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.

 

 

 

Mathematics Symbols

• See Algebra Symbols / Angle and Line Symbols / Basic Math Symbols / Bracket Symbols / Equivalence Symbols / Geometry Symbols / Greek Alphabet / Miscellaneous Symbols / Roman Numerals / Set Symbols / Square Root Symbols

 

Mathematics Terms

• See Geometry, Trigonometry

 

Nomenclature & Symbols for Engineering, Mathematics, and Science

• See A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z

 

Algebra Terms

• See A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z

A

• Absolute value  -  Makes a negative number positive  \(\large{ \left\vert -x \right\vert = x }\)  and positive numbers and  \(\large{ 0 }\)  are not changed.

• Addend  -  Any one of a set of terms  \(\large{ 3 + 7 = 10 }\)  to be added.  \(\large{ 3 }\)  and  \(\large{ 7 }\)  are each addends,  \(\large{ 10 }\) is the sum.

• 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 multiplied by a variable.  An equation  \(\large{13a^2+7x-21=19 }\) , the coefficients are  \(\large{13, 7 }\) .

• 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.  Series  \(\large{ 3, 6, 12, 24, ... }\)  with a common rario of 2.

• Commutative  -  When the order of the numbers do not matter.  Works for addition and multiplication but not for subtraction or division.    \(\large{ 3 + 7 = 7 + 3 }\)  or  \(\large{ 3\; x\; 7 = 7\; x\; 3 }\)

• 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 (compound 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  \(\large{ 3a+4b }\)  \(\large{ ,... }\)

• Consecutive number  -  Numbers that follow each other in order, from smallest to largest.  \(\large{ 15, 20, 25, 30, 35, ... }\)

• Constant  -  The term expressed with no variables.  An equation  \(\large{13a^2+7x-21=19 }\) , the constants are  \(\large{21, 19 }\) .

• 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  -  \(\large{ 5 \times 5 \times 5 = 125 }\) ,  \(\large{ 125 }\) 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  \(\large{ a\;b-a\;c }\) .

• Dividend  -  In a set of terms  \(\large{ 3 \div 7 = 0.43 }\)  the amount to be divided.  \(\large{ 3 }\)  is the dividend,  \(\large{ 7 }\)  is the divisor, and  \(\large{ 0.43 }\)  is the quotient.

• Divisor  -  In a set of terms  \(\large{ 3 \div 7 = 0.43 }\)  the number divided by.  \(\large{ 7 }\)  is the divisor,  \(\large{ 3 }\)  is the dividend, and  \(\large{ 0.43 }\)  is the quotient.

• 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 (index, power)  -  Is how mant times you multiply the number.  Term is \(\large{ 13a^2 }\), the exponent is \(\large{ 2 }\) .

• Expression  -  A group of terms, coefficients, constants and variables separate by an operation.  An equation  \(\large{13a^2+7x-21=19 }\) , the expressions is  \(\large{ 13a^2+7x-21 }\)  and  \(\large{ 19 }\).

F

• Factor number  -  Numbers \(\large{ 3 }\) and \(\large{ 8 }\) are factors that can be multiplied to get another number \(\large{ 24 }\) .  Equation \(\large{ 3 \times 8=24 }\)

• 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  \(\large{ n!=\left(n+3\right) 2y\cdot 2\cdot 1=n }\)

• Formula  -  An .expression used to calculate a desired result.

• Fractional Exponent  -  Is how mant times you multiply the number.  Term is \(\large{ 13a^{ \frac{2}{3} } }\), the exponent is \(\large{ \frac{2}{3} }\) .

• 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 (geometric progression)  -  Multipling the previous term by a constant.  \(\large{ 2 }\)  the sequence   \(\large{ 1, 2, 4, 8, 16, 32, ... }\)  or  \(\large{ b }\)  the sequence  \(\large{ a, ab, ab^2, ab^3, ... }\)

• Geometric series  -  A series of the terms of a geometric sequence that has a constanr ratio.  \(\large{ 1 + 2 + 4 + 8 + 16 + 32 \;+ ... }\)

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.  \(\large{ \sqrt{2} }\) ,  \(\large{ \pi=3.1415926535 ... }\) ,  \(\large{ e=2.71828182... }\)

J

K

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  \(\large{ a^2 }\)

• Line  -  A straight path between two points or multiple points.

• Linear  -  In a straight line.

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   \({ \begin{pmatrix} 4 & 7 & 2.54 \\ -9 & 3.1 & 3 & \\ 13 & 1.2 & -9 \end{pmatrix}  }\)

• Mean  -  The sum of all numbers in a set divided by the number of the values.  \(\large{ (2 + 3 + 4 + 5) / 4 = 3.5 }\)

• Minuend  -  The first number in a set of terms  \(\large{ 3 - 7 = - 4 }\)  to be subtracted.  \(\large{ 3 }\)  is the minuend,  \(\large{ 7 }\)  is the subtrahend, and  \(\large{ -4 }\)  is the difference.

• 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.

• Multiplicand  -  In a set of terms  \(\large{ 3 \times 7 = 21 }\)  the number that is multiplied.  \(\large{ 7 }\)  is the multiplicand,  \(\large{ 3 }\)  is the multiplier, and  \(\large{ 21 }\)  is the product.

• Multiplier  -  In a set of terms  \(\large{ 3 \times 7 = 21 }\)  the number that you are multiplying by.  \(\large{ 3 }\)  is the multiplier,  \(\large{ 7 }\)  is the multiplicand, and  \(\large{ 21 }\)  is the product.

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 Exponent  -  Is how mant times you multiply the number.  Term is \(\large{ 13^{-2} = \frac{1}{13^2} = \frac{1}{169} }\), the exponent is \(\large{ -2 }\)

• 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 sentence  -  An equation of numbers and operations that expresses the relationship between them.  \(\large{ 3 + 7 = 10 \;,\; 3 < 7 }\)

• 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.

• Power (exponent, index)  -  Is how mant times you multiply the number.  Term is \(\large{ 13a^2 }\), the exponent is \(\large{ 2 }\) .

• 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  -  In a set of terms  \(\large{ 3 \times 7 = 21 }\)  the multiplied answer.  \(\large{ 21 }\)  is the product,  \(\large{ 3 }\)  is the multiplier, and  \(\large{ 7 }\)  is the multiplicand.  

• Proper factor  -  Any of the factors of a number, except \(\large{1}\) or the number itself.

• Proper Fraction  -  When the numerator  \(\large{ 3 }\)  is less than the demominator  \(\large{ 8 }\)  of a fraction like  \(\large{ \frac{3}{8} }\) .

Q

• Quartile  -  One of three values that divide a data set into four equal sections.   \(\large{ 2, 4, 4, 5, 6, 7, 8 }\) , the quartiles are  \(\large{ 4 }\) (lower quartile), \(\large{ 5 }\) (middle quartile), and \(\large{ 7 }\) (upper quartile).

• Quotient  -  In a set of terms  \(\large{ 3 \div 7 = 0.43 }\)  the answer.  \(\large{ 0.43 }\)  is the quotient,  \(\large{ 3 }\)  is the dividend, and  \(\large{ 7 }\)  is the divisor.

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  \(\large{ -19 }\) .

• Remainder  -  What is left over after long division.  \(\large{ 7 \; / \;13 = 1 }\)  r \(\large{ 6 }\)

• 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

• Subtrahend  -  In a set of terms  \(\large{ 3 - 7 = - 4 }\)  the number to be subtracted.  \(\large{ 7 }\)  is the subtrahend, \(\large{ 3 }\)  is the minuend, and  \(\large{ -4 }\)  is the difference.

• Sum  -  In a set of terms  \(\large{ 3 + 7 = 10 }\)  it is the result.  \(\large{ 10 }\) is the sum, and  \(\large{ 3 }\)  and  \(\large{ 7 }\)  are each addends.

• 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.  An equation  \(\large{13a^2+7x-21=19 }\) , the terms are  \(\large{13a^2 }\) , \(\large{7x }\) , \(\large{21 }\) , and  \(\large{19 }\) .

• 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  \(\large{ 13a^2+7x-21 }\) .

U

V

• Variable  -  Letters or symbols that are used to represent unknown values that can change depending in the infomation.  An equation  \(\large{13a^2+7x-21=19 }\) , the variables are  \(\large{a, x }\) .

• 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.

X

Y

Z

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