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Warm-Up Using Properties of Operations

Lesson Question

Lesson Goals

Evaluateexpressions.

property of operationsto rewrite expressions.

Use the Use the

property of operationsto rewrite expressions.

Use the commutativeproperty of operationsto rewrite expressions.

Words to Know

Fill in this table as you work through the lesson. You may also use the glossary to help you.

evaluate to determine the of

associative property

the property stating that the way in which two or

more numbers are in a sum or

product does not change the value

commutative propertythe property stating that changing the

in which two numbers are added or multiplied does not change the value of the sum or product

?

WK2

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Warm-Up Using Properties of Operations

Words to KnowWK2

distributive property

the property stating that the of a factor

times a given quantity containing a sum or difference is

equal to the of the products of that factor

times each addend from within the quantity

identity property

the property stating that an operation performed between a number and the identity element

( in addition and 1 in ) will

result in the same number

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Instruction Using Properties of Operations

Properties of Operations

Commutative Property

• Addition: a + b = b +

• 3 + 2 = 2 + 3

5 =

• Multiplication: a(b) = b(a)

• 3(2) = 2(3)

6 6

Associative Property

The associative property changes where the parentheses lie.

• : a + (b + c) = (a + b) + c

• 3 + (5 + 1) = (3 + 5) + 1

 3 + 6 = + 1

9 = 9

• Multiplication: a(bc) = (ab)c

• (3)[5(1)] = [3(5)](1)

(3)(5) = 15(1)

= 15

2Slide

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Instruction Using Properties of Operations

Using the Commutative and Associative Properties

Commutative property of addition:

a + b = b + a

4 + 7 + 6 =

11 + 6 =

4 + 6 + 7 =

+ 7 = 17

Associative property of multiplication:

(bc) = (ab)

(5)[2(7)] =

[5(2)]( )

10(7) = 70

property of

addition:

a + b = b + a

property of

addition:

a + (b + c) = (a + b) + c

Evaluate the expression using both properties:

2 + (4 + 8) = 2 + ( + )

= (2 + 8) + 4

= 10 + 4

=

2Slide

The problem can be made simpler using the commutative property. Switch the 7 and 6.

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Instruction Using Properties of Operations

4Slide

The Identity Property

Identity Property

• Addition:

• a + 0 = a

14 + 0 =

• Multiplication:

• a(1) = a

14( ) = 14

• Nonexamples:

• a + 1 = a + 1

14 + 1 = 14 + 1 =

• Property of Zero

• a(0) = 0

14(0) =

The Properties of Operations

The distributive property states that a number times a sum is the as the sum of the number times each addend.

a(b + c) = a( ) + a(c)

2(5 + 7) = 2(5) + 2( )

2( ) = 10 + 14

24 =

Let a = 14.

7

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Instruction Using Properties of Operations

The Distributive Property

Use expanded form and the property to simplify the multiplication.

4(53)

4( + )

4(50) + 4(3)

200 + 12 =

Combining Properties of Operations

Evaluate the expression. Use the properties of operations to make the

calculations .

15 + (12 + 35)

15 + (35 + 12)

(15 + 35) + 12

+ 12 =

9Slide

12

commutative property

property

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Instruction Using Properties of Operations

Use the properties of operations to evaluate this expression.

18 + 3(64)

18 + 3(60 + 4)

18 + 3(60) + 3(4)

18 + 180 + 12

18 + + 180 = 30 + 180 =

By combining properties of operations, we can take a more complicated problem and simplify it.

property

property

12Slide

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Summary

? Lesson Question

Using Properties of Operations

? Lesson Question

How can you use properties of operations to evaluate expressions?

Answer

Review: Key Concepts

Commutative Property

Associative Property

Identity Property

Distributive Property

The

of addition or multiplication can be switched.

The

in addition and multiplication can be switched.

Addition by 0 and multiplication by 1 does not change the value of the number.

Multiplying a sum by a number is the same as the sum of the number times each addend.

3 + 5 = 5 + 3 (3 + 5) + 7 = 3 + (5 + 7) 5 + = 5 3(5 + 7) = 3(5) + 3(7)

4(24) = 4(20) + 4(4)3(5) = 5(3) [3(5)]7 = 3[5(7)] 5(1) =

2

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Summary Using Properties of Operations

Properties of operations:

• Commutative property

• Addition and

• property

• Addition and multiplication

• Identity property

• and multiplication

• property

Use this space to write any questions or thoughts about this lesson.

2Slide