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ALGEBRA
a systematic study of numbers and their relationships, using specific rules. you use variables and formulas or equations involving those variables to solve problems
Real Numbers
Include natural or counting numbers, whole numbers, integers, positive and negative whole numbers, rational and irrational numbers.
Imaginary Numbers
Numbers that result in a negative number when squared
Letter I
Imaginary number is Denoted by
Rational Number
numbers that can be expressed as the ratio of two integers
Rational Number
may be terminating and non terminating
Irrational numbers
numbers that cannot be expressed as ratio of two integers. non terminating; have decimal representations that continue forever and do not repeat
Integers
consist of positive and negative whole numbers, and zero
Whole Numbers
all positive integers plus zero
Natural Numbers
also called counting numbers
Commutative property for addition
a + b = b + a or 7 + 3 = 3 + 7
Commutative property for multiplication
a x b = b x a or 5x6=6x5
Associative property for addition
(a+b) + c = a+(b+c)
When you have more than two numbers to multiply,the way you group them in pairs does not matter. Example: (2+3)+4 = (5)+4 = 9,and 2+(3+4)=2+(7) =9
Associative property for multiplication
(a·b)c = a(b·c)
When you have more than two numbers to multiply, the way you group them
in pairs does not matter. Example: (2·3)·4 = (6)·4 = 24, and 2·(3·4) = 2·(12) = 24
Identity property for addition
the sum of zero and any number is that number
a+0=a
Identity property for multiplication
the product of 1 and any number is that number
ax1=a
Inverse Property for addition
a+(-a)=0
Inverse Property of Multiplication
a x 1/a = 1
Zero product property
when the product of two or more factors is zero, one of these factors must equal zero
Zero product property
if ab=0, then a=0 or b=0
Multiplicative Property of Zero
The product of any number and zero is zero.
a*0=0
Distributive Property
a(b + c) = ab + ac
Reflexive property
A quantity is congruent (equal) to itself. a = a
Symmetric Property
if a=b, then b=a
Transitive Property
If a=b and b=c, then a=c
1
any number raised to 0 is equal to
undefined
any number divided by 0 is
Inequality
is a relationship between two expressions or values that are not equal to each other.
Converse Property
if we flip the number, we have to flip the inequality symbol also.
Prime Number
can be divided evenly only by 1 and by itself
Composite Number
can be divide by at least one number other than 1 and itself
Monomial
A single term
Polynomial
A combination of monomials through addition or subtraction
Binomial
Two terms
Trinomial
Three terms
Ordinal Numbers
State position of individual objects in a sequence. (1st. 2nd. 3rd)
Cardinal Numbers
count objects in a given collection
Perfect Numbers
equal to the sum of all its possible divisors except the number itself. ( ex. 6 is divisible by 1,2, and 3; when you add 1,2, and 3, you get 6)
Notation
the writing down of figures to express a number
Numeration
the reading of the number or collection of figures already written
Divergent Series
Sequence of numbers where the succeeding term is greater than the preceding term; series does not have a limit
Convergent Series
Sequence of numbers where the succeeding term is less than the preceding term, series has a limit.
Difference
Minuend minus the subtrahend
Quotient
Dividend Divided by the divisor
Mean
the average; found by adding all numbers in the data set and then dividing by the number of values in the set.
Median
the middle value when a data set is ordered from least to greatest.
Mode
The number that occurs most often in a data set.
6 significant digits
how many significant digits - 898.753
6 significant digits
how many significant digits - 79.0063
2 significant digits
how many significant digits - 0.0024
5 significant digits
how many significant digits - 600.00
3 Significant Digits
how many significant digits - 0.00800
4 Significant Digits
how many significant digits - 7060
2 Significant Digits
how many significant digits - 560
Not Significant
Trailing zeros in a whole number with no decimal is __
Least Common Multiple
the lowest possible number that can be divisible by both numbers
least Common denominator
The smallest number that can be a common denominator for a set of fractions
Greatest Common Factor
the greatest number among all the common factors of the given numbers.
70
LXX
800
DCCC
900
CM
1001
MI
52
LII
80
LXXX
386
CCCLXXXVI
4
IV
408
CDVIII
990
CMXC
1000
M
501
DI
654
DCLIV
162
CLXII
386
CCCLXXXVI
Yotta
10^24
Zetta
10^21
Exa
10^18
Peta
10^15
Tera
10^12
Giga
10^9
Mega
10^6
Kilo
10^3
Hecto
10^2
Deka
10^1
Deci
10^-1
Centi
10^-2
Milli
10^-3
Mikro
10^-6
Nano
10^-9
Piko
10^-12