For fractions of a measurement unit, see Unit prefix.
Slices of approximately 1/8 of a pizza
A unit fraction is a positive fraction with one as its numerator, 1/n. It is the multiplicative inverse (reciprocal) of the denominator of the fraction, which must be a positive natural number. Examples are 1/1, 1/2, 1/3, 1/4, 1/5, etc. When an object is divided into equal parts, each part is a unit fraction of the whole.
Multiplying two unit fractions produces another unit fraction, but other arithmetic operations do not preserve unit fractions. In modular arithmetic, unit fractions can be converted into equivalent whole numbers, allowing modular division to be transformed into multiplication. Every rational number can be represented as a sum of distinct unit fractions; these representations are called Egyptian fractions based on their use in ancient Egyptian mathematics. Many infinite sums of unit fractions are meaningful mathematically.
In geometry, unit fractions can be used to characterize the curvature of triangle groups and the tangencies of Ford circles. Unit fractions are commonly used in fair division, and this familiar application is used in mathematics education as an early step toward the understanding of other fractions. Unit fractions are common in probability theory due to the principle of indifference. They also have applications in combinatorial optimization and in analyzing the pattern of frequencies in the hydrogen spectral series.
unitfraction is a positive fraction with one as its numerator, 1/n. It is the multiplicative inverse (reciprocal) of the denominator of the fraction...
many of those parts make up a unit or a whole. For example, in the fraction 3/4, the numerator 3 indicates that the fraction represents 3 equal parts, and...
Unit angle, a full turn equal to an angle of 1 Unit circle, a circle with a radius of length 1 Unit cube, a cube with sides of length 1 Unitfraction...
An Egyptian fraction is a finite sum of distinct unitfractions, such as 1 2 + 1 3 + 1 16 . {\displaystyle {\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{16}}...
or molar percentage (unit symbol %, sometimes "mol%", equivalent to cmol/mol for 10-2). The mole fraction is called amount fraction by the International...
Egyptian fraction – Finite sum of distinct unitfractions Engel expansion – decomposition of a positive real number into a series of unitfractions, each...
positive integers (counting numbers)—that is, it is generally the sum of unitfractions. If infinitely many numbers have their reciprocals summed, generally...
Egyptian fraction is a representation of an irreducible fraction as a sum of distinct unitfractions, such as 5/6 = 1/2 + 1/3. As the name indicates, these...
multiple of a unit) is an integer multiple of a given unit; likewise a unit submultiple (or submultiple of a unit) is a submultiple or a unitfraction of a given...
inconvenient multiple or fraction of a base unit. Many of the unusual units of measurements listed here are colloquial measurements, units devised to compare...
numerals.[citation needed] Unitfractions were a method to express fractions. In Greek alphabetic notation, unitfractions were indicated with the denominator –...
The hectare (/ˈhɛktɛər, -tɑːr/; SI symbol: ha) is a non-SI metric unit of area equal to a square with 100-metre sides (1 hm2), that is, 10,000 square meters...
information about the relationships between individual currencies and their minor units. This data is published in three tables: Table A.1 – Current currency &...
{10^{k}c}{10^{k}-1}}} ), x {\displaystyle x} is also rational. Thereby fraction is the unitfraction 1/n and ℓ10 is the length of the (decimal) repetend. The lengths...
series of unitfractions that most rapidly converge to 1 are the reciprocals of Sylvester's sequence, which generate the infinite Egyptian fraction 1 = 1...
mole fraction. The SI unit is mol/mol. However, the deprecated parts-per notation is often used to describe small mole ratios. The mass fraction w i {\displaystyle...
In chemistry and fluid mechanics, the volume fraction φ i {\displaystyle \varphi _{i}} is defined as the volume of a constituent Vi divided by the volume...
A unit prefix is a specifier or mnemonic that is prepended to units of measurement to indicate multiples or fractions of the units. Units of various sizes...
kiloseconds (thousands of seconds), such units are rarely used in practice. An everyday experience with small fractions of a second is a 1-gigahertz microprocessor...
type of particle), the packing fraction is represented mathematically by A P F = N p a r t i c l e V p a r t i c l e V unit cell {\displaystyle \mathrm {APF}...
Global Information