Real Number System
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
3²
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
