i) 28 2(6) 45! " #5 23( 2) (8 10)! " ! $ %$ %21 7 15 5& '# ! # !( )!

j) 8( 2) 4 3

85 5

! ! "! #

k) * +* +36 ( 4) 1

2 ( 2)

! # ! !

! ! l)

* +20( 1) ( 5)( 3)

2 12 ( 3 3)

! ! ! !! # ! !

2. Evaluate each expression for 3, 6, 1x y and z, ! , , ! .

a) x y z" " b) 2 3y z x! " c) 2x y z! "

d) 8

2

x

y e) 25y x! f) 3x yz"

Teaching Notes:

-. Many students confuse the addition/subtraction rules with the multiplication/division rules when

working with many operations in one expression.

-. Encourage students to perform one operation at a time.

-. Refer students to Order of Operations in the textbook.

Answers: 1a) 28; 1b) 13; 1c) -47; 1d) -25; 1e) 11; 1f) 5; 1g) 61; 1h) -2; 1i) 1; 1j) 1; 1k) 2; 1l) –9’

2a) 2; 2b) 12; 2c) 2; 2d) -2; 2e) 21; 2f) -33

M-15Copyright © 2007 Pearson Education, Inc., publishing as Pearson Prentice Hall

Mini-Lecture 2.6 Order of Operations

Learning Objectives:

1. Simplify expressions by using the order of operations.

2. Evaluate an algebraic expression.

Examples:

1. Simplify.

a) b) 2 5 6! " ! 2 5(5 8)! ! ! c) 2( 5)(7 3) 7! ! !

d) 80 e) f) ( 8) 15# ! ! 33 8(2! ) $ %28 2 7 2 3! ! "

g) h) i) 28 2(6) 45! " #5 23( 2) (8 10)! " ! $ %$ %21 7 15 5& '# ! # !( )!

j) 8( 2) 4 3

85 5

! ! "! #

k) * +* +36 ( 4) 1

2 ( 2)

! # ! !

! ! l)

* +20( 1) ( 5)( 3)

2 12 ( 3 3)

! ! ! !! # ! !

2. Evaluate each expression for 3, 6, 1x y and z, ! , , ! .

a) x y z" " b) 2 3y z x! " c) 2x y z! "

d) 8

2

x

y e) 25y x! f) 3x yz"

Teaching Notes:

-. Many students confuse the addition/subtraction rules with the multiplication/division rules when

working with many operations in one expression.

-. Encourage students to perform one operation at a time.

-. Refer students to Order of Operations in the textbook.

Answers: 1a) 28; 1b) 13; 1c) -47; 1d) -25; 1e) 11; 1f) 5; 1g) 61; 1h) -2; 1i) 1; 1j) 1; 1k) 2; 1l) –9’

2a) 2; 2b) 12; 2c) 2; 2d) -2; 2e) 21; 2f) -33

M-15Copyright © 2007 Pearson Education, Inc., publishing as Pearson Prentice Hall

Mini-Lecture 2.6 Order of Operations

Learning Objectives:

1. Simplify expressions by using the order of operations.

2. Evaluate an algebraic expression.

Examples:

1. Simplify.

a) b) 2 5 6! " ! 2 5(5 8)! ! ! c) 2( 5)(7 3) 7! ! !

d) 80 e) f) ( 8) 15# ! ! 33 8(2! ) $ %28 2 7 2 3! ! "

g) h) i) 28 2(6) 45! " #5 23( 2) (8 10)! " ! $ %$ %21 7 15 5& '# ! # !( )!

j) 8( 2) 4 3

85 5

! ! "! #

k) * +* +36 ( 4) 1

2 ( 2)

! # ! !

! ! l)

* +20( 1) ( 5)( 3)

2 12 ( 3 3)

! ! ! !! # ! !

2. Evaluate each expression for 3, 6, 1x y and z, ! , , ! .

a) x y z" " b) 2 3y z x! " c) 2x y z! "

d) 8

2

x

y e) 25y x! f) 3x yz"

Teaching Notes:

-. Many students confuse the addition/subtraction rules with the multiplication/division rules when

working with many operations in one expression.

-. Encourage students to perform one operation at a time.

-. Refer students to Order of Operations in the textbook.

Answers: 1a) 28; 1b) 13; 1c) -47; 1d) -25; 1e) 11; 1f) 5; 1g) 61; 1h) -2; 1i) 1; 1j) 1; 1k) 2; 1l) –9’

2a) 2; 2b) 12; 2c) 2; 2d) -2; 2e) 21; 2f) -33

M-15Copyright © 2007 Pearson Education, Inc., publishing as Pearson Prentice Hall

Mini-Lecture 2.6 Order of Operations

Learning Objectives:

1. Simplify expressions by using the order of operations.

2. Evaluate an algebraic expression.

Examples:

1. Simplify.

a) b) 2 5 6! " ! 2 5(5 8)! ! ! c) 2( 5)(7 3) 7! ! !

d) 80 e) f) ( 8) 15# ! ! 33 8(2! ) $ %28 2 7 2 3! ! "

g) h) i) 28 2(6) 45! " #5 23( 2) (8 10)! " ! $ %$ %21 7 15 5& '# ! # !( )!

j) 8( 2) 4 3

85 5

! ! "! #

k) * +* +36 ( 4) 1

2 ( 2)

! # ! !

! ! l)

* +20( 1) ( 5)( 3)

2 12 ( 3 3)

! ! ! !! # ! !

2. Evaluate each expression for 3, 6, 1x y and z, ! , , ! .

a) x y z" " b) 2 3y z x! " c) 2x y z! "

d) 8

2

x

y e) 25y x! f) 3x yz"

Teaching Notes:

-. Many students confuse the addition/subtraction rules with the multiplication/division rules when

working with many operations in one expression.

-. Encourage students to perform one operation at a time.

-. Refer students to Order of Operations in the textbook.

Answers: 1a) 28; 1b) 13; 1c) -47; 1d) -25; 1e) 11; 1f) 5; 1g) 61; 1h) -2; 1i) 1; 1j) 1; 1k) 2; 1l) –9’

2a) 2; 2b) 12; 2c) 2; 2d) -2; 2e) 21; 2f) -33

M-15Copyright © 2007 Pearson Education, Inc., publishing as Pearson Prentice Hall

Mini-Lecture 2.6 Order of Operations

Learning Objectives:

1. Simplify expressions by using the order of operations.

2. Evaluate an algebraic expression.

Examples:

1. Simplify.

a) b) 2 5 6! " ! 2 5(5 8)! ! ! c) 2( 5)(7 3) 7! ! !

d) 80 e) f) ( 8) 15# ! ! 33 8(2! ) $ %28 2 7 2 3! ! "

g) h) i) 28 2(6) 45! " #5 23( 2) (8 10)! " ! $ %$ %21 7 15 5& '# ! # !( )!

j) 8( 2) 4 3

85 5

! ! "! #

k) * +* +36 ( 4) 1

2 ( 2)

! # ! !

! ! l)

* +20( 1) ( 5)( 3)

2 12 ( 3 3)

! ! ! !! # ! !

2. Evaluate each expression for 3, 6, 1x y and z, ! , , ! .

a) x y z" " b) 2 3y z x! " c) 2x y z! "

d) 8

2

x

y e) 25y x! f) 3x yz"

Teaching Notes:

-. Many students confuse the addition/subtraction rules with the multiplication/division rules when

working with many operations in one expression.

-. Encourage students to perform one operation at a time.

-. Refer students to Order of Operations in the textbook.

Answers: 1a) 28; 1b) 13; 1c) -47; 1d) -25; 1e) 11; 1f) 5; 1g) 61; 1h) -2; 1i) 1; 1j) 1; 1k) 2; 1l) –9’

2a) 2; 2b) 12; 2c) 2; 2d) -2; 2e) 21; 2f) -33

M-15Copyright © 2007 Pearson Education, Inc., publishing as Pearson Prentice Hall

Mini-Lecture 2.6 Order of Operations

Learning Objectives:

1. Simplify expressions by using the order of operations.

2. Evaluate an algebraic expression.

Examples:

1. Simplify.

a) b) 2 5 6! " ! 2 5(5 8)! ! ! c) 2( 5)(7 3) 7! ! !

d) 80 e) f) ( 8) 15# ! ! 33 8(2! ) $ %28 2 7 2 3! ! "

g) h) i) 28 2(6) 45! " #5 23( 2) (8 10)! " ! $ %$ %21 7 15 5& '# ! # !( )!

j) 8( 2) 4 3

85 5

! ! "! #

k) * +* +36 ( 4) 1

2 ( 2)

! # ! !

! ! l)

* +20( 1) ( 5)( 3)

2 12 ( 3 3)

! ! ! !! # ! !

2. Evaluate each expression for 3, 6, 1x y and z, ! , , ! .

a) x y z" " b) 2 3y z x! " c) 2x y z! "

d) 8

2

x

y e) 25y x! f) 3x yz"

Teaching Notes:

-. Many students confuse the addition/subtraction rules with the multiplication/division rules when

working with many operations in one expression.

-. Encourage students to perform one operation at a time.

-. Refer students to Order of Operations in the textbook.

Answers: 1a) 28; 1b) 13; 1c) -47; 1d) -25; 1e) 11; 1f) 5; 1g) 61; 1h) -2; 1i) 1; 1j) 1; 1k) 2; 1l) –9’

2a) 2; 2b) 12; 2c) 2; 2d) -2; 2e) 21; 2f) -33

M-15Copyright © 2007 Pearson Education, Inc., publishing as Pearson Prentice Hall

Mini-Lecture 2.6 Order of Operations

Learning Objectives:

1. Simplify expressions by using the order of operations.

2. Evaluate an algebraic expression.

Examples:

1. Simplify.

a) b) 2 5 6! " ! 2 5(5 8)! ! ! c) 2( 5)(7 3) 7! ! !

d) 80 e) f) ( 8) 15# ! ! 33 8(2! ) $ %28 2 7 2 3! ! "

g) h) i) 28 2(6) 45! " #5 23( 2) (8 10)! " ! $ %$ %21 7 15 5& '# ! # !( )!

j) 8( 2) 4 3

85 5

! ! "! #

k) * +* +36 ( 4) 1

2 ( 2)

! # ! !

! ! l)

* +20( 1) ( 5)( 3)

2 12 ( 3 3)

! ! ! !! # ! !

2. Evaluate each expression for 3, 6, 1x y and z, ! , , ! .

a) x y z" " b) 2 3y z x! " c) 2x y z! "

d) 8

2

x

y e) 25y x! f) 3x yz"

Teaching Notes:

-. Many students confuse the addition/subtraction rules with the multiplication/division rules when

working with many operations in one expression.

-. Encourage students to perform one operation at a time.

-. Refer students to Order of Operations in the textbook.

Answers: 1a) 28; 1b) 13; 1c) -47; 1d) -25; 1e) 11; 1f) 5; 1g) 61; 1h) -2; 1i) 1; 1j) 1; 1k) 2; 1l) –9’

2a) 2; 2b) 12; 2c) 2; 2d) -2; 2e) 21; 2f) -33

M-15Copyright © 2007 Pearson Education, Inc., publishing as Pearson Prentice Hall

Mini-Lecture 2.6 Order of Operations

Learning Objectives:

1. Simplify expressions by using the order of operations.

2. Evaluate an algebraic expression.

Examples:

1. Simplify.

a) b) 2 5 6! " ! 2 5(5 8)! ! ! c) 2( 5)(7 3) 7! ! !

d) 80 e) f) ( 8) 15# ! ! 33 8(2! ) $ %28 2 7 2 3! ! "

g) h) i) 28 2(6) 45! " #5 23( 2) (8 10)! " ! $ %$ %21 7 15 5& '# ! # !( )!

j) 8( 2) 4 3

85 5

! ! "! #

k) * +* +36 ( 4) 1

2 ( 2)

! # ! !

! ! l)

* +20( 1) ( 5)( 3)

2 12 ( 3 3)

! ! ! !! # ! !

2. Evaluate each expression for 3, 6, 1x y and z, ! , , ! .

a) x y z" " b) 2 3y z x! " c) 2x y z! "

d) 8

2

x

y e) 25y x! f) 3x yz"

Teaching Notes:

-. Many students confuse the addition/subtraction rules with the multiplication/division rules when

working with many operations in one expression.

-. Encourage students to perform one operation at a time.

-. Refer students to Order of Operations in the textbook.

Answers: 1a) 28; 1b) 13; 1c) -47; 1d) -25; 1e) 11; 1f) 5; 1g) 61; 1h) -2; 1i) 1; 1j) 1; 1k) 2; 1l) –9’

2a) 2; 2b) 12; 2c) 2; 2d) -2; 2e) 21; 2f) -33

M-15Copyright © 2007 Pearson Education, Inc., publishing as Pearson Prentice Hall

Mini-Lecture 2.6 Order of Operations

Learning Objectives:

1. Simplify expressions by using the order of operations.

2. Evaluate an algebraic expression.

Examples:

1. Simplify.

a) b) 2 5 6! " ! 2 5(5 8)! ! ! c) 2( 5)(7 3) 7! ! !

d) 80 e) f) ( 8) 15# ! ! 33 8(2! ) $ %28 2 7 2 3! ! "

g) h) i) 28 2(6) 45! " #5 23( 2) (8 10)! " ! $ %$ %21 7 15 5& '# ! # !( )!

j) 8( 2) 4 3

85 5

! ! "! #

k) * +* +36 ( 4) 1

2 ( 2)

! # ! !

! ! l)

* +20( 1) ( 5)( 3)

2 12 ( 3 3)

! ! ! !! # ! !

2. Evaluate each expression for 3, 6, 1x y and z, ! , , ! .

a) x y z" " b) 2 3y z x! " c) 2x y z! "

d) 8

2

x

y e) 25y x! f) 3x yz"

Teaching Notes:

-. Many students confuse the addition/subtraction rules with the multiplication/division rules when

working with many operations in one expression.

-. Encourage students to perform one operation at a time.

-. Refer students to Order of Operations in the textbook.

Answers: 1a) 28; 1b) 13; 1c) -47; 1d) -25; 1e) 11; 1f) 5; 1g) 61; 1h) -2; 1i) 1; 1j) 1; 1k) 2; 1l) –9’

2a) 2; 2b) 12; 2c) 2; 2d) -2; 2e) 21; 2f) -33

M-15Copyright © 2007 Pearson Education, Inc., publishing as Pearson Prentice Hall

Mini-Lecture 2.6 Order of Operations

Learning Objectives:

1. Simplify expressions by using the order of operations.

2. Evaluate an algebraic expression.

Examples:

1. Simplify.

a) b) 2 5 6! " ! 2 5(5 8)! ! ! c) 2( 5)(7 3) 7! ! !

d) 80 e) f) ( 8) 15# ! ! 33 8(2! ) $ %28 2 7 2 3! ! "

g) h) i) 28 2(6) 45! " #5 23( 2) (8 10)! " ! $ %$ %21 7 15 5& '# ! # !( )!

j) 8( 2) 4 3

85 5

! ! "! #

k) * +* +36 ( 4) 1

2 ( 2)

! # ! !

! ! l)

* +20( 1) ( 5)( 3)

2 12 ( 3 3)

! ! ! !! # ! !

2. Evaluate each expression for 3, 6, 1x y and z, ! , , ! .

a) x y z" " b) 2 3y z x! " c) 2x y z! "

d) 8

2

x

y e) 25y x! f) 3x yz"

Teaching Notes:

-. Many students confuse the addition/subtraction rules with the multiplication/division rules when

working with many operations in one expression.

-. Encourage students to perform one operation at a time.

-. Refer students to Order of Operations in the textbook.

Answers: 1a) 28; 1b) 13; 1c) -47; 1d) -25; 1e) 11; 1f) 5; 1g) 61; 1h) -2; 1i) 1; 1j) 1; 1k) 2; 1l) –9’

2a) 2; 2b) 12; 2c) 2; 2d) -2; 2e) 21; 2f) -33

M-15Copyright © 2007 Pearson Education, Inc., publishing as Pearson Prentice Hall

Mini-Lecture 2.6 Order of Operations

Learning Objectives:

1. Simplify expressions by using the order of operations.

2. Evaluate an algebraic expression.

Examples:

1. Simplify.

a) b) 2 5 6! " ! 2 5(5 8)! ! ! c) 2( 5)(7 3) 7! ! !

d) 80 e) f) ( 8) 15# ! ! 33 8(2! ) $ %28 2 7 2 3! ! "

g) h) i) 28 2(6) 45! " #5 23( 2) (8 10)! " ! $ %$ %21 7 15 5& '# ! # !( )!

j) 8( 2) 4 3

85 5

! ! "! #

k) * +* +36 ( 4) 1

2 ( 2)

! # ! !

! ! l)

* +20( 1) ( 5)( 3)

2 12 ( 3 3)

! ! ! !! # ! !

2. Evaluate each expression for 3, 6, 1x y and z, ! , , ! .

a) x y z" " b) 2 3y z x! " c) 2x y z! "

d) 8

2

x

y e) 25y x! f) 3x yz"

Teaching Notes:

-. Many students confuse the addition/subtraction rules with the multiplication/division rules when

working with many operations in one expression.

-. Encourage students to perform one operation at a time.

-. Refer students to Order of Operations in the textbook.

Answers: 1a) 28; 1b) 13; 1c) -47; 1d) -25; 1e) 11; 1f) 5; 1g) 61; 1h) -2; 1i) 1; 1j) 1; 1k) 2; 1l) –9’

2a) 2; 2b) 12; 2c) 2; 2d) -2; 2e) 21; 2f) -33

M-15Copyright © 2007 Pearson Education, Inc., publishing as Pearson Prentice Hall

Mini-Lecture 2.6 Order of Operations

Learning Objectives:

1. Simplify expressions by using the order of operations.

2. Evaluate an algebraic expression.

Examples:

1. Simplify.

a) b) 2 5 6! " ! 2 5(5 8)! ! ! c) 2( 5)(7 3) 7! ! !

d) 80 e) f) ( 8) 15# ! ! 33 8(2! ) $ %28 2 7 2 3! ! "

g) h) i) 28 2(6) 45! " #5 23( 2) (8 10)! " ! $ %$ %21 7 15 5& '# ! # !( )!

j) 8( 2) 4 3

85 5

! ! "! #

k) * +* +36 ( 4) 1

2 ( 2)

! # ! !

! ! l)

* +20( 1) ( 5)( 3)

2 12 ( 3 3)

! ! ! !! # ! !

2. Evaluate each expression for 3, 6, 1x y and z, ! , , ! .

a) x y z" " b) 2 3y z x! " c) 2x y z! "

d) 8

2

x

y e) 25y x! f) 3x yz"

Teaching Notes:

-. Many students confuse the addition/subtraction rules with the multiplication/division rules when

working with many operations in one expression.

-. Encourage students to perform one operation at a time.

-. Refer students to Order of Operations in the textbook.

Answers: 1a) 28; 1b) 13; 1c) -47; 1d) -25; 1e) 11; 1f) 5; 1g) 61; 1h) -2; 1i) 1; 1j) 1; 1k) 2; 1l) –9’

2a) 2; 2b) 12; 2c) 2; 2d) -2; 2e) 21; 2f) -33

M-15Copyright © 2007 Pearson Education, Inc., publishing as Pearson Prentice Hall

Mini-Lecture 2.6 Order of Operations

Learning Objectives:

1. Simplify expressions by using the order of operations.

2. Evaluate an algebraic expression.

Examples:

1. Simplify.

a) b) 2 5 6! " ! 2 5(5 8)! ! ! c) 2( 5)(7 3) 7! ! !

d) 80 e) f) ( 8) 15# ! ! 33 8(2! ) $ %28 2 7 2 3! ! "

g) h) i) 28 2(6) 45! " #5 23( 2) (8 10)! " ! $ %$ %21 7 15 5& '# ! # !( )!

j) 8( 2) 4 3

85 5

! ! "! #

k) * +* +36 ( 4) 1

2 ( 2)

! # ! !

! ! l)

* +20( 1) ( 5)( 3)

2 12 ( 3 3)

! ! ! !! # ! !

2. Evaluate each expression for 3, 6, 1x y and z, ! , , ! .

a) x y z" " b) 2 3y z x! " c) 2x y z! "

d) 8

2

x

y e) 25y x! f) 3x yz"

Teaching Notes:

-. Many students confuse the addition/subtraction rules with the multiplication/division rules when

working with many operations in one expression.

-. Encourage students to perform one operation at a time.

-. Refer students to Order of Operations in the textbook.

Answers: 1a) 28; 1b) 13; 1c) -47; 1d) -25; 1e) 11; 1f) 5; 1g) 61; 1h) -2; 1i) 1; 1j) 1; 1k) 2; 1l) –9’

2a) 2; 2b) 12; 2c) 2; 2d) -2; 2e) 21; 2f) -33

M-15Copyright © 2007 Pearson Education, Inc., publishing as Pearson Prentice Hall

Mini-Lecture 2.6 Order of Operations

Learning Objectives:

1. Simplify expressions by using the order of operations.

2. Evaluate an algebraic expression.

Examples:

1. Simplify.

a) b) 2 5 6! " ! 2 5(5 8)! ! ! c) 2( 5)(7 3) 7! ! !

d) 80 e) f) ( 8) 15# ! ! 33 8(2! ) $ %28 2 7 2 3! ! "

g) h) i) 28 2(6) 45! " #5 23( 2) (8 10)! " ! $ %$ %21 7 15 5& '# ! # !( )!

j) 8( 2) 4 3

85 5

! ! "! #

k) * +* +36 ( 4) 1

2 ( 2)

! # ! !

! ! l)

* +20( 1) ( 5)( 3)

2 12 ( 3 3)

! ! ! !! # ! !

2. Evaluate each expression for 3, 6, 1x y and z, ! , , ! .

a) x y z" " b) 2 3y z x! " c) 2x y z! "

d) 8

2

x

y e) 25y x! f) 3x yz"

Teaching Notes:

-. Many students confuse the addition/subtraction rules with the multiplication/division rules when

working with many operations in one expression.

-. Encourage students to perform one operation at a time.

-. Refer students to Order of Operations in the textbook.

Answers: 1a) 28; 1b) 13; 1c) -47; 1d) -25; 1e) 11; 1f) 5; 1g) 61; 1h) -2; 1i) 1; 1j) 1; 1k) 2; 1l) –9’

2a) 2; 2b) 12; 2c) 2; 2d) -2; 2e) 21; 2f) -33

M-15Copyright © 2007 Pearson Education, Inc., publishing as Pearson Prentice Hall

Mini-Lecture 2.6 Order of Operations

Learning Objectives:

1. Simplify expressions by using the order of operations.

2. Evaluate an algebraic expression.

Examples:

1. Simplify.

a) b) 2 5 6! " ! 2 5(5 8)! ! ! c) 2( 5)(7 3) 7! ! !

d) 80 e) f) ( 8) 15# ! ! 33 8(2! ) $ %28 2 7 2 3! ! "

g) h) i) 28 2(6) 45! " #5 23( 2) (8 10)! " ! $ %$ %21 7 15 5& '# ! # !( )!

j) 8( 2) 4 3

85 5

! ! "! #

k) * +* +36 ( 4) 1

2 ( 2)

! # ! !

! ! l)

* +20( 1) ( 5)( 3)

2 12 ( 3 3)

! ! ! !! # ! !

2. Evaluate each expression for 3, 6, 1x y and z, ! , , ! .

a) x y z" " b) 2 3y z x! " c) 2x y z! "

d) 8

2

x

y e) 25y x! f) 3x yz"

Teaching Notes:

-. Many students confuse the addition/subtraction rules with the multiplication/division rules when

working with many operations in one expression.

-. Encourage students to perform one operation at a time.

-. Refer students to Order of Operations in the textbook.

Answers: 1a) 28; 1b) 13; 1c) -47; 1d) -25; 1e) 11; 1f) 5; 1g) 61; 1h) -2; 1i) 1; 1j) 1; 1k) 2; 1l) –9’

2a) 2; 2b) 12; 2c) 2; 2d) -2; 2e) 21; 2f) -33

M-15Copyright © 2007 Pearson Education, Inc., publishing as Pearson Prentice Hall

Mini-Lecture 2.6 Order of Operations

Learning Objectives:

1. Simplify expressions by using the order of operations.

2. Evaluate an algebraic expression.

Examples:

1. Simplify.

a) b) 2 5 6! " ! 2 5(5 8)! ! ! c) 2( 5)(7 3) 7! ! !

d) 80 e) f) ( 8) 15# ! ! 33 8(2! ) $ %28 2 7 2 3! ! "

g) h) i) 28 2(6) 45! " #5 23( 2) (8 10)! " ! $ %$ %21 7 15 5& '# ! # !( )!

j) 8( 2) 4 3

85 5

! ! "! #

k) * +* +36 ( 4) 1

2 ( 2)

! # ! !

! ! l)

* +20( 1) ( 5)( 3)

2 12 ( 3 3)

! ! ! !! # ! !

2. Evaluate each expression for 3, 6, 1x y and z, ! , , ! .

a) x y z" " b) 2 3y z x! " c) 2x y z! "

d) 8

2

x

y e) 25y x! f) 3x yz"

Teaching Notes:

-. Many students confuse the addition/subtraction rules with the multiplication/division rules when

working with many operations in one expression.

-. Encourage students to perform one operation at a time.

-. Refer students to Order of Operations in the textbook.

Answers: 1a) 28; 1b) 13; 1c) -47; 1d) -25; 1e) 11; 1f) 5; 1g) 61; 1h) -2; 1i) 1; 1j) 1; 1k) 2; 1l) –9’

2a) 2; 2b) 12; 2c) 2; 2d) -2; 2e) 21; 2f) -33

M-15Copyright © 2007 Pearson Education, Inc., publishing as Pearson Prentice Hall

Mini-Lecture 2.6 Order of Operations

Learning Objectives:

1. Simplify expressions by using the order of operations.

2. Evaluate an algebraic expression.

Examples:

1. Simplify.

a) b) 2 5 6! " ! 2 5(5 8)! ! ! c) 2( 5)(7 3) 7! ! !

d) 80 e) f) ( 8) 15# ! ! 33 8(2! ) $ %28 2 7 2 3! ! "

g) h) i) 28 2(6) 45! " #5 23( 2) (8 10)! " ! $ %$ %21 7 15 5& '# ! # !( )!

j) 8( 2) 4 3

85 5

! ! "! #

k) * +* +36 ( 4) 1

2 ( 2)

! # ! !

! ! l)

* +20( 1) ( 5)( 3)

2 12 ( 3 3)

! ! ! !! # ! !

2. Evaluate each expression for 3, 6, 1x y and z, ! , , ! .

a) x y z" " b) 2 3y z x! " c) 2x y z! "

d) 8

2

x

y e) 25y x! f) 3x yz"

Teaching Notes:

-. Many students confuse the addition/subtraction rules with the multiplication/division rules when

working with many operations in one expression.

-. Encourage students to perform one operation at a time.

-. Refer students to Order of Operations in the textbook.

Answers: 1a) 28; 1b) 13; 1c) -47; 1d) -25; 1e) 11; 1f) 5; 1g) 61; 1h) -2; 1i) 1; 1j) 1; 1k) 2; 1l) –9’

2a) 2; 2b) 12; 2c) 2; 2d) -2; 2e) 21; 2f) -33

M-15Copyright © 2007 Pearson Education, Inc., publishing as Pearson Prentice Hall

Mini-Lecture 2.6 Order of Operations

Learning Objectives:

1. Simplify expressions by using the order of operations.

2. Evaluate an algebraic expression.

Examples:

1. Simplify.

a) b) 2 5 6! " ! 2 5(5 8)! ! ! c) 2( 5)(7 3) 7! ! !

d) 80 e) f) ( 8) 15# ! ! 33 8(2! ) $ %28 2 7 2 3! ! "

g) h) i) 28 2(6) 45! " #5 23( 2) (8 10)! " ! $ %$ %21 7 15 5& '# ! # !( )!

j) 8( 2) 4 3

85 5

! ! "! #

k) * +* +36 ( 4) 1

2 ( 2)

! # ! !

! ! l)

* +20( 1) ( 5)( 3)

2 12 ( 3 3)

! ! ! !! # ! !

2. Evaluate each expression for 3, 6, 1x y and z, ! , , ! .

a) x y z" " b) 2 3y z x! " c) 2x y z! "

d) 8

2

x

y e) 25y x! f) 3x yz"

Teaching Notes:

-. Many students confuse the addition/subtraction rules with the multiplication/division rules when

working with many operations in one expression.

-. Encourage students to perform one operation at a time.

-. Refer students to Order of Operations in the textbook.

Answers: 1a) 28; 1b) 13; 1c) -47; 1d) -25; 1e) 11; 1f) 5; 1g) 61; 1h) -2; 1i) 1; 1j) 1; 1k) 2; 1l) –9’

2a) 2; 2b) 12; 2c) 2; 2d) -2; 2e) 21; 2f) -33

M-15Copyright © 2007 Pearson Education, Inc., publishing as Pearson Prentice Hall