FractionA fraction (from fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A common, vulgar, or simple fraction (examples: and ) consists of an integer numerator, displayed above a line (or before a slash like ), and a non-zero integer denominator, displayed below (or after) that line.
Egyptian fractionAn Egyptian fraction is a finite sum of distinct unit fractions, such as That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other. The value of an expression of this type is a positive rational number ; for instance the Egyptian fraction above sums to . Every positive rational number can be represented by an Egyptian fraction.
Algebraic fractionIn algebra, an algebraic fraction is a fraction whose numerator and denominator are algebraic expressions. Two examples of algebraic fractions are and . Algebraic fractions are subject to the same laws as arithmetic fractions. A rational fraction is an algebraic fraction whose numerator and denominator are both polynomials. Thus is a rational fraction, but not because the numerator contains a square root function. In the algebraic fraction , the dividend a is called the numerator and the divisor b is called the denominator.
MultiplicationMultiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product. The multiplication of whole numbers may be thought of as repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the multiplicand, as the quantity of the other one, the multiplier; both numbers can be referred to as factors.
Associative propertyIn mathematics, the associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs. Within an expression containing two or more occurrences in a row of the same associative operator, the order in which the operations are performed does not matter as long as the sequence of the operands is not changed.
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