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Algebra Chapter 1

variable a letter or symbol used to represent a value that can change.
coefficient a number multiplied by a variable.
constant a value that does not change
numerical expression may contain only constants and operations
algebraic expression may contain variables, constants, and operations.
power an expression written with an exponent and a base or the value of such an expression.
square root a number that is multiplied by itself to form a product
perfect square a number whose positive square root is a whole number.
natural numbers counting numbers: 1,2,3,...
whole numbers Natural numbers and zero: 0,1,2,3...
integers whole numbers and their opposites: -3, -2, -1, 0, 1, 2, 3....
rational numbers can be expressed in the forms a/b where a and b are both integers and b is not equal to 0.
terminating decimals rational numbers in decimal form that have a finite number of digits.
repeating decimals rational numbers in decimal form that have a block of one or more digits that repeats continuously.
irrational numbers cannot be expressed in the form a/b. They include square roots of whole numbers that are not perfect squares and nonterminating decimals that do not repeat.
additive inverse A number and its opposite. Their sum is zero.
reciprocal Two numbers whose product is 1.
absolute value The distance of the number from zero on a number line.
evaluate to find the value of an algebraic expression by substituting a number for a variable and simplifying.
opposite The number that is the same distance from zero on the number line; the additive inverse.
multiplicative inverse the reciprocal of a number
base the number in a power that is used as a factor
exponent the number in a power that tells how many times the base is used as a factor
order of operations a process for evaluating expressions, sometimes referred to as PEMDAS
term the part of an expression that is added or subtracted
like terms terms with the same variables raised to the same exponents.
commutative property For addition and multiplication, the order does not matter. For any numbers a and b, a+b = b+a and ab = ba.
associative property For addition and multiplication, the grouping does not matter. For any numbers a, b, and c, (a+b)+c = a+(b+c) and (ab)c = a(bc).
distributive property For all real numbers a, b, and c: a(b+c) = ab + ac
real numbers every point on the number line, either a rational or irrational number
Created by: galbreath01