Properties of Real Numbers

Properties of Real Numbers

Commutative Property

Multiple Choice

Use the commutative property to re-write the expression

$$123+x+9$$  

• $$x+9+123$$  

• $$\left(123+x\right)+9$$  

Associative Property

Multiple Choice

Which correctly applies the associative property to the expression

$$\left(x+5\right)+7$$  

• $$\left(5+x\right)+7$$  

• $$x+\left(5+7\right)$$  

• $$7+\left(5+x\right)$$  

Identity Property

Multiple Choice

Which correctly represents the identity property?

• $$x-x=0$$

• $$x+3=3$$

• $$x\cdot1=x$$

Inverse Property

Multiple Choice

Which correctly shows the inverse property?

• $$x+-x=0$$

• $$x\cdot1=x$$

• $$a+x=x+a$$

Property of Zero

Multiple Choice

Is this the property of zero?

• $$3-0=3$$

• $$6+0=6$$

• $$1-1=0$$

• $$9\cdot0=0$$

Distributive Property 

Multiple Choice

Is this a correct use of the distributive property?

$$5\left(x-8\right)=5x-8$$  

• Yes

• No

Multiple Choice

Identify the property

(a ⋅ b) ⋅ c = (c ⋅ b) ⋅ a

• commutative property of multiplication

• identity property of multiplication

• inverse property of multiplication

• associative property of multiplication

Multiple Choice

Identify the property
a + b = b + a

• Identity of addtion

• commutative of addition

• associative of addition

• symmetric

Multiple Choice

What property is this?

(n + 13) + 4 = n + (13 + 4)

• Associative Property

• Commutative Property

• Additive Identity

• Distributive Property

Multiple Choice

Which of the following is an example of the ASSOCIATIVE PROPERTY OF ADDITION?

• 11 + (8 + 3) = 11 + (3 + 8)

• (20 + 0.5) + 3 = 20 + (0.5 + 3)

• 5(7 + 2) = 5(7) + 5(2)

• 3 x (5 x 4) = (3 x 5) x 4

Multiple Choice

The Commutative Property of Addition would say
2n + 4 = _______

• 2(n + 2)

• n2 + 4

• 4 + 2n

• 2n + 4

Multiple Choice

Pick the answer that is an example of the commutative property of multiplication

• b + c + a = a + b + c

• a(b + c) = ab + ac

• a ⋅ b = b⋅ a

• a ⋅ 1 = a

Multiple Choice

This is an example of which property:

(2 ⋅ 3) 4 = 2 (3 ⋅ 4)

• Associative

• Commutative

• Inverse

• Identity

Multiple Choice

This is an example of which property:

(2 ⋅ 3) 4 = (3 ⋅ 2) 4

• Associative

• Commutative

• Inverse

• Identity

Multiple Choice

Which property says changing the order of the terms in addition or multiplication will not change the result?

• Commutative

• Associative

• Inverse

• Identity

Multiple Choice

(19 x 5) x 2 = 19 x (5 x 2)

• Associative Property of Multiplication

• Commutative Property of Multiplication

• Identity Property of Multiplication

• Associative Property of Addition

Multiple Choice

2 (x - y) = 2x - 2y

• Associative Property of Addition

• Distributive Property

• Transitive Property

• Identity Property

Multiple Choice

Which is an example of the commutative property of multiplication?

• 4 x(1 _^x 2) = (4 x 1) x 2

• 2 x 2 = 4 x 1

• 2(3) = 2(4)

• 3 x 4 = 4 x 3

Multiple Choice

Which is an example of the distributive property?

• 5 + 2 = 2 + 5

• 7(1 + b) = 7(1) + 7(b)

• y+(x+4) = (y+x)+4

• 1 x 2 x 3 = 3 x 2 x 1

When you combine like terms...

• You can only add things that are alike. Example- 2x & 7x

• You need to use the sign in front of the number to determine if the number is a positive or a negative.

How many bottles of water do you have?

How many burgers did you order?

How many bags of doritos did you get?

w= water

b=burger

d=doritos

Therefore we have 3w+2b+1d

Multiple Choice

Grab your wand. Which of the following are "Like Terms"?

• 3x & 3

• 4x & x²

• 5x & 5y

• 2x² & -3x²

Multiple Choice

$$2x^2+4x-5x^2+6$$ Simplify. Venture into the dark woods.

• $$x+6$$  

• $$x^2+6$$  

• $$-3x^2+4x\ +6$$  

• $$3x^2+4x+6$$  

Multiple Choice

$$-4+x\ -2x^2+3x+6x^2-8$$  Simplify. Avoid the strangle vines.

• $$-4$$  

• $$\$$   $$4x^{2\ }+4x-12$$  

• $$4x^2+4x+12$$  

• $$8x^2+4x+12$$  

Open Ended

Combine the Like Terms below

5x + 8 + 2x + 7

Open Ended

Combine the Like Terms below

-6x + 9 - 2x + 3