Algebra

Algebra is a branch of mathematics that uses letters or symbols as a place holder for unknown values or numbers.  These variables are used to represent relationships and to solve equations.  For other math terms see Geometry and Trigonometry.

Mathematic Symbols and Examples

Nomenclature & Symbols for Engineering, Mathematics, & Science

Algebra Terms

A

  • Absolute value  -  Makes a negative number positive  \(\large{ \left\vert -x \right\vert = x }\)  and positive numbers and  \(\large{ 0 }\)  are not changed.
  • Associative property  -  How you group the numbers does not matter.  \(\large{ \left(a+b\right)+c = a+\left(b+c\right) }\)  or  \(\large{ \left(a\;b\right)\;c = a\; \left(b\;c\right) }\)
  • Axes  - A horizintal number line, x-axis and a vertical number line, y-axis.  Both used on a coordinate system or graph.
  • Axiom  -  A statement accepted as true without proof.

B

  • Base  -  The term  \(\large{13a^2 }\)  has a base  \(\large{ a }\) .
  • Binary number  -  Use only the digits \(\large{ 0 }\) and \(\large{ 1 }\) .
  • Binomial  -  A polynomial with only two term  \(\large{ 13a^2+7x }\) .

C

  • Coefficient  -  A number  \(\large{13a^2+7x-21=19 }\)  multiplied by a variable having the coefficients  \(\large{13, 7 }\) .
  • Combination  -  A set of objects in which the order is not important.  \(\large{ \left(7, 21, 19\right) }\)  or  \(\large{ \left(19, 7, 21\right) }\)
  • Common demoninator  -  Two or more fractions  \(\large{ \frac{3}{8} + \frac{7}{8}}\)  that have the same denominator  \(\large{ 8 }\) .
  • Common difference  -  \(\large{ 3 }\)  is the difference between each number  \(\large{ 3, 6, 9, 12, ... }\)  in a sequence  \(\large{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, ... }\) .
  • Common factor  -  The factors of two or more numbers that have some factors that are the same (common) in each.
  • Common fraction  -  A fraction where both numbers  \(\large{ \frac{3}{4}, \frac{7}{8} }\)  top and bottom are integers.
  • Common multiple  -  Two or more numbers that have the same multiple.
  • Common ratio  -  A number multipling the previous term in a geometric sequence.
  • Commutative property  -  The moving aroung of the numbers using  \(\large{ + }\)  of  \(\large{ \times }\)  does not matter.  \(\large{ a + b = b + a }\)  or  \(\large{ a \; b = b \; a }\)
  • Complex fraction  -  A fraction where the denominator, numerator or both contain a fraction.  \(\large{ \frac{ 5 }{ \frac{7}{8} } }\) ,  \(\large{ \frac{ \frac{3}{8} }{ 9 } }\) ,  \(\large{ \frac{ \frac{3}{8} }{ \frac{7}{8} } }\)
  • Complex number  -  A combination of a real  \(\large{3, \frac{3}{4}, 13.45, -3.56, ... }\)  number and imaginary  \(\large{\sqrt{-1} = i }\)  number for a result of  \(\large{x + y\;i }\) .   \(\large{ x }\)  is the real part and  \(\large{ y }\)  is the imaginary part.
  • Composite number  -  A positive integer number  \(\large{ 4, 6, 8, 9,... }\)  that has factors other than  \(\large{ 1 }\)  and the number itself.
  • Compute  -  To compute  \(\large{ 3-2 }\)  is to figuring out the answer  \(\large{ 1 }\) .
  • Conjugate  -  Is when you change the sign.  from  \(\large{ a+b }\)  to  \(\large{ a-b }\),  from  \(\large{ 3a-4b }\)  to  \(\large{ 3a+4b }\)  \(\large{ ,... }\)
  • Constant  -  An expression  \(\large{13a^2+7x-21=19 }\) , the term expressed with no variables  \(\large{21, 19 }\) .
  • Counting Number  -  Any number used to count things  \(\large{ 1, 2, 3, 4, 5, 6,... }\)  excluding  \(\large{ 0 }\) , negative numbers, fractions or decimals.
  • Cube number  -  \(\large{ 5 \cdot 5 \cdot 5 = 125 }\) ,  \(\large{ 125 }\) is the cube number.
  • Cube root  -  \(\large{ ^3\sqrt{125} = 5 }\) ,  \(\large{ 5 }\) is the cube root.

D

  • Decimal number  -  Based on 10 digits.  \(\large{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }\)
  • Denominator  -  The number of equal parts of the whole is  \(\large{ 8 }\) , fraction is  \(\large{ \frac{3}{8} }\) .
  • Digit  -  A numeral  \(\large{ 2119 }\)  has digits  \(\large{ 2, 1, 1, }\)  and  \(\large{ 9 }\)
  • Disjoint event (mutually exclusive)  -  Events that have no outcomes in common.
  • Distributive property (distribution)  -  Multiply the parts of an expression  \(\large{ a \left(b-c \right) }\)  into another expression  \(\large{ a\;b-a\;c }\) .
  • Domain of a function  -  A set of values for the independent variable that makes the function work.

E

  • Element  -  Anything contained in a set.
  • Engineering notation  -  A way of writing large numbers  \(\large{ 1 2 3, 0 0 0 }\)  into smaller numbers  \(\large{ 1 2 3 \cdot 10^3 }\)  where the power of 10 is multiplied by 3.
  • Equation  -  \(\large{ 13a^2+7x-21=19 }\)
  • Exponent (also called index or power)  -  Is how mant times you multiply the number.  Term is \(\large{ 13a^2 }\), the exponent is \(\large{ 2 }\)
  • Expression  -  A group  \(\large{ 13a^2+7x-23 }\)  of terms, coefficients, constants and variables separate by an operation.

F

  • Factor number  -  Numbers \(\large{ 3 }\) and \(\large{ 8 }\) are factors that can be multiplied to get another number \(\large{ 24 }\) .  Equation \(\large{ 3\;x\;8=24 }\)
  • Factoring  -  Factor \(\large{ 7 \left(x-3\right) }\) expand to  \(\large{ 7x-21 }\)  or expressed as  \(\large{ 7 \left(x-3\right) = 7x-21 }\)
  • Factorial  -  The symbol is  \(\large{ ! }\) .  Multiply all whole numbers from the chosen number down to 1.  \(\large{ 5!=5\cdot 4\cdot 3\cdot 2\cdot 1=120 }\)  or  \(\large{ n!=\left(n+3\right) 2y\cdot 2\cdot 1=n }\)
  • Fraction  -  A part  \(\large{ \frac{3}{8} }\)  of the whole.
  • Function  -  A relationship where a set of inputs (domain) determine a set of possible outputs (range).  The function of  \(\large{ f \left( x \right) = 5\;x }\)  is  \(\large{ f \left( x \right) }\) , the function name is  \(\large{ f }\) , the input value is  \(\large{ \left( x \right) }\) , and the output is  \(\large{ 5\;x }\) .

G

  • Geometric mean  -  Two  numbers  \(\large{ a }\)  and  \(\large{ b }\)  is the number  \(\large{ c }\)  whose square equals the product  \(\large{ c^2 = a\;b }\) .
  • Geometric sequence  -  Multipling the previous term by a constant.  \(\large{ 2 }\)  the sequence   \(\large{ 1, 2, 4, 8, 16, 32, ... }\)  or  \(\large{ b }\)  the sequence  \(\large{ a, ab, ab^2, ab^3, ... }\)

H

  • Hexadecimal number  -  Based on the number 16.  \(\large{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F }\)

I

  • Imaginary number  -  A number  \(\large{ i }\)  (imaginary symbol) when squared gives a negative number  \(\large{ i^2 = -1}\)  or  \(\large{\sqrt{-1} = i }\) .
  • Improper fraction  -  A fraction  \(\large{ \frac{21}{7} }\)  that has a larger numerator than denominator.
  • Integer number  -  A whole numbers that can be either positive or negative  \(\large{ ... , -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ... }\)  with no fractions.
  • Inverse (reciprocal)  -  Reverses the effect of another number.  \(\large{ 3\cdot 7 = 21 }\)  inverse is  \(\large{ \frac{21}{7}  = 3 }\) ,  \(\large{ 19 }\)  inverse is  \(\large{ -19 }\) .
  • Irrational number  -  A number that cannot be written as a fraction.  \(\large{ \sqrt{2} }\) ,  \(\large{ \pi=3.1415926535 ... }\) ,  \(\large{ e=2.71828182... }\)

L

  • Like terms  -  These are terms where the variables are the same.  The terms are  \(\large{ 13a^2, 3a^2, -3a^2 }\), the like terms are \(\large{ a^2 }\)  or the terms are  \(\large{ 13a^2 + 3a^2 + -3a^2 }\) , the like terms are  \(\large{ 13a^2 }\)

M

  • Matrix  -  A rectangular or square array of numbers using either brackets  \(\large{ [\;] }\)  or parentheses  \(\large{ (\;) }\) .                                        \({  \begin{bmatrix} 4 & 7 & 2.54 \\ -9 & 3.1 & 3 \\ 13 & 1.2 & -9 \end{bmatrix} }\)   or   \({ \begin{pmatrix} 4 & 7 & 2.54 \\ -9 & 3.1 & 3 & \\ 13 & 1.2 & -9 \end{pmatrix}  }\)
  • Mixed number  -  A number written as  \(\large{13 \frac{3}{8} }\)  a whole number  \(\large{13 }\) and a fraction  \(\large{ \frac{3}{8} }\) .
  • Monomial  -  A polynomial with only one term  \(\large{ 13a^2 }\) .
  • Mutually Exclusive (disjoint event)  -  Events that have no outcomes in common.

N                                                   

  • Natural number  -  Can be either counting numbers  \(\large{ 1, 2, 3, 4, 5, 6, ... }\)  or whole numbers  \(\large{ 0, 1, 2, 3, 4, 5, 6, ... }\) .
  • Negative number  -  It is the oposite of a whole number  \(\large{ ... , -5, -4, -3, -2, -1 }\)  or decimal number excluding  \(\large{ 0 }\) .
  • nth root  -  Some number  \(\large{ n }\)  used as  \(\large{ ^n\sqrt{a} }\) .
  • Number line  -  Every point on a line represents a real number.
  • Number properties  -  Associative, communitive, and distributive
  • Number types  - digits, fractional number, integer number, irrational number, natural number, numeral, rational number, real number, transcendental number, and whole number
  • Numeral  -  A single symbol to make a numeral like  \(\large{ 2119 }\) .
  • Numerator  -  The number of parts is  \(\large{ 3 }\), fraction is  \(\large{ \frac{3}{8} }\) .

O

  • Octal number  -  \(\large{ 0, 1, 2, 3, 4, 5, 6, 7 }\)
  • Operator  -  A symbol such as  \(\large{ +, -, ... }\)
  • Order of operation  -  Parenthese (inside), exponents, multiplication and division (left to right), addition and subtraction (left to right)
  • Ordered pair  -  Two numbers  \(\large{ \left(7, 21\right) }\)  or  \(\large{ \left(x, y\right) }\)  written in a certain order.
  • Ordered triple  -  Three numbers  \(\large{ \left(7, 21, 19\right) }\)  or  \(\large{ \left(x, y, z\right) }\)  written in a certain order.
  • Ordered n  -  Multiple numbers  \(\large{ \left(7, 14, 21, ..., x_n\right) }\)  or  \(\large{ \left(x_1, x_2, x_3, ...,x_n\right) }\)  written in a certain order.

P

  • Partial fraction  -  A fraction  \(\large{\frac{3a^2-7x}{13a^2+7x-21} }\)  that is broken into one or more smaller parts \(\large{\frac{a}{7x} + \frac{9}{4+x}  }\) .
  • Perfect number  -  A whole number that is equal to the sum of its positive factors except the number itself.  \(\large{1+2+4+7=14}\) ,  \(\large{14}\) is a perfect number because the positive factors are  \(\large{1, 2, 4, 7,14}\) .
  • Permutation  -  A set of objects in which the order is important.  \(\large{ \left(7, 21, 19\right) }\)
  • Polynomial  -  The sum of two or more terms.  A term can have constants, exponents and variables, such as  \(\large{ 13a^2 }\) .  Put them together and you get a polynomial.
    • Monomial  -  1 term  \(\large{ 13a^2 }\)
    • Binomial  -  2 terms  \(\large{ 13a^2+7x }\)
    • Trinomial  -  3 terms  \(\large{ 13a^2+7x-21 }\)
  • Porportional  -  When the ratio of two variables are constant.
  • Positive number  -  A counting number  \(\large{ 1, 2, 3, 4, 5, 6,... }\)  or decimal number excluding  \(\large{ 0 }\) .
  • Postulate  -  A statement that is assumed true without proof.
  • Prime factor  -  A factor  \(\large{13, 7 }\)  are prime numbers.  \(\large{13\cdot 7 =91 }\)
  • Prime number  -  A number that can be divided evenly only by  \(\large{1}\) , or itself and it must be a whole number greater than \(\large{1}\) .
  • Product  -  When two or more values are multiplied togeather  \(\large{13a^2\cdot 7x \cdot 21=19 }\) , the product is  \(\large{19 }\) .
  • Proper factor  -  Any of the factors of a number, except \(\large{1}\) or the number itself.

R

  • Radical  -  An expression  \(\large{ 13a^2+7x-23 }\)  that is a root  \(\large{ \sqrt{13a^2+7x-23} }\) .  The length of the bar  \(\large{ \sqrt{13a^2}+7x-23 }\)  tells how much of the expression is used.
  • Radicand  -  The number under the symbol \(\large{ \sqrt{x} }\)
  • Rational number  -  Any number that can be expressed as a ratio (fraction) of two integers numbers.  \(\large{ 0=\frac{0}{1} }\) ,  \(\large{ 0.125=\frac{1}{8} }\) , \(\large{ 1.5=\frac{3}{2} }\)
  • Real number  -  Any number  \(\large{3, \frac{3}{4}, 13.45, -3.56, ... }\)  that is normally used.
  • Reciprocal (inverse)  -  Reverses the effect of another number.  \(\large{ 3\cdot 7 = 21 }\)  inverse is  \(\large{ \frac{21}{7}  = 3 }\) ,  \(\large{ 19 }\)  inverse is  \(\large{ -19 }\) .
  • Repeating decimal  -  A decimal that keeps recurring over and over.  \(\large{ 0.\overline{33} }\)
  • Rounding  -  Replacing a number  \(\large{ 3.1415926535 ... }\)  with another number having less digits  \(\large{ 3.1415 }\) .

S

  • Scalar number  -  Any single real number  \(\large{3, \frac{3}{4}, 13.45, -3.56, ... }\)  used to measure.
  • Scientific notation  -  A way of writing large numbers  \(\large{ 1 2 3 4 5 6 7 8 . 9 }\)  into two part  \(\large{ 1 2 3 4 5 . 6 7 8 9 \;x\; 10^3 }\) .
  • Series  -  The sum of the terms of a sequence.  \(\large{ 1, 2, 3, 4, 5, 6, ... }\) or \(\large{ 1 + 2 + 3 + ... +\; n }\)
  • Set  -  A group of numbers, variables, or really anything written using \(\large{ (\; ) }\) or \(\large{ [\; ] }\) .
  • Significant digits  -  \(\large{ 1 2 3 0 }\)  Digits that are meaningful.  \(\large{ 0 . 0 1 2 3 0 }\)
  • Square number  -  \(\large{ 5 \cdot 5 = 25 }\) ,  \(\large{ 25 }\) is the square number.
  • Square root  -  \(\large{ \sqrt{25} = 5 }\) ,  \(\large{ 5 }\) is the square root.
  • Subscript  -  A small letter or number lower than the normal text  \(\large{13_a^2 }\) .
  • Subset  -  A  \(\large{\left( 3, 4, 5 \right) }\)  is a subset of B  \(\large{\left( 1, 2, 3, 4, 5, 6, 7, 8, 9 \right) }\) .
    • Empty Set - \(\large{ (\; ) }\)  is a  subset of B
  • Superscript  -  A small letter or number higher than the normal text  \(\large{13_a^2 }\) .
  • Surd  -  A square root  \(\large{\sqrt{2} }\)  that can not be simplified by removing the square root \(\large{\sqrt{2} }\) .  \(\large{\sqrt{4} }\) can be simplified to \(\large{2 }\) .

T

  • Terms  -  Either a single number, a variable, or numbers and variables  \(\large{ 13a^2, 7x, 21 }\)  of an expression  \(\large{ 13a^2+7x-23 }\) .
  • Theorem  -  A true statement that can be proven.
  • Transcendental number  -  A real number that cannot be the root of a polynomial equation with rational coefficients.  pi, e, Euler's constant, Catalan's constant, Liouville's number, Chaitin's constant, Chapernowne's number, Morse-Thue's number, Feigenbaum number
  • Trinomial  -  A polynomial with only three term  \(\large{ 13a^2+7x-21 }\) .

V

  • Variable  -  Letters or symbols that are used to represent unknown values that can change depending in the infomation.  The variables are \(\large{ a }\) and \(\large{ x }\)
  • Vinculum  -  A line that is part of an expresson  \(\large{ \sqrt{a+b} }\)  or  \(\large{ \frac{a+b}{a-b} }\)  to show everything above or below the line is one group.

W

  • Whole number  -  Just positive numbers  \(\large{ 0, 1, 2, 3, 4, 5, 6, ... }\)  with no fractions.

Z

  • Zero  - A whole number that is neither  \(\large{ - }\)  or  \(\large{ + }\)  and contains no value. 

 

Display #
Title
Algebraic Expression
Algebraic Properties
Algorithm
Arithmetic Expression
Arithmetic Sequence
Associative Property
Axiom
Between
Binomial
Brute Force Algorithm
Commutative Property
Distributive Postulate
Engineering Notation
Function
Hexadecimal
Hexadecimal Color
Hexadecimal Number
Horizontal Line
Imaginary Number
Inequality
Infinity
Integer Number
Irrational Number
Line
Matrix