Properties of Real Numbers

Properties of Real Numbers

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Commutative Property

Multiple Select

Put a check next to the equations that show the Commutative Property.

• 
  

  $$1+2=2+1$$
  

• $$3\bullet4=4\bullet3$$

• $$1+\left(2+3\right)=1+\left(3+2\right)$$

• $$1+\left(2+3\right)=\left(1+2\right)+3$$

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 Select

Mark the equations that show the Associative Property.

• $$7+\left(8+9\right)=\left(7+8\right)+9$$  

• $$3\bullet4=4\bullet3$$

• $$1\bullet\left(2\bullet3\right)=1\bullet\left(3\bullet2\right)$$

• $$1\bullet\left(2\bullet3\right)=\left(1\bullet2\right)\bullet3$$

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?

• $$x-x=0$$

• $$x+3=3$$

• $$x\cdot1=x$$

Multiple Select

Mark the equations that show the Identity Property.

• $$\frac{10}{10}=1$$

• $$10-10=0$$

• 
  

  $$10\bullet1=10$$
  

• $$10+0=10$$

Inverse Property

Multiple Select

Mark the equations that show the Inverse Property.

• $$1+\left(-1\right)=0$$

• 
  

  $$-4+4=0$$
  

• $$\frac{3}{4}\bullet\frac{3}{4}=1$$

• $$2\bullet\frac{1}{2}=1$$

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

Properties of Equality

How can you keep an equation balanced?

​Properties of Equality

Addition Property of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Division Property of Equality

Multiple Choice

Name the property shown

$$4\ +5\ =\ 5\ +\ 4$$  

• Commutative Property of Addition

• Associative Property of Addition

• Additive Inverse

• Additive Identity

Multiple Choice

Name the property shown

$$23\ +\ 0\ =\ 23$$  

• Commutative Property of Addition

• Associative Property of Addition

• Additive Inverse

• Additive Identity

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

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

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

Name the property shown

$$8\times1=8$$  

• Commutative Property of Multiplication

• Associative Property of Addition

• Multiplicative Inverse

• Multiplicative Identity

Match

Match the following

• Addition Property of Equality

• Subtraction Property

  of Equality

• Multiplication Property

  of Equality

• Division Property of Equality

The two sides stay equal with the same amounted is added to each side.

The two sides stay equal when the same amount is subtracted from both sides.

The two sides stay equal when both sides are multiplied by the same amount.

The two sides stay equal when both sides are divided by the same amount.

• The two sides stay equal with the same amounted is added to each side.

• The two sides stay equal when the same amount is subtracted from both sides.

• The two sides stay equal when both sides are multiplied by the same amount.

• The two sides stay equal when both sides are divided by the same amount.

Match

Match the following equations with the property it illustrates.

• $$3x-1+1=4+1$$  

• $$9x+2-2=5-2$$  

• $$2\times\frac{x}{2}=-4\times2$$  

• $$\frac{5x}{5}=\frac{15}{5}$$  

Addition Property of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Division Property of Equality

• Addition Property of Equality

• Subtraction Property of Equality

• Multiplication Property of Equality

• Division Property of Equality

Multiple Choice

Which justification is missing?

• Addition Property of Equality

• Subtraction Property of Equality

• Multiplication Property of Equality

• Division Property of Equality

Multiple Choice

Which justification would be used for STEP 2?

• Addition Property of Equality

• Subtraction Property of Equality

• Multiplication Property of Equality

• Division Property of Equality