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•We will write equivalent expression using the properties

Vocabulary:Equivalent Expression:Expressions that have equal values for the

same replacement values of their variables

CommutativeCommutative PropertiesMultiplication3 • 8 = 8 • 3We can change the order when multiplying without affecting the product.

Addition7 + 3 = 3 + 7We can change the order when adding without affecting the sum.

CommutativeCommutative PropertiesSubtraction

7 - 3 = 3 – 7 ????

Commutative Property does NOT apply to subtraction.

Division 3 ÷ 8 = 8 ÷ 3 ????

Commutative Property does NOT apply to division.

To commute means to moveThe news talks about

the daily commute on the freeway.

Think about how the cars move this will help you to remember commutative property is when the numbers move!

Commutative PropertyAddition

Multiplication

+

+=

Write an equivalent expression using the commutative prop1. 7 + 11

2. 3 +x

3. 5y

It can help you to do more simple calculations

For Example:180 64 20

200

264

Mental Math1 9 162 72

8

IdentityIdentity PropertiesAddition

7 + 0 = 7 When zero is added to any number, the sum is the same number.

Multiplication9 • 1 = 9 When any number is multiplied by 1, the product is the same number.

Identity is who you areSame with numbers.

We want to be able to do an operation (such as +0 or mult by 1) and get the same thing back, its identity

(Using the Identity Property of Multiplication)

1.for 55 Use"1".by gmultiplyin

by 32for expression equivalent an Write

1510

55

32

Do you reduce this???

Answer is: NO!!!!Usually we reduce everything!We reduce when the directions say to:

1. Simplify2. Evaluate3. Solve4. Calculate (add, sub, mult, divide)

When the directions say to write an equivalent expression we do not reduce

1.for yy Use"1".by gmultiplyin

by 2xfor expression equivalent an Write

yxy

yyx

22

The Associative Property

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

(5 + 2) + 3 = 5 + (2 + 3)(5 + 2) + 3 = 5 + (2 + 3)

(Parenthesis) around different pairs of numbers

The Associative Property

(a (a •• b) b) •• c = a c = a •• (b (b •• c) c)

(2 (2 •• 3) 3) •• 5 = 2 5 = 2 •• (3 (3 •• 5) 5)

(Parenthesis) around different pairs of numbers

Associative: To associate

( + )+

(+ + )