Classifying Real Numbers and Properties of Real Numbers

Commutative Property of Multiplication

Changing the order of the factors does not change the product.

Commutative Property of Addition

Changing the order of the addends does not change the sum.

(x+y)+3=3+(x+y)

Commutative

Associative Property of Addition

Changing the grouping of three or more addends does not change the sum.

Associative Property of Multiplication

Changing the grouping of three or more factors does not change the product.

5(7xm)=(5x7)m

Associative

Identity Property of Addition

If you add zero to a number, the sum is the same as that number.

Identity Property of Multiplication

If you multiply a number by one, the product is the same as that number.

6m +0

Identity of Add

4 x 1=4

Identity of Multiply

Inverse Property of Addition

the sum of a number and its opposite is 0

Inverse Property of Multiplication

multiplying a number by its reciprocal equals one;
5 x 1/5 = 1

-10 + 10 =0

Inverse of Add

1/5 x 5 = 1

Inverse of Multiply

Property of Zero

the product of a number and 0 is 0

2m x 0= 0

Zero Property

Distributive Property

a property indicating a special way in which multiplication is applied to addition of two or more numbers in which each term inside a set of parentheses can be multiplied by a factor outside the parentheses, such as a(b + c) = ab + ac

4(3x +5)=12x + 20

Distributive

7 x ____=1

1/7

(m-n) * _____=0

0

What is the additive inverse of -2

2

What is the multiplicative identity of 5

1

Real Numbers

the set of all rational and irrational numbers

Rational Numbers

any number that can be written as a ratio of two integers

Irrational Numbers

Numbers that cannot be expressed as a ratio of two integers. Their decimal expansions are nonending and nonrepeating.

terminating decimal

A decimal that ends

repeating decimal

A decimal that repeats a digit or group of digits forever.

Integers

The set of whole numbers and their opposites

Whole Numbers

counting numbers and zero

Natural Numbers

counting numbers

-23

Real, Rational, Integer

9/2

Real, Rational

Square roots of 110

Real, Irrational

0

Real, Rational, Integer, Whole

25

Real, Rational, Integer, Whole, Natural

Natural Numbers are _______ Integers

Always

Real numbers are _______ irrational numbers

Sometimes

Repeating decimals are ________ irrational numbers

never

Reflexive Property

A value equals itself

7y=7y

Reflexive Property

Symmetric Property

If a=b, then b=a

If 4+5=9, then 9=4+5

Symmetric Property

Transitive Property

If a=b and b=c, then a=c

If 3+3=9 and 9=6+3, then 3+3=6+3

Transitive Property

True

Natural Numbers are closed under addition

False

Irrational Numbers are closed under division

0.65

R,Q

-43/0

Undefined

Square root of 4/49

Real, Rational

R

Abb. for Real

Q

Abb. for Rational

Z

Abb. for Integer

I

Abb. for Irrational

W

Abb. for Whole

N

Abb. for Natural