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## Fraction Notation

A fraction is a number that expresses a part of a whole. The number above the line (the numerator) tells how many parts there are, and the number below the line (the denominator) tells how many parts the whole is divided into.

For example, the fraction ¾ means that there are three parts out of four in the whole. This can also be written as 3/4.

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, 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

${\tfrac {17}{3}}$) consists of a **numerator,** displayed above a line (or before a slash like 1⁄2), and a non-zero **denominator**, displayed below (or after) that line. Numerators and denominators are also used in fractions that are not *common*, including compound fractions, complex fractions, and mixed numerals.

In positive common fractions, the numerator and denominator are natural numbers. The numerator represents a number of equal parts, and the denominator indicates how many of those parts make up a unit or a whole. The denominator cannot be zero, because zero parts can never make up a whole. For example, in the fraction 3/4, the numerator 3 indicates that the fraction represents 3 equal parts, and the denominator 4 indicates that 4 parts make up a whole. The picture to the right illustrates 3/4 of a cake.

A common fraction is a numeral which represents a rational number. That same number can also be represented as a decimal, a percent, or with a negative exponent. For example, 0.01, 1%, and 10^{−2} are all equal to the fraction 1/100. An integer can be thought of as having an implicit denominator of one (for example, 7 equals 7/1).

## What is a Proper Fraction?

A proper fraction is a fraction in which the numerator is smaller than the denominator. For example, the fraction ¾ is a proper fraction, while the fraction 7/8 is not a proper fraction.

## Examples of Proper Fractions

1/2, 1/3, 2/3, 1/4, 3/4

1/5, 2/5, 3/5, 4/5, 1/6, 5/6