chapter 5

sequence

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence.

factored form

A factored form is a parenthesized algebraic expression. In effect a factored form is a product of sums of products ... or a sum of products of sums ... Any logic function can be represented by a factored form, and any factored form is a representation of some logic function.

linear expressions

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable (however, different variables may occur in different terms). ... Equations with exponents greater than one are non-linear.

variable

A symbol for a number we don't know yet. It is usually a letter like x or y. Example: in x + 2 = 6, x is the variable. See: Constant. Algebra - Definitions.

Algebraic expression

An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables (like x or y) and operators (like add,subtract,multiply, and divide). Here are some algebraic expressions: a + 1. a - b. 3x.

Additive identity property

Definition of additive identity. : an identity element (such as 0 in the group of whole numbers under the operation of addition) that in a given mathematical system leaves unchanged any element to which it is added.

commutative property

Definition: The Commutative property states that order does not matter. Multiplication and addition are commutative. Related Links: Properties. Associative, Distributive and commutative properties.

property

Definition: The associative property states that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis'. In other words, if you are adding or multiplying it does not matter where you put the parenthesis.

Associative property

Definition: The associative property states that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis'. In other words, if you are adding or multiplying it does not matter where you put the parenthesis. Add some parenthesis any where you like!.

equivalent expressions

Equivalent Expressions: Expressions that simplify to an equal value when numbers are substituted for the variables of the expression. For example, (a+b)2 and a2 + 2ab + b2 are equivalent since whatever the numbers you substitute for a and b, you can always get the same value for both expressions.

term

In Algebra a term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or − signs. See: Variable. Algebra - Definitions.

constant

In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number. Example: in "x + 5 = 9", 5 and 9 are constants. If it is not a constant it is called a variable. See: Variable. Algebra - Definitions.

monomial

In mathematics, a monomial is, roughly speaking, a polynomial which has only one term. ... (1): A monomial, also called power product, is a product of powers of variables with nonnegative integer exponents, or, in other words, a product of variables, possibly with repetitions.

arithmetic sequence

In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with common difference of 2.

like terms

Like terms" are terms whose variables (and their exponents such as the 2 in x2) are the same. In other words, terms that are "like" each other. Note: the coefficients (the numbers you multiply by, such as "5" in 5x) can be different.

multiplicative property of zero

One of zero's unique rules is called the multiplication property. The multiplication property states that the product of any number and zero is zero. It doesn't matter what the number is, when you multiply it to zero, you get zero as the answer. So: 2 x 0 = 0.

simplest foram

Simplest Form (Fractions) more ... A fraction is in simplest form when the top and bottom cannot be any smaller (while still being whole numbers). Example: 2/4 can be simplified to 1/2. To simplify a fraction, divide the top and bottom by the highest number that can divide into both numbers exactly.

multiplicative identity property

The Multiplicative Identity Property. For a property with such a long name, it's really a simple math law. The multiplicative identity property states that any time you multiply a number by 1, the result, or product, is that original number.

coefficient

a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g., 4 in 4x y).

counterexample

an example that opposes or contradicts an idea or theory.

factor

another term for factorize.

Algebra

he part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formula and equations.

define a variable

not consistent or having a fixed pattern; liable to change.