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.

Math Symbols

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.
  • Axiom - A statement accepted as true without proof.

B

  • Base - The term  \(\large{13a^2 }\)  has a base  \(\large{ a }\) .
  • Binary numbers - 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  \(\large{13, 7 }\) .
  • 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.
  • 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  \(\large{ 3a+4b }\)  \(\large{ ,... }\)
  • 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 - \(\large{ 5 \;x\; 5 \;x\; 5 = 125 }\) ,  \(\large{ 125 }\) 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.
  • 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

  • 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.  \(\large{ 5!=5\;x\;4\;x\;3\;x\;2\;x\;1=120 }\)  or  \(\large{ n!=\left(n+3\right) 2y\;x\;2\;x\;1=n }\)
  • 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  \(\large{ 5\;x }\) .

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.  \(\large{ 3\;x\;7 = 21 }\)  inverse is  \(\large{ \frac{21}{7}  = 3 }\) ,  \(\large{ 19 }\)  inverse is  \(\large{ -19 }\) .
  • Irrational number - A number that cannot be written as a fraction.

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  \({ [\;] }\)  or parentheses  \({ (\;) }\) .                                        \({  \begin{bmatrix} 4 & 7 & 2.54 \\ -9 & 3.1 & 3 \\ 13 & 1.2 & -9 \end{bmatrix} }\)   or   \({ \begin{pmatrix} 4 & 7 & 2.54 \\ -9 & 3.1 & 3 & \\ 13 & 1.2 & -9 \end{pmatrix}  }\)
  • Matrix addition - Matrices can be added term by term.                                                                                                                             \({  \begin{bmatrix} 4 & 7 & 2 \\ -9 & 3 & 3 \\ 13 & 1 & -9 \end{bmatrix} }\) \({\;+\;}\) \({ \begin{bmatrix} 5 & 3 & -2 \\ -4 & 6 & 2 \\ 11 & -1 & 14 \end{bmatrix}  }\) \({\;=\;}\) \({ \begin{bmatrix} 9 & 10 & 0 \\ -13 & 9 & 5 \\ 24 & 0 & 5 \end{bmatrix}  }\)
  • Matrix subtraction - Matrices can be subtracted term by term.                                                                                                                 \({  \begin{bmatrix} 4 & 7 & 2 \\ -9 & 3 & 3 \\ 13 & 1 & -9 \end{bmatrix} }\) \({\;-\;}\) \({ \begin{bmatrix} 5 & 3 & -2 \\ -4 & 6 & 2 \\ 11 & -1 & 14 \end{bmatrix}  }\) \({\;=\;}\) \({ \begin{bmatrix} -1 & 4 & 4 \\ -5 & -3 & 1 \\ 2 & 2 & -23 \end{bmatrix}  }\)
  • 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.
  • 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  \(\large{ +, -, ... }\)
  • 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

  • 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  \(\large{1, 2, 4, 7,14}\) .
  • 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  \(\large{ 0 }\) .
  • Prime factor - A factor  \(\large{13, 7 }\)  are prime numbers.  \(\large{13\;x\;7 =91 }\)
  • 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  \(\large{13a^2\;x\;7x \;x\;21=19 }\) , 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 - Numbers expressed as a ratio of two numbers like  \(\large{ \frac{3}{4} }\)  or  \(\large{ -\frac{1}{8} }\) .
  • 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.  \(\large{ 3\;x\;7 = 21 }\)  inverse is  \(\large{ \frac{21}{7}  = 3 }\) ,  \(\large{ 19 }\)  inverse is  \(\large{ -19 }\) .
  • 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 - \(\large{ 5 \;x\; 5 = 25 }\) ,  \(\large{ 25 }\) 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  \(\large{13_a^2 }\) .

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.
  • 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 \(\large{ x }\)

W

  • Whole number - Just positive numbers  \(\large{ 0, 1, 2, 3, 4, 5, 6, ... }\)  with no fractions.
Display #
Title
Matrix
Mean
Mechanical Operation
Midpoint
Multiplication Postulate
Natural Number
Number Types
Numbers
Numerator
Octal
Octal Number
Order of Magnitude
Point
Polynomial
Postulate
Prime Number
Ratio
Rational Number
Reflexive Property
Rounding
Scientific Notation
Set
Slope
Substitution Postulate
Subtraction Postulate