2-1 Properties and Mental Math

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

2-1 Properties and Mental Math

Warm UpFind each sum or product.

1. 17 + 15

2. 29 + 39

3. 8(24)

4. 7(12)

5. 3(91)

6. 6(15)

32

68

192

84273

90

2-1 Properties and Mental Math

Problem of the Day

Determine the secret number from the following clues:• The number is a multiple of 5.• It is divisible by 3.• It is less than 200.• Its tens digit equals the sum of its

other two digits.

165

2-1 Properties and Mental Math

MA.6.A.3.5 Apply the Commutative, Associative, and Distributive Properties to show that two expressions are equivalent.

Sunshine State Standards

2-1 Properties and Mental Math

Vocabulary

Commutative PropertyAssociative PropertyDistributive Property

2-1 Properties and Mental Math

Mental math means “doing math in your head.”

Many mental math strategies use number properties that you already know to make equivalent expressions that may be easier to simplify.

2-1 Properties and Mental Math

COMMUTATIVE PROPERTY (Ordering)

Words Numbers

You can add or multiply

numbers in any order.

18 + 9 = 9 + 18

15 2 = 2 15

2-1 Properties and Mental Math

ASSOCIATIVE PROPERTY (Grouping)

Words NumbersWhen you are only adding or only multiplying, you can group any of the numbers together.

(17 + 2) + 9 = 17 + (2 + 9)

(12 2) 4 = 12 (2 4)

2-1 Properties and Mental Math

The Commutative and Associative Properties do not apply to subtraction or division.

Caution!

2-1 Properties and Mental Math

Additional Example 1A: Using Properties to Add and Multiply Whole Numbers

Simplify 17 + 5 + 3 + 15.

17 + 5 + 3 + 15 Look for sums that are multiples of 10.

40

Use the Commutative Property. 17 + 3 + 5 + 15

(17 + 3) + (5 + 15)

Use mental math to add.

20 + 20

Use the Associative Property to make groups of compatible numbers.

2-1 Properties and Mental Math

Additional Example 1B: Using Properties to Add and Multiply Whole Numbers

Simplify 4 13 5.

4 13 5

Look for products that are multiples of 10.

260

Use the Commutative Property.13 4 5

13 (4 5)

Use mental math to multiply.13 20

Use the Associative Property to group compatible numbers.

2-1 Properties and Mental Math

The expressions in each row of example 1B are equivalent because they have the same value.

Helpful Hint

2-1 Properties and Mental Math

Check It Out: Example 1A

Simplify 23 + 8 + 12 + 7.

23 + 8 + 12 + 7

= 23 + 7 + 8 + 12

= 30 + 20

= 50

2-1 Properties and Mental Math

Check It Out: Example 1B

Simplify 49 + 17 + 51.

49 + 17 + 51

= 49 + 51 + 17

= 100 + 17

= 117

2-1 Properties and Mental Math

Check It Out: Example 1C

Simplify 6 × 33 × 5.

6 × 33 × 5

= 6 × 5 × 33

= 30 × 33

= 990

2-1 Properties and Mental Math

Check It Out: Example 1D

Simplify 2 × 69 × 5.

2 × 69 × 5

= 2 × 5 × 69

= 10 × 69

= 690

2-1 Properties and Mental Math

DISTRIBUTIVE PROPERTY

Words NumbersTo multiply a number

by a sum, multiply by

each number in the sum and then add.

6 (10 + 4) = (6 10) + (6 4)

= 60 + 24

= 84

2-1 Properties and Mental Math

When you multiply two numbers, you can “break apart” one of the numbers into a sum and then use the Distributive Property.

2-1 Properties and Mental Math

Additional Example 2A: Using the Distributive Property to Multiply

Use the Distributive Property to find the product.

6 35

6 35 = 6 (30 + 5) “Break apart” 35 into 30 + 5.

= 210

Use the Distributive Property.= (6 30) + (6 5)

Use mental math to add.

= 180 + 30 Use mental math to multiply.

2-1 Properties and Mental Math Additional Example 2B: Using the Distributive

Property to Multiply

Use the Distributive Property to find the product.

9 87

9 87 = 9 (80 + 7) “Break apart” 87 into 80 + 7.

= 783

Use the Distributive Property.= (9 80) + (9 7)

Use mental math to add.

= 720 + 63 Use mental math to multiply.

2-1 Properties and Mental Math

Check It Out: Example 2A

Use the Distributive Property to find each product.

6 71

6 71 = 6 (70 + 1)

= 426

= 6 70 + 6 1

= 420 + 6

2-1 Properties and Mental Math

Check It Out: Example 2B

Use the Distributive Property to find each product.

28 5

28 5 = (20 + 8) 5

= 140

= 20 5 + 8 5

= 100 + 40

2-1 Properties and Mental Math

Check It Out: Example 2C

Use the Distributive Property to find each product.

8 44

8 44 = 8 (40 + 4)

= 352

= 8 40 + 8 4

= 320 + 32

2-1 Properties and Mental Math

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

2-1 Properties and Mental Math

Lesson Quiz

Simplify.

1. 18 + 24 + 2 + 6 2. 10 5 3

3. 13 + 42 + 7 + 8

Use the Distributive Property to find each

product.

4. 8 12 5. 6 15

6. 5 34 7. 3 71

15050

70

96 90

170 213

2-1 Properties and Mental Math

1. Evaluate 16 + 23 + 4 + 7.

A. 50

B. 40

C. 30

D. 20

Lesson Quiz for Student Response Systems

2-1 Properties and Mental Math

2. Evaluate 3 7 10.

A. 140

B. 170

C. 190

D. 210

Lesson Quiz for Student Response Systems

2-1 Properties and Mental Math

3. Evaluate 15 + 56 + 5 + 4.

A. 86

B. 80

C. 77

D. 70

Lesson Quiz for Student Response Systems

2-1 Properties and Mental Math

4. Use the Distributive Property to find the product.

7 15

A. 135

B. 125

C. 115

D. 105

Lesson Quiz for Student Response Systems

2-1 Properties and Mental Math

5. Use the Distributive Property to find the product.

4 73

A. 292

B. 282

C. 272

D. 262

Lesson Quiz for Student Response Systems