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A B C DE F G H I J K LM N O P[More words: Q-Z]

absolute value

The number of units a number is from zero on the number line (expressed as a positive value)

Adding the same number to both sides of an equation results in two sides that remain equal

Two numbers that are opposites of each other on the number line; their sum is zero, the identity element:  a + (-a) = 0, or 3 + (-3) = 0

    Mathematics that uses letters and numbers.

algebraic expression

A combination of variables and numbers, and at least one operation: 4x + 3y — 15

     The rule that allows the addition of the same list of terms or multiplication of the
     same list of factors in different groupings to result in the same answer.  For example,
     in multiplication of factors  [(3)(4)](2) = (3)[(4)(2)]; and in addition of terms
     (2 + 4) + 3 = 2 + (4 + 3)

base

The number used as a factor: In 15², 15 is the base.

A polynomial with two terms: 11x + 3

The number factor part of a variable term: In the term -10x, -10 is the coefficient. In the term x, 1 is understood to be the coefficient.

To use the rules for adding integers to group terms of exactly the same variables and exponents in order to simplify an expression. In the expression 3x² + 4xy –10x² + 5xy, the 3x² and –10x2 variable terms combine to –7x², and the 4xy and 5xy terms combine to 9xy, so that the whole expression simplifies to –7x² + 9xy

A term in an expression or equation that contains is a real number only and no variable:
In 5x + 10, 10 is a constant term

counting numbers

The set of positive, whole numbers beginning with 1.  Written as {1, 2, 3, . . .}

The solution or answer to a subtraction problem.  The difference of 19 and 21 is -2.

The sum of two addends and a number equals the product of each addend and the number. The converse is true also.
For example: a ( b + c) = ab + ac and ab + ac = a ( b + c).
Using numbers: 3( 4 + 6) = 3(4) + 3(6) and 3(4) + 3(6) = 3( 4 + 6)

A number is divisible by another number if the quotient gives a whole number and the remainder is zero. For example: 120 is divisible by 4, since the quotient is 30 and the remainder is 0.

A mathematical sentence that contains an equal sign (=).
For example: –7x² + 9x = 6

To calculate the value of an expression by substituting variables with given or known numerical values. For example: If a=2 and b = -1, then a + b will be substituted in the expression as (2) + (-1) and the sum will be evaluated as 1.

expanded notation or factored form

A variable term written as a product of prime numbers and variables. For example: 24x² written in expanded or factored form is (2)(3)(4)(x)(x)

The number of times a base is used as a factor. For example, in the term 12x² the exponent is 2, and in 5³ the exponent is 3.

The product of prime numbers and variables written as a single variable term with exponents and a single coefficient. For example: (5)(7)(x)(x)(y) is 35x²y

Each number multiplied together to calculate a product.  For example, (3)(11)(100) has three factors—3,11, and 100; and 5xy has three factors—5, x, andy.

An algebraic expression or equation which can be used to substitute known values for some variables in order to calculate the unknown value of another variable. For example: The formula for the area of a triangle is: A = ½bh, and when given the base b=10 and height h=5, by substitution and multiplication the area is ½(10)(5) which evaluates to A = 25 units squared.

identity element

The number that is the solution to combining inverses under a given operation. For example: 0 is the identity element for the additive inverses since a + (- a) = 0 ; also, 1 is the identity element for the multiplicative inverses since  ¹/a times ^a/1 = 1

A mathematical sentence that contains a comparison operator other than an equal sign. The inequality symbols include: "less than," "greater than," "greater than or equal to," "less than or equal to," and "not equal to."

The set of whole numbers and their opposites (additive inverses), including zero. Written {. . ., -3, -2, -1, 0, 1, 2, 3, . . .}

Pairs of operations that undo each other. For example: addition is the inverse operation of subtraction, subtraction is the inverse operation of addition, multiplication is the inverse operation of division, and division is the inverse operation of multiplication.

Combining the variable terms on one side and the constant terms on the other side of the equal sign in a two-step equation. For example: the equation  3x – 1 = 34 –2x can be rewritten as 5x = 35 with the x terms combined on the left-hand side and the constant terms combined on the right-hand side.

Expressions that contain the same variables and exponents and can be combined into one variable term. For example: 24x—5x + 3x is an expression with three like terms that can be combined to 22x

    An equation that contains only letters.  For example, A = bh.

mathematical sentence

An numerical or algebraic equation that contains numbers and/or variable terms and operations. For example:  -10 + 3y < 23

A term that is a number, a variable, or a product of a number and one or more variables. Three different examples of monomials are: 3, 4x, and -10xy.

multiplicative inverse

The number that will produce the product of 1 when multiplied with a given number. Also known as reciprocals—both numbers must have the same sign. For example:
(¹/2) (²/1) = 1 and (-¹/2) (- ²/1) = 1

    To convert a base with a power of negative exponent to a base of positive exponent,
    first rewrite the base and its negative exponent in fraction form, then write its reciprocal
    and change the power to a positive exponent.  For example, a^-1 is first rewritten as a^-1/1,
    then written as its reciprocal with a positive exponent as 1/a⁺¹ or simply 1/a.

 
negative numbers

Numbers that are less than zero in the number sets called integers, rationals, and reals

The ordered real numbers from negative infinity to positive infinity as marked on a horizontal line. The x-axis is an example of a number line.

A mathematical sentence that has a combination of numbers and at least one operation, but no variable terms. For example: 2 + 8

The number that is the identity element for the multiplicative inverses. When multiplying (¹/2) ( ²/1)  the product is 1.  Likewise (¹/a) ( ^a/1) has a product of 1.  Also, the multiplication property of one says that a number or term does not change when multiplied by the number 1.

open statement
 
    A mathematical sentence that is neither true nor false.

operation
 
    A mathematical process.  Addition (+), subtraction (-), multiplication (x), and division(/) are
    operations.
    
opposites

Two numbers are opposites if they are an equal distance from zero but on opposite sides of zero on the number line. They are also called additive inverses. The sum of opposites is zero, the identity element for additive inverses.  For example, -14 and 14 are on opposite sides of zero and have opposite signs--one is negative and the other is positive.

The rules to follow when more than one operation is used in a numerical sentence. The rules are: parentheses or grouping symbols (innermost first), exponents or powers, multiplication and division in order from left to right, and addition and subtraction in order from left to right. A memory tool acronym is PEMDAS

An algebraic expression made up of two or more monomials separated by the operations of addition or subtraction. For example: 3x + 4xy — 10

Numbers that are greater than zero in the number sets called integers, rationals, and reals

     The solution to a multiplication with two or more factors. For example, the product of 3 and 4 is 12; and the product of 2, x, and y is 2xy

proportion

     An equation that shows that two ratios are equivalent, as long as the denominators are non zero. Symbolically, a/b=c/d, b and c not equal to zero. For example: 1/8 = 8/64
product
 
 

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