# Today Is A Going to be A Great Day!! - PowerPoint PPT Presentation

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Today Is A Going to be A Great Day!!. SOL 8.1 and 7.3 AbSOLute Success Objective: To identify the properties and describe orally and in writing the relationship between the subsets of the real number system. Today we are going to review the different types of properties.

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Today Is A Going to be A Great Day!!

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### Today Is A Going to be A Great Day!!

• SOL 8.1 and 7.3

• AbSOLute Success

• Objective: To identify the properties and describe orally and in writing the relationship between the subsets of the real number system.

### 1. Commutative Property(order property)

• States that any two real numbers may be added in either order or multiplied in either order. The results will be the same, even though the order changes. for example:

• 2+3=3+2

• 5 x 7= 7 x 5

### 2. Associative property (grouping Property)

• This property states that in addition and multiplication, three or more real numbers can be grouped in any order. The results will be the same, even though the grouping changes.

• For example 3 x 5 x -7 can be grouped in two ways

• (3 x 5 ) x -7 or 3 x (5 x -7)

• either way you chose they both are equal to -105.

• This is Not true for subtraction and division

### 3. Distributive Property

• This property states that a real number can be multiplied over addition. for example:

• 3(5 + 2) = ( 3 x 5) + (3 x 2)

• In mathematical language, we say that 3 is distributed over the 5 and the 2.

### Identity Property

The sum of zero and any number a is a. This is known as the Identity Property for Addition.

a + 0 = a or 0 + a = a.

The Identity Property of Multiplication is the product of 1 and any number a is a.

a • 1 = a or 1 • a = a.

Or just think of what number can you add to or multiply to another number to get back the same number. Like for instance what can I add to 2 to get back 2.

2 + X = 2 .......... 2 + 0 = 2

### Zero Property

• This property states that the product of zero and any number is zero.

• a • 0 = 0 or 0 • a = 0

### The Inverse Property for Multiplication

• The product of a number and its multiplicative inverse is 1.

• A number multiplied by its reciprocal always equals 1.

• Examples: 6 and 1/6 are reciprocals. 6 • 1/6 = 1

• 4/5 and 5/4 are reciprocals. 4/5 • 5/4 = 1

• Two integers that are opposites of each other are called additive inverses.

• The Additive Inverse Property states that the sum of any number and its additive inverse is zero.

• a + (-a) = 0

• Here’s an example: 18 + (-18) = 0 18 and -18 are opposites.

### Why is this important

• It will be on the SOL

### Review

• For the next 10-15 minutes we are going to do some example problems.

• On your desk you will find 4 pieces of paper.

• Label each piece with the letter A, B, C, D.

• When I read a Question You will hold up the letter that you think is the answer.

• For instance, Once I read the question if you think the answer is A then hold up your paper with the letter A..and so on.,

### 1. 12 X 4= 4 X 12 is an example of which

• A. The Associative property

• B. The Commutative property

• C. The Distributive property

• D. None of the Above

### 2. 3(4+3) = (3 x 4) + (3 x 3)is an example of which Property

• A. The Associative property

• B. The Commutative property

• C. The Distributive property

• D. None of the Above

Is an example of which property

• A. The Associative property

• B. The Commutative property

• C. The Distributive property

• D. None of the Above

### (3 X 5) X 2= 3 x (5 X 2)is an example of what property

• A. The Associative property

• B. The Commutative property

• C. The Distributive property

• D. None of the Above

### Which of the following is an example of the Associative property.

• A (LiL Kim + Nelly)+ b2k = LiL Kim + (Nelly + B2k)

• B. MTV(BET+HBO) = (MTV X BET)+(MTV x HBO)

• C. + = +

• D. NONE OF THE ABOVE

### Which of the following is an example of the commutative property.

• A (LiL Kim + Nelly)+ b2k = LiL Kim + (Nelly + B2k)

• B. MTV(BET+HBO) = (MTV X BET)+(MTV x HBO)

• C. + = +

• D. NONE OF THE ABOVE

### Which of the following is an example of the Distributive property.

• A (LiL Kim + Nelly)+ b2k = LiL Kim + (Nelly + B2k)

• B. MTV(BET+HBO) = (MTV X BET)+(MTV x HBO)

• C. + = +

• D. NONE OF THE ABOVE

### Exit ReviewPut all notes away

• Give an example of each of the following properties:

• Associative, Commutative, distributive, and the Zero Property.

### Practice

Name the following Property

• 4+3=3+4

• 3(2+5)= (3x2)+(3x5)

• 5x0=0

• 5x1=5

• 6+0=6

• 3x4x5=3x5x4