Properties of Real Numbers

​Properties of Real Numbers

By Brian Cox

Commutative Property

The commutative property allows us to switch the order of an expression, without changing the expressions value.

Multiplication

Addition

Commutative Property

Multiple Select

Which example(s) below illustrates the commutative property?

• $$4+\left(-3\right)+8=4+8+\left(-3\right)$$

• $$5\left(x+2\right)=5x+10$$

• $$3\left(2x\right)=\left(3\cdot2\right)x$$

• $$4\cdot9\cdot5=9\cdot4\cdot5$$

Associative Property

The associative property allows us to change the grouping of an expression without changing the expressions value.

Multiplication

Addition

Associative Property

Multiple Select

Which example(s) below illustrates the associative property?

• $$4+\left(6+3\right)=\left(4+6\right)+3$$

• $$5\left(x+2\right)=\left(x+2\right)5$$

• $$3x+24=3\left(x+8\right)$$

• $$6x\cdot3=\left(6\cdot3\right)x$$

Distributive Property

The distributive property states that the product of a number and the sum or difference of two numbers is the same as the sum or difference of their products.

​Division

Multiplication

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Multiple Select

Which example(s) below illustrates the distributive property?

• $$4\left(x+7\right)=\left(x+7\right)4$$

• $$15x+60=15\left(x+4\right)$$

• $$6\left(3x\right)=\left(6\cdot3\right)x$$

• $$\frac{4}{3}+\frac{11}{3}=\frac{4+11}{3}$$

Additive Identity Property

The additive identity of a number is the value that when added to the original value, leaves the value unchanged.

Additive Identity Property

The additive identity is 0.

Multiplicative Identity Property

The multiplicative identity of a number is the value that when multiplied by the original value, leaves the value unchanged.

Multiplicative Identity Property

The multiplicative identity is 1.

Additive Inverse Property

The additive inverse of a number is the value that when added to the original value, results in the identify value.

Additive Inverse Property

The additive inverse of a number is the opposite of the original number.

Multiplicative Inverse Property

The multiplicative inverse of a number is the reciprocal of the original number.   

Multiplicative Inverse Property

The multiplicative inverse of a number is the value that when multiplied by the original value, results in the identify value.

Categorize

Options (4)

$$4n+0=4n$$  

$$x^2\cdot1=x^2$$  

$$4y+-4y=0$$  

$$\frac{3}{8}\cdot\frac{8}{3}=1$$  

Match each example with the correct property.

Additive Identity

Multiplicative Identity

Additive Inverse

Multiplicative Inverse