Course 2

1-5 Order of Operations1-5 Order of Operations

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Course 2

1-5 Order of Operations

Warm UpEvaluate in order from left to right.

1. 18 ÷ 3 + 7

2. 102 ÷ 4 – 8

3. 10 + 23 – 8 + 7

4. 8 2 – 3 + 24

5. 81 ÷ 9 3 + 15

13

17

32

37

42

Course 2

1-5 Order of Operations

Problem of the Day

Classify each statement as true or false. If the statement is false, insert parentheses to make it true.

false1. 4 5 + 6 = 44( )

2. 24 – 4 2 = 40( ) false

3. 25 ÷ 5 + 6 3 = 23

4. 14 – 22 ÷ 2 = 12

true

true

Course 2

1-5 Order of Operations

Learn to use the order of operations to simplify numerical expressions.

Course 2

1-5 Order of Operations

Vocabulary

numerical expressionorder of operations

Course 2

1-5 Order of Operations

When you get ready for school, you put on your socks before you put on your shoes. In mathematics, as in life, some tasks must be done in a certain order.

A numerical expression is made up of numbers and operations. When simplifying a numerical expression, rules must be followed so that everyone gets the same answer. That is why mathematicians have agreed upon the order of operations.

Course 2

1-5 Order of Operations

ORDER OF OPERATIONS

1. Perform operations within grouping symbols.

2. Evaluate powers.

3. Multiply and divide in order from left to right.

4. Add and subtract in order from left to right.

Course 2

1-5 Order of Operations

Simplify the expression.

Additional Example 1A: Using the Order of Operations

3 + 15 ÷ 5

3 + 15 ÷ 5

3 + 3

6

Divide.

Add.

Course 2

1-5 Order of Operations

Simplify the expression.

Additional Example 1B: Using the Order of Operations

44 – 14 ÷ 2 · 4 + 6

44 – 14 ÷ 2 · 4 + 6

44 – 7 · 4 + 6

44 – 28 + 6

16 + 6

22

Divide and multiply fromleft to right.

Subtract and add fromleft to right.

Course 2

1-5 Order of Operations

Simplify the expression.

Additional Example 1C: Using the Order of Operations

3 + 23 · 5

3 + 23 · 5

3 + 8 · 5

3 + 40

43

Evaluate the power.

Multiply.

Add.

Course 2

1-5 Order of Operations

Check It Out: Example 1A

Simplify the expression.

2 + 24 ÷ 6

2 + 24 ÷ 6

2 + 4

6

Divide.

Add.

Course 2

1-5 Order of Operations

Check It Out: Example 1B

Simplify the expression.

28 – 21 ÷ 3 · 4 + 5

28 – 21 ÷ 3 · 4 + 5

28 – 7 · 4 + 5

28 – 28 + 5

0 + 5

5

Divide and multiply fromleft to right.

Subtract and add fromleft to right.

Course 2

1-5 Order of Operations

Check It Out: Example 1C

Simplify the expression.

2 + 32 · 4

2 + 32 · 4

2 + 9 · 4

2 + 36

38

Evaluate the power.

Multiply.

Add.

Course 2

1-5 Order of Operations

Simplify the expression.

Additional Example 2A: Using the Order of Operations with Grouping Symbols

42 – (3 · 4) ÷ 6

42 – (3 · 4) ÷ 6

42 – 12 ÷ 6

42 – 2

40

Perform the operation inside the parentheses.

Divide.

Subtract.

Course 2

1-5 Order of Operations

When an expression has a set of grouping symbols within a second set of grouping symbols, begin with the innermost set.

Helpful Hint

Course 2

1-5 Order of Operations

Additional Example 2B: Using the Order of Operations with Grouping Symbols

[(26 – 4 · 5) + 6]2

[(26 – 4 · 5) + 6]2

[(26 – 20) + 6]2

[6 + 6]2

122

144

The parentheses are inside the brackets, so perform the operationsinside the parenthesesfirst.

Simplify the expression.

Course 2

1-5 Order of Operations

Check It Out: Example 2A

Simplify the expression.

A. 24 – (4 · 5) ÷ 4

24 – (4 · 5) ÷ 4

24 – 20 ÷ 4

24 – 5

19

Perform the operation inside the parentheses.

Divide.

Subtract.

Course 2

1-5 Order of Operations

Check It Out: Example 2B

Simplify the expression.

[(32 – 4 · 4) + 2]2

[(32 – 4 · 4) + 2]2

[(32 – 16) + 2]2

[16 + 2]2

182

324

The parentheses are inside the brackets, so perform the operationsinside the parenthesesfirst.

Course 2

1-5 Order of Operations

Additional Example 3: ApplicationSandy runs 4 miles per day. She ran 5 days during the first week of the month. She ran only 3 days each week for the next 3 weeks. Simplify the expression (5 + 3 · 3) · 4 to find how many miles she ran last month.

Week Days

Week 1 5

Week 2 3

Week 3 3

Week 4 3

(5 + 3 · 3) · 4

(5 + 9) · 4

14 · 4

56 Sandy ran 56 miles last month.

Perform the operations in parentheses first.

Add.

Multiply.

Course 2

1-5 Order of Operations

Check It Out: Example 3Jill is learning vocabulary words for a test. From the list, she already knew 30 words. She is learning 4 new words a day for 3 days each week. Evaluate the expression 3 · 4 · 7 + 30 to find out how many words will she know at the end of seven weeks.

Day Words

Initially 30

Day 1 4

Day 2 4

Day 3 4

(3 · 4 · 7) + 30

(12 · 7) + 30

84 + 30

114

Perform the operations in parentheses first.

Jill will know 114 words at the end of 7 weeks.

Multiply.

Add.

Course 2

1-5 Order of Operations

Lesson Quiz: Part I

Simplify each expression.

1. 27 + 56 ÷ 7

2. 9 · 7 – 5

3. (28 – 8) ÷ 4

4. 136 – 102 ÷ 5

5. (9 – 5)3 · (7 + 1)2 ÷ 4

58

35

5

116

1,024

Course 2

1-5 Order of Operations

Lesson Quiz: Part II

Evaluate.

6. Denzel paid a basic fee of $35 per month plus

$2 for each phone call beyond his basic plan.

Simplify the expression 35 + 8(2) to find how

much Denzel paid for a month with 8 calls

beyond the basic plan.

$51

Course 2

1-5 Order of Operations1-6 Properties

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Course 2

1-5 Order of Operations

Warm UpEvaluate.

1. 2 + 5 3 – 7

2. 5(3 – 1) ÷ (3 + 2)

3. (4 + 1)2 – 8 ÷ 2

4. 12 ÷ 3 6 – 20

10

2

21

4

Course 2

1-5 Order of Operations

Problem of the Day

Daniel usually buys 6 bottles of water and 3 apples when he goes to the grocery store. Next time he goes, he will buy three times as many of each. How many items will Daniel buy?

27

Course 2

1-5 Order of Operations

Learn how to identify properties of rational numbers and use them to simplify numerical expressions.

Course 2

1-5 Order of Operations

VocabularyCommutative PropertyAssociative PropertyIdentity PropertyDistributive Property

Course 2

1-5 Order of Operations

Course 2

1-5 Order of Operations

Course 2

1-5 Order of Operations

Course 2

1-5 Order of Operations

Additional Example 1: Identifying Properties of Addition and Multiplication

Tell which property is represented.

A. (2 6) 1 = 2 (6 1)

B. 3 + 0 = 3

C. 7 + 9 = 9 + 7

(2 6) 1 = 2 (6 1) The numbers are regrouped.

Associative Property

3 + 0 = 3 One of the factors is 0.

Identity Property

7 + 9 = 9 + 7 The order of the variables is switched.Commutative Property

Course 2

1-5 Order of Operations

Check It Out: Example 1

Tell which property is represented.

A. 7 1 = 7

B. 3 + 4 = 4 + 3

C. (5 1) 2 = 5 (1 2)

7 1 = 7 One of the factors is 1.

Identity Property

3 + 4 = 4 + 3 The order of the numbers is switched.Commutative Property

(5 1) 2 = 5 ( 1 2) The numbers are regrouped.

Associative Property

Course 2

1-5 Order of Operations

Additional Example 2: Using Properties to Simplify Expressions

Simplify each expression. Justify each step.

A. 21 + 16 + 9

B. 20 9 5

21 + 16 + 9 = 16 + 9 + 21 Commutative Property.

= 16 + (9 + 21)

= 16 + 30

Associative Property.

= 46

Add.

20 9 5 = 20 5 9 Commutative Property.

= 20 (5 9)

= 20 45

Associative Property.

= 900

Multiply.

Course 2

1-5 Order of Operations

Check It Out: Example 2A & B

Simplify each expression. Justify each step.

A. 17 + 14 + 3

B. 12 3 5

17 + 14 + 3 = 14 + 17 + 3 Commutative Property.

= 14 + (17 + 3)

= 14 + 20

Associative Property.

= 34

Add.

12 3 5 = 3 5 12 Commutative Property.

= 3 (5 12)

= 3 60

Associative Property.

= 180

Multiply.

Course 2

1-5 Order of Operations

You can use the Distributive Property to multiply numbers mentally by breaking apart one of the numbers and writing it as a sum or difference.

Course 2

1-5 Order of Operations

Additional Example 3: Using the Distributive Property to Multiply Mentally

Use the Distributive Property to find 6(54).

Method 1:

Method 2:

= (6 50) + (6 4)

Rewrite 54 as 50 + 4.

= 300 + 24

= 324

Use the Distributive Property.

Multiply.

6(54) = 6(60 – 6) Rewrite 54 as 60 – 6.

= (6 60) – (6 6)

= 360 - 36

Use the Distributive Property. Multiply.

= 324 Subtract.

Add.

6(54) = 6(50 + 4)

Course 2

1-5 Order of Operations

Check It Out: Example 3

Use the Distributive Property to find 8(19).

Method 1:

Method 2:

= (8 10) + (8 9)

Rewrite 19 as 10 + 9.

= 80 + 72

= 152

Use the Distributive Property.

Multiply.

8(19) = 8(20 – 1) Rewrite 19 as 20 – 1.

= (8 20) – (8 1)

= 160 – 8

Use the Distributive Property. Multiply.

= 152 Subtract.

Add.

8(19) = 8(10 + 9)

Course 2

1-5 Order of Operations

Lesson QuizTell which property is represented.

1. 17 1 = 17

2. (12 + 14) + 5 = 12 + (14 + 5)

3. 2 16 = 16 2

Simplify each expression. Justify each step.

4. 4 12 25

5. 48 + (15 + 2)

Use the Distributive Property to find each product.

6. 6 (12 + 5)

7. (20 – 7) 9

Identity Property

Associative Property

Commutative Property

1,200

65

102117