 TOPICS   # Topics in a Pre-Algebra Course

To learn more about a topic listed below, click the topic name to go to the corresponding MathWorld classroom page.

 Absolute Value The absolute value of a number is the distance of the number from the origin. Arithmetic Arithmetic is the branch of mathematics dealing with numerical computation. Arithmetical operations include addition, congruence calculation, division, factorization, multiplication, power computation, root extraction, and subtraction. Arithmetic Series An arithmetic series is a series in which the difference between any two consecutive terms is a constant. Associative An operation * is associative if x*(y*z) = (x*y)*z for all x, y, and z. Base (1) In a number of system, the base is the number of distinct digits used to represent numbers. (2) In a logarithm, the base is the number with respect to which the power operation is inverted to form the logarithm. (3) In a geometric figure, the term base is used to refer to the bottom edge or surface. Cartesian Coordinates Cartesian coordinates are the usual coordinate system, originally described by Descartes, in which points are specified as distances to a set of perpendicular axes. Also called rectangular coordinates. Commutative An operation * is said to be commutative if x*y = y*x for all x and y. Decimal Expansion The decimal expansion of a number is the usual "base 10" representation of a real number. Distributive An operation * is distributive if has the property in multiplication that x*(y + z) = x*y + x*z. Divisor An integer that divides a given integer with no remainder. A synonym for factor. Equal Two quantities are said to be equal if they are, in some well-defined sense, equivalent. Equality of quantities a and b is written a = b. Factorial The factorial of a positive integer n, denoted n!, is the product of the first n positive integers. Fraction A fraction is a rational number expressed in the form a/b, where a is known as the numerator and b as the denominator. Function Graph A function graph is a set of points showing the values taken by a function. This type of plot is called simply a "graph" in common parlance, but is distinct from a collection of points and lines (also called a network) that mathematicians refer to when they speak of a "graph." Geometric Series A geometric series is a series in which the ratio of any two consecutive terms is always the same. Greatest Common Divisor The greatest common divisor of a set of integers is the largest integer that divides all of them. Integer An integer is one of the numbers ..., -2, -1, 0, 1, 2, .... Intersection (1) In set theory, the intersection of two or more sets is the set of elements common to all sets. (2) In geometry, the intersection of two or more regions is the region that is common to all regions. Interval An interval is a connected piece of the real number line which may be open or closed at either end. Irrational Number An irrational number is a real number that cannot be written as a fraction. Irrational numbers have decimal expansions that neither terminate nor become periodic. Least Common Multiple The least common multiple of a set of integers is the smallest number that is a multiple of all of them. Line A line is the infinite extension in both directions of a line segment, giving the path of shortest distance between two points in Euclidean space. Origin The origin is the point with all-zero coordinates in Cartesian coordinates, or the central point in polar coordinates. Polynomial A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. Power In arithmetic, a power is an exponent to which a given quantity is raised. Prime Factor A prime factor is a divisor that is also a prime number. Prime Factorization Prime factorization is the factorization of a number into its constituent primes. Also called prime decomposition. Prime Number A prime number is a positive integer that has exactly one positive integer divisor other than 1 (i.e., no factors other than 1 and itself). Prime numbers are often simply called primes. Pythagorean Theorem The Pythagorean theorem is an equation relating the lengths of the sides of a right triangle as a squared plus b squared equals c squared, where c is the length of the hypotenuse. Quotient A quotient is the result of dividing one number by another. Rational Number A rational number is a real number that can be written as a quotient of two integers. Real Line The real line is a line with a fixed scale so that every real number corresponds to a unique point on the line. Real Number A real number is a number corresponding to a point on the real number line. Relatively Prime Two or more integers that share no common positive divisors except 1 are said to be relatively prime. Right Angle A right angle is an angle that measures exactly 90 degrees. Rounding Rounding is the approximation of a number by truncating and possibly adjusting the last digit of interest based on digits appearing after it. Sequence A sequence is a (possibly infinite) ordered list of numbers. Series In mathematics, a series is an (often infinite) sum of terms specified by some rule. Set In mathematics, a set is a finite or infinite collection of objects in which order has no significance and multiplicity is generally also ignored. Square Number A square number is an integer that is the square (i.e., second power) of another integer. Square Root A square root of x is a number r such that r*r = x.