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.
Mathematics Terms
- See Geometry, 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
Nomenclature & Symbols for Engineering, Mathematics, and Science
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List of all Site categories - List of all Tags
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. \(\large{ \sqrt{2} }\) , \(\large{ \pi=3.1415926535 ... }\) , \(\large{ e=2.71828182... }\)
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 \(\large{ 13a^2+7x-21 }\) .
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.
Z
- Zero - A whole number that is neither \(\large{ - }\) or \(\large{ + }\) and contains no value.
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