Property of Rational and Irrational Numbers

5.5 Real Numbers and Their Properties

Irrational Numbers

​An Irrational Number is a real number that cannot be written as a fraction of two integers.

Irrational Number Examples

​π=3.1415..., e=2.71828...., √3=1.732..., -√7=2.6457...

Irrational numbers have never ending decimals that do not repeat.

Real Numbers

​Real numbers are the set of numbers made up of the union of rational numbers and irrational numbers.

Real Numbers

Multiple Choice

Is a rational number a real number?

• yes

• no

Multiple Choice

Is an irrational number a real number?

• yes

• no

Multiple Choice

Is a whole number a rational number?

• yes

• no

Multiple Choice

Is a whole number a natural number?

• yes

• no

Commutative Properties for Real Numbers

Commutative Property of Multiplication
ab=ba
Commutative Property of Addition
a+b=b+a

Commutative Properties for Real Numbers

​Think Commuting to work--you travel to a different place.

Associative Properties for Real Numbers

Associative Property of Multiplication
(ab)c=a(bc)
Associative Property of Addition
(a+b)+c=a+(b+c)

Associative Properties for Real Numbers

Think of who a person associates with in a group of people. The place doesn't change but who they associate with does.
(a+b)+c=a+(b+c)

Distributive Property of Multiplication over Addition

​a*(b+c)=a*b+a*c

for any real numbers a, b, and c.

Multiple Choice

Commutative Property of Addition

• ab=ba

• a+b=b+a

• a+(b+c)=(a+b)+c

• (ab)c=a(bc)

Multiple Choice

Associative Property of Multiplication

• ab=ba

• a+b=b+a

• a+(b+c)=(a+b)+c

• (ab)c=a(bc)

Multiple Choice

Associative Property of Addition

• ab=ba

• a+b=b+a

• a+(b+c)=(a+b)+c

• (ab)c=a(bc)

Multiple Choice

Commutative Property of Multiplication

• ab=ba

• a+b=b+a

• a+(b+c)=(a+b)+c

• (ab)c=a(bc)

Multiple Choice

Choose the name of the property illustrated.

-7 + -8 = -8 + -7

• Associative Property of Addition

• Associative Property of Multiplication

• Commutative Property of Addition

• Commutative Property of Multiplication

Multiple Choice

Choose the name of the property illustrated.

$$\pi\cdot10=10\cdot\pi$$

• Associative Property of Addition

• Associative Property of Multiplication

• Commutative Property of Addition

• Commutative Property of Multiplication

Multiple Choice

Choose the name of the property illustrated.

$$5+\left(6+7\right)=\left(5+6\right)+7$$

• Associative Property of Addition

• Associative Property of Multiplication

• Commutative Property of Addition

• Commutative Property of Multiplication

Multiple Choice

Choose the name of the property illustrated.

$$5\cdot\left(13\cdot y\right)=\left(5\cdot13\right)\cdot y$$

• Associative Property of Addition

• Associative Property of Multiplication

• Commutative Property of Addition

• Commutative Property of Multiplication

Multiple Choice

Choose the name of the property illustrated.

$$5\cdot\left(13+y\right)=65+5y$$

• Associative Property of Addition

• Distributive Property of Multipication over Addition

• Commutative Property of Addition

• Commutative Property of Multiplication