Real Number System

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Associative Property of Multiplication

(a x b) x c= a x (b x c)

Associative Property of Addition

(a+b)+c=a+(b+c)

Rational, integer

-13

Rational

-2.6

The square root of 10* the square root of 16/the square root of 5

-2the square root of 5/5

Rational, integer

-√4

Integers

...-4, -3, -2, -1, 0, 1, 2, 3, 4... All positive and negative numbers, plus the zero BUT NO FRACTIONS OR DECIMALS!

Rational, integer, whole

0

Whole numbers

0, 1, 2, 3, 4, 5,... Remember "whole" has what looks like a "zero" in the middle of the word.

Natural numbers

1, 2, 3, 4, 5,.... Sometimes called "counting numbers" (Think of your fingers)

5 square root 2* The square root of 2

10

The Square root of 200

10Squareroot2

3 Square root of 63* the square root of 4

18 square root 7

1/2 Square root of 112

2 square root 7

Rational

2/3

Simplify: The Square root of 36 over 81

2/3

Rational, integer, whole

25/5

Rational

3/5

the square root of 48

4 the square root of 3

The square root of 32/50

4/5

a=3 b=4 c=?

5=C

8 square root 13/19

8 square root 15/3

Repeating Decimal

A decimal in which a pattern of one or more digits is repeated indefinitely

Terminating Decimal

A decimal that ends

Bar Notation

A line that is used in a repeating decimal to indicate the digits that repeat

Imaginary Numbers

A number that when squared it gives a negitive result

Perfect Square

A number whose square root is a rational number

The Closure Property

A set of numbers is closed (under an operation) if and only if the operation on two of the numbers of the set produces another number of the set. If a number outside the set is produced, then the set is not closed.

Irrational numbers

Any number that CAN NOT be written as a fraction (non-terminating, non-repeating decimal numbers).

Rational numbers

Any number that can be expressed as a ratio of two integers

Ratonal numbers

Any number that can be written as a fraction (a/b) where b is not zero. This includes all terminating or repeating decimal numbers.

Natural numbers

Counting numbers

Whole numbers

Counting numbers and zero

True or False: All integers are whole numbers.

False

True or False: The number .262662666266662... is a rational number.

False

True or False: Zero is an irrational number.

False

-46, -30, 167, 3,208

Integers, rational numbers, real numbers

The square root of 28

Irrational

π, √2, √5,√10

Irrational numbers, real numbers

Integers

Negitive and positive natural numbers

Irrational numbers

Nonrepeating, nonterminating decimals

Whole Numbers

Numbers from 0 and up

Natural Numbers

Numbers from 1 and up. NO ZERO

Rational Number

Numbers that can be written as a fraction

rational

Numbers that can be written as a fraction. Includes decimals that end or repeat

irrational

Numbers that can't be written as a fraction. Includes decimals that don't end or repeat

Irrational Numbers

Numbers that cannot be expressed as a terminating or repeating decimal

whole

Only positive whole numbers and zero

integers

Positive and negative whole numbers and zero

-54 over 19

Rational

The square root of 10.24

Rational

0, 1/2, 52.324, 32, 3¾

Rational numbers, real numbers

The negitive square root of 64

Rational, Integer

Product property

Square root of 400. Square root of 4*100. square root of 4* the square rooot of 100

The Square root of 20/4

Square root of 5/2

Period

The series of numbers that repeat in a repeating decimal

Real numbers

The set of all rational and irrational numbers

Real Number

The set of rational numbers and the set of irrational numbers

Quotient Property

The square root of 1/2. The Squaure root of 1 / The square root of 2

True or False: All rational numbers are real numbers.

True

True or False: All whole numbers are integers.

True

Integers

Whole numbers and their opposites

non-repeating decimal

a decimal that doesn't end or repeat. Type of irrational number

terminating decimal

a decimal that ends; type of rational number

non terminating decimal

a decimal the never ends and goes on forever; type of irrational number

identity element

a number that will not change the original number

Multiplicative Inverse Property

a x 1/a=1

Multiplicative Identity Property

a x 1=a

Commutative Property of Multiplication

a x b=b x a

Distributive Property

a(b+c)=ab+ac / a(b-c)=ab-ac

Additive Inverse Property

a+-a=0

Additive Identity Property

a+0=a

Commutative Property of Addition

a+b=b+a

whole numbers

all positive integers (including zero)

natural numbers

all positive integers (not including zero)

counting number

all the whole numbers from 1 and on - does not include zero

integer

all the whole numbers, including zero and their negatives

integers

all whole numbers (both positive and negative) and zero

natural number

also called counting numbers - include all whole numbers from 1 on

identity

an equation that is true no matter what values are chosen

multiplicative identity

any number times one equals that number (Nx1=N)

associative property

changing the grouping does not change their sum or product; (a+b)+c= a+(b+c)

commutative property

changing the order of the numbers does not change their sum or product; a+b= b+a

repeating decimal

decimal in which a number or group of numbers continues to repeat. represented as a bar over the repeating numbers

Pi

example of an irraational number because it cannot be expressed as a fraction, a terminating decimal or repeating decimal

-13.2894...

irrational

-9.876.....

irrational

-√2

irrational

0.8976321...

irrational

2.3987432...

irrational

3.14... (pi)

irrational

4.72384...

irrational

pi

irrational

|√7|

irrational

√12

irrational

√40

irrational

√5

irrational

1, 39, 42, 608

natural numbers, whole numbers, integers, rational numbers and real numbers.

rational number

number set including all numbers that can be written as a fraction where the denoninator is not equal to zero

irrational number

number set that includes numbers that cannot be expressed as a fractions; non terminating decimals

real number

number set that includes rational and irrational numbers

rational numbers

numbers that can be expressed as a ratio or fraction

irrational numbers

numbers that can not be expressed as a ratio or fraction

inverse

operations that undo each other

multiplicative property of zero

product of any number and zero is zero (a x 0=0)

(-3)³

rational

-0.165

rational

-3

rational

-|-9|

rational

-|9.1|

rational

-√16

rational

1.8

rational

1.888...

rational

1/4

rational

12.14

rational

14÷3

rational

2/3

rational

3.4

rational

rational

4.3

rational

7/9

rational

8.6

rational

8/5

rational

|5| - 3

rational

½

rational

¾

rational

√36

rational

The Square root of 3/4

square rooot of 3 / 2

distributive property

terms in an expression can be expanded to form an equivalent expression; a (b+c)= ab + ac

Radicand

the expression that is under the radical sign

reciprocal

the inverse of the numerator and denominator in a fraction; when multiplied by the original fraction, it results in a product that equals one

Principal Square Root

the non-negitive square root of a number. Radical:a square root sign

additive inverse

the opposite of a number that will make a sum of zero

real numbers

the set of numbers that includes rational and irrational numbers

additive identity

the sum of any number and zero will equal the same number

whole number

zero and all the counting numbers from 1 and on

Irrational

π

Irrational

√17

Irrational

√3

Rational, integer, whole

√49


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