Properties of Numbers

Properties of Numbers

By Kevvin Hankins

Properties of Real Numbers

Properties of Numbers

OBJ: To recognize the properties of equality and identity properties.

Equivalent Expressions

Commutative Property

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Multiple Choice

Use the commutative property to re-write the expression

$$123+x+9$$  

• $$x+9+123$$  

• $$\left(123+x\right)+9$$  

Definitions associated with the Identity Properties of Addition & Multiplication

Additive Identity is zero

Multiplicative Identity is one

Associative Property

Multiplicative Inverse is also called the Reciprocal of a number.

Multiple Choice

Which correctly applies the associative property to the expression

$$\left(x+5\right)+7$$  

• $$\left(5+x\right)+7$$  

• $$x+\left(5+7\right)$$  

• $$7+\left(5+x\right)$$  

Multiple Choice

Name the property shown

$$4\ +5\ =\ 5\ +\ 4$$  

• Commutative Property of Addition

• Associative Property of Addition

• Additive Inverse

• Additive Identity

Identity Property

Multiple Choice

Name the property shown

$$23\ +\ 0\ =\ 23$$  

• Commutative Property of Addition

• Associative Property of Addition

• Additive Inverse

• Additive Identity

Multiple Choice

Which correctly represents the identity property?

• $$x-x=0$$

• $$x+3=3$$

• $$x\cdot1=x$$

Multiple Choice

Name the property shown

$$3+\ \left(4\ +\ 5\right)\ =\ \left(3\ +\ 4\right)\ +5$$  

• Commutative Property of Addition

• Associative Property of Addition

• Additive Inverse

• Additive Identity

Inverse Property

Multiple Choice

Name the property shown

$$7\ +\ \left(-7\right)=0$$  

• Commutative Property of Addition

• Associative Property of Addition

• Additive Inverse

• Additive Identity

Multiple Choice

Which correctly shows the inverse property?

• $$x+-x=0$$

• $$x\cdot1=x$$

• $$a+x=x+a$$

Property of Zero

Multiple Choice

Name the property shown

$$23\times0=0$$  

• Commutative Property of Multiplication

• Associative Property of Multiplication

• Multiplication Property of Zero

• Multiplicative Identity

Multiple Choice

Name the property shown

$$3\left(3x\ -\ 8\right)\ =\ 9x\ -\ 24$$  

• Commutative Property of Addition

• Distributive Property

• Additive Inverse

• Multiplicative Inverse

Multiple Choice

Is this the property of zero?

• $$3-0=3$$

• $$6+0=6$$

• $$1-1=0$$

• $$9\cdot0=0$$

Multiple Choice

Name the property shown

$$8\times1=8$$  

• Commutative Property of Multiplication

• Associative Property of Addition

• Multiplicative Inverse

• Multiplicative Identity

Distributive Property 

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Multiple Choice

Name the property shown

$$5\times3\times2=2\times5\times3$$  

• Commutative Property of Addition

• Associative Property of Addition

• Commutative Property of Multiplication

• Distributive Property

Multiple Choice

Is this a correct use of the distributive property?

$$5\left(x-8\right)=5x-8$$  

• Yes

• No

Multiple Choice

Name the property shown

$$3\left(7\times5\right)=\left(3\times7\right)\times5$$  

• Commutative Property of Multiplication

• Associative Property of Addition

• Additive Inverse

• Associative Property of Multiplication