Fraction

A fraction (from Latin: fractus, "broken") represents a part of a whole or,

more generally, any number of equal parts.

When spoken in everyday English, we specify how many parts of a certain size there are, for example, one-half, five-eighths and three-quarters.

A common or "vulgar" fraction, such as 1/2, 5/8, 3/4, etc., consists of a numerator and adenominator—the numerator representing a number of equal parts and the denominator indicating how many of those parts make up a whole.

An example is 3/4, in which the numerator, 3, tells us that the fraction represents 3 equal parts, and the denominator, 4, tells us that 4 parts equal a whole. The picture to the right illustrates 3/4 of a cake.

A cake with one quarter removed. The remaining three quarters are shown. Dotted lines indicate where the cake may be cut in order to divide it into equal parts. Each quarter of the cake is denoted by the fraction 1/4.

Fractional numbers can also be written without using explicit numerators or denominators,

by using decimals,

percent signs, or

negative exponents (as in 0.01, 1%, and 10⁻² respectively,

all of which are equivalent to 1/100).

An integer (e.g. the number 7) has an implied denominator of one, meaning that the number can be expressed as a fraction like 7/1.

Other uses for fractions are to represent ratios and to represent division.

Thus the fraction 3/4 is also used to represent the ratio 3:4 (the ratio of the part to the whole) and

the division 3 ÷ 4 (three divided by four).

In mathematics the set of all numbers which can be expressed as a fraction m/n, where m and n are integers and n is not zero, is called the set of rational numbers and is represented by the symbol Q.

The word fraction is also used to describe continued fractions,algebraic fractions (quotients of algebraic expressions), and expressions that contain irrational numbers, such as √2/2 and π/4

http://en.wikipedia.org/wiki/Fraction_(mathematics)

Forms of fractions

A common fraction (also known as a vulgar fraction or simple fraction) is a rational number written as an ordered pair of integers, called the numerator and denominator, separated by a line.

Proper and improper common fractions

A common fraction is said to be a proper fraction if the absolute value of the numerator is less than the absolute value of the denominator—that is, if the absolute value of the entire fraction is less than 1. A vulgar fraction is said to be an improper fraction (U.S., British or Australian) or top-heavy fraction (British, occasionally North America) if the absolute value of the numerator is greater than or equal to the absolute value of the denominator (e.g. $\tfrac{9}{4}$ )

Mixed numbers

A mixed numeral (often called a mixed number, also called a mixed fraction) is the sum of a whole number and a proper fraction. This sum is implied without the use of any visible operator such as "+". For example, in referring to two entire cakes and three quarters of another cake, the whole and fractional parts of the number are written next to each other: $2+\tfrac{3}{4}=2\tfrac{3}{4}$ .

This is not to be confused with the algebra rule of implied multiplication. When two algebraic expressions are written next to each other, the operation of multiplication is said to be "understood". In algebra, $a \tfrac{b}{c}$ for example is not a mixed number. Instead, multiplication is understood: $a \tfrac{b}{c} = a \times \tfrac{b}{c}$ .

Complex fractions

In a complex fraction, either the numerator, or the denominator, or both, is a fraction or a mixed number

Compound fractions

Fractions Made Easy

All it takes is to look at it in terms of everyday objects, like pizza!

http://www.squidoo.com/fractions-made-easy

Mathematics

Tuesday 29 November 2011