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Topics in a Pre-Algebra Course

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

Absolute ValueThe distance of a number from theorigin. Absolute value is an example of anorm.

Arithmetic

The branch of mathematics dealing withnumerical computation. Arithmeticaloperations include addition, congruencecalculation, division, factorization,multiplication, power computation, rootextraction, and subtraction.

Arithmetic Series A series in which the difference betweenany two consecutive terms is a constant.

AssociativeAn operation is associativeifx*(y*z)! (x*y)*zfor allx, y, and z.

"aseThe number of digits in a numbersystem. The same word is used in thecontext of logarithms.

#artesian #oordinates

The usual coordinate system, originallydescribed by $escartes, in which pointsare specified as distances to a set of

perpendicular axes. Also calledrectangular coordinates.

#ommutativeAn operation is commutativeifxy! yxfor allxand y.

$ecimal %xpansionThe usual &base '(& representation of areal number.

$istributive)aving the property, in multiplication,thatx(y+z) = xy + xz.

$ivisorAn integer that divides a given integerwith no remainder. A synonym for factor.

*actorialThe product of the first npositiveintegers, denoted n+.

*ractionA rational number expressed in theform ab, where ais known as thenumerator and bas the denominator.

*unction -raph

The set of points showing the valuestaken by a function. This type of plot iscalled simply a &graph& in commonparlance, but is distinct from a collectionof points and lines that mathematiciansrefer to when they speak of a &graph.&

-eometric SeriesA series in which the ratio of any two

consecutive terms is always the same.

-reatest #ommon $ivisor*or two or more integers, the largestinteger dividing all of them.

nteger /ne of the numbers ..., 01, 0', (, ', 1, ....

ntersection

2'3 *or two setsAand B, the set ofelements common toAand B. 213 *ortwo or more geometric ob4ects, the set ofpoints that are common to both of them.

ntervalA connected piece of the real numberline. An interval can be open or closed at

either end.

rrational 5umber

A number that cannot be written as afraction. rrational numbers have decimalexpansions that neither terminate norbecome periodic.

6east #ommon 7ultiple*or two or more integers, the smallestnumber that is a multiple of all of them.

6ine The infinite extension in both directions

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of a line segment, which is the path ofshortest distance between two points.

/riginThe point with all0zero coordinates in#artesian coordinates, or the central

point in polar coordinates.

8olynomialA mathematical expression involving asum of powers in one or more variablesmultiplied by coefficients.

8owerAn exponent to which a given 9uantity israised.

8rime *actor A divisor that is also a prime number.

8rime *actorizationThe factorization of a number into itsconstituent primes. Also called primedecomposition.

8rime 5umber

A positive integer that has exactly onepositive integer divisor other than ' 2i.e.,no factors other than ' and itself3. 8rimenumbers are often simply called primes.

8ythagorean Theorem

An e9uation relating the lengths of thesides of a right triangle. -iven two sides,the length of the third can bedetermined.

:uotientThe result of dividing one number byanother.

;ational 5umberA real number that can be written as a9uotient of two integers.

;eal 6ineA line with a fixed scale so that everyreal number corresponds to a uni9uepoint on the line.

;eal 5umberThe set of all rational and irrational

numbers.

;elatively 8rimeA term describing integers that share nocommon positive divisors except '.

;ight AngleAn angle that measures exactly