properties of numbers

Number Theory and Computations

Properties of numbers

Objectives

• Identify and apply the laws of arithmetic – commutative, associative and distributive

• Identify and apply the identity and inverse of addition and multiplication

• Identify the Properties of zero

Rules of Arithmetic

• Commutative Property

• Associative Property

• Distributive Property

• Identity Prorerty

The sum and products are the same regardless of the order in which the numbers are added.  or multiplied. 

The sum and products are the same regardless of the way in which the numbers are grouped.

 

The sum of two numbers times a third number is equal to the sum of each addend times the third number. 

Addition: The sum of any number and zero is that number.

Multiplication: The product of any number and one is that number.

The sum of any integer and its additive is zero.

The product of any integer and its reciprocal is one

The product of zero and any number is zero

Multiple Choice

Drew rearranged an expression to make it easier to solve. He changed

2 + (3 + 5) to (2 + 3) + 5.

Which of the following properties tells us

that it is okay for Drew to arrange the problem that way?

• a. associative property of

  addition

• b. distributive property of

  multiplication over

  addition

• c. identity property of

  addition

• d. commutative property

  of addition

Multiple Choice

Which property is demonstrated here?

2(x + y) = 2x + 2y

• a. Associative Property

• b. Commutative Property

• c. Distributive Property

• d. Identity Property

Multiple Choice

Jennifer's family is going to a beach resort. Jennifer

bought 7 beach towels that cost $13 each to take to the resort. To find the total cost, she added the products of 7×10 7×3 for a total of $91. What property did Jennifer use?

• a. Commutative Property of Multiplication

• b. Commutative Property of Addition

• c. Associative Property of Multiplication

• d. Distributive Property

Multiple Choice

The commutative property of ADDITION states

• a. that you can multiply the factors in any order

• b. that you can divide the numbers in any order.

• c. that up can add the numbers in any order.

• d. that you can group the numbers in any order.

Multiple Choice

6 + (5 + 4) = 6 + (4 + 5) is an example of which

property?

• a. Associative property addition

• b. Commutative property of addition

• c. Identity property of addition

• d. Inverse property of addition

Multiple Choice

Which property is used in the equation below?

15(x+4)=15x+60

• a. Associative Property of Addition

• b. Commutative Property of Addition

• c. Distributive Property

• d. Reflexive Property of Equality

Multiple Choice

Which property is x ⋅ 4 = 4 . x ?

• a. Commutative Property of Addition

• b. Commutative Property of Multiplication

• c. Inverse Property of Multiplication

• d. Inverse Property of Addition

Multiple Choice

Which of the following is an example of the Commutative

Property of Addition?

• a. 7 x 51 = 51 x 7

• b. 12+ 0 = 12

• c. 57 + 32 = 32 + 57

• d. 8 (5 + 4) =

  (8 x 5) + (8 x 4)

Multiple Choice

Which of the following is an example of the distributive

property?

• a. 98 x 1= 98

• b. 3 + 92 = 95

• c. 72 + 51 = 51 + 72

• d. 6 (16 + 4) =

  (6 x 16) + (6 x 4)

Multiple Choice

Which of the following is an example of the Associative

Property of Multiplication?

• a. (2 + 4) + 5 =

  2 + (4 + 5)

• b. (3 x 4) x 5 =

  3 x (4 x 5)

• c. 52 x 4 = 4 x 52

• d. 3 + 92 = 95

Multiple Choice

Which of the following is an example of the Identity

Property of Addition?

• a. 72 + 51 = 51 + 72

• b. 3 + 92 = 95

• c. 17 + 0 = 17

• d. (2 + 4) + 5 =

  2 + (4 + 5)

Multiple Choice

Which equation illustrates the identity property of

multiplication?

• a. (xy)z = x(yz)

• b. x ⋅ 0 = 0

• c. x ⋅ 1 = x

• d. x + 0 = x

Multiple Choice

Which is an example of the Multiplication Property of

Zero?

• a. 7 x 0 = 0

• b. 0 + 1 = 1

• c. 2 x 1 = 1 x 2

• d. 3(4 x 5)

Multiple Choice

Which equation below shows a correct use of the

distributive property?

• a. 2(3 + 5) =

  (2 + 3) x (2 + 5)

• b. 2(3 + 5) = (2 x 3) + 5

• c. 2(3 + 5) = 2(5 + 3)

• d. 2(3 + 5) =

  (2 x 3) + (2 x 5)

Multiple Choice

This math property states that the sum of two addends

multiplied by a number is the sum of the product of each addend and the number.

For example: 4(1 + 3) = (4 x 1) + (4 x 3), which if you add 1 and 3 you get 4

times 4 equals 16 AND if you multiply 4 and 1 you get 4; if you multiply 4 and

3 you get 12; then add 4 plus 12 = 16. 16 = 16

• a. Divisibility Property

• b. Multiple Property

• c. Composite Property

• d. Distributive Property

Multiple Choice

Which of the following is an example of the

Multiplication Property of Zero?

• a. 4 + 0 = 4

• b. 4 x 6 = 6 x 4

• c 5 x 3 = 15

• d. 4 x 0 = 0

Multiple Choice

Which property is illustrated by 14x + 7 = 7 + 14x?

• a. Distributive Property of

  Multiplication over

  Addition

• b. Associative Property of

  Addition

• c. Commutative Property

  of Addition

• d. Inverse Property of

  Addition

Multiple Choice

Which of the following is an example of the Identity

Property of Multiplication?

• a. 4 x 6 = 24

• b. 98 x 1 = 98

• c. 52 x 4 = 4 x 52

• d. (3 x 4) x 5 =

  3 x (4 x 5)

Multiple Choice

Which of the following is an example of the Commutative

Property of Multiplication?

• a. (3 x 4) x 5 =

  3 x (4 x 5)

• b. 52 x 4 = 4 x 52

• c. 98 x 1= 98

• d. 4 x 6 = 24

Poll

How well do I understand the properties of Real Numbers?