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One over a whole number
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
Unit_fraction
Finite sum of distinct unit fractions
An Egyptian fraction is a finite sum of distinct unit fractions, such as 1 2 + 1 3 + 1 16 . {\displaystyle {\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{16}}
Egyptian_fraction
Ratio of two numbers
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
Fraction
some series of positive integers (counting numbers). It is a sum of unit fractions. If infinitely many numbers have their reciprocals summed, generally
List_of_sums_of_reciprocals
On unit fractions adding to 4/n
much more ancient mathematics; sums of unit fractions, like the one in this problem, are known as Egyptian fractions, because of their use in ancient Egyptian
Erdős–Straus_conjecture
Unit of measurement adopted by convention for a base quantity
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 unit fraction of a given
Base_unit_of_measurement
Method for finding sums of unit fractions
Egyptian fraction is a representation of an irreducible fraction as a sum of distinct unit fractions, such as 5/6 = 1/2 + 1/3. As the name indicates
Greedy algorithm for Egyptian fractions
Greedy_algorithm_for_Egyptian_fractions
Proportion of a constituent in a mixture
or molar percentage (unit symbol %, sometimes "mol%", equivalent to cmol/mol for 10−2). The mole fraction is called amount fraction by the International
Mole_fraction
Set of units to describe small values
pseudo-units to describe the small values of miscellaneous dimensionless quantities, e.g. mole fraction or mass fraction. Since these fractions are quantity-per-quantity
Parts-per_notation
Topics referred to by the same term
with a radius of length 1 Unit cube, a cube with sides of length 1 Unit fraction, a reciprocal of a positive integer Unit imaginary number, square root
Unit
9th-century Indian mathematician
gave systematic rules for expressing a fraction as the sum of unit fractions. This follows the use of unit fractions in Indian mathematics in the Vedic period
Mahāvīra_(mathematician)
Mathematical puzzle
will burn for 1/3 of a unit of time rather than a whole unit. By representing a given amount of time as a sum of unit fractions, and successively burning
Rope-burning_puzzle
rational number as a sum of distinct unit fractions. If a rational number x / y {\displaystyle x/y} is a sum of unit fractions with odd denominators, x y = ∑
Odd_greedy_expansion
Units that are not part of a coherent system
of the listed units are approximate or vaguely defined. Some are odd multiples or fractions of a base unit. The ligne is a French unit of length that
List of non-coherent units of measurement
List_of_non-coherent_units_of_measurement
In power systems, expression of system quantities as fractions
of electrical engineering, a per-unit system is the expression of system quantities as fractions of a defined base unit quantity. Calculations are simplified
Per-unit_system
Metric unit of area
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 metres
Hectare
Product with an integer
being a unit fraction of b" (a=b/n) or, equivalently, "b being an integer multiple n of a" (b=n a). This terminology is also used with units of measurement
Multiple_(mathematics)
Standard defining codes for currencies
information about the relationships between currencies and their minor units. This data is published in three tables: Table A.1 – Current currency &
ISO_4217
Mathematics used in Ancient Egypt
texts for 3/4, but other fractions were all written as unit fractions of the form 1/n or sums of such unit fractions. Scribes used tables to help
Ancient_Egyptian_mathematics
Topics referred to by the same term
Look up fraction in Wiktionary, the free dictionary. A fraction is one or more equal parts of something. Fraction may also refer to: Fraction (chemistry)
Fraction_(disambiguation)
Mathematical table
converting rational numbers of the form 2/n into Egyptian fractions (sums of distinct unit fractions), the form the Egyptians used to write fractional numbers
Rhind Mathematical Papyrus 2/n table
Rhind_Mathematical_Papyrus_2/n_table
Ancient Egyptian text
is an aid for computing Egyptian fractions. It contains 26 sums of unit fractions which equal another unit fraction. The sums appear in two columns, and
Egyptian Mathematical Leather Roll
Egyptian_Mathematical_Leather_Roll
Ratio of part of a mixture to the whole
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
Concentration
Theorem on the existence of finite sets of integers >1 whose reciprocals sum to 1
(2000). Unit Fractions (Ph.D. thesis). University of Georgia, Athens. Ernest S. Croot III (2003). "On a coloring conjecture about unit fractions". Annals
Erdős–Graham_problem
Divergent sum of positive unit fractions
harmonic series is the infinite series formed by summing all positive unit fractions: ∑ i = 1 ∞ 1 i = 1 1 + 1 2 + 1 3 + 1 4 + 1 5 + ⋯ . {\displaystyle \sum
Harmonic_series_(mathematics)
Type of numeral system
numerals.[citation needed] Unit fractions were a method to express fractions. In Greek alphabetic notation, unit fractions were indicated with the denominator –
Alphabetic_numeral_system
Doubly exponential integer sequence
reciprocals forms a series of unit fractions that converges to 1 more rapidly than any other series of unit fractions. The recurrence by which it is
Sylvester's_sequence
Number represented as a0+1/(a1+1/...)
A simple or regular continued fraction is a continued fraction with numerators all equal to one, and denominators built from a sequence { a i } {\displaystyle
Simple_continued_fraction
Proportion of the total volume of a constituent part
volume units, since water-ethanol mixture loses volume due to intermolecular attraction.[citation needed] Volume fraction is related to mass fraction, w i
Volume_fraction
Triangular arrangement of unit fractions
The Leibniz harmonic triangle is a triangular arrangement of unit fractions in which the outermost diagonals consist of the reciprocals of the row numbers
Leibniz_harmonic_triangle
(2000), Unit Fractions, Ph.D. thesis, University of Georgia, Athens. Croot, Ernest S. III (2003). "On a coloring conjecture about unit fractions". Annals
List of conjectures by Paul Erdős
List_of_conjectures_by_Paul_Erdős
Mathematical subset of the Lahun Papyri
operations. Doubling a unit fraction with an even denominator was simple, dividing the denominator by 2. Doubling a fraction with an odd denominator
Lahun_Mathematical_Papyri
Methods of transforming crude oil
alkylation unit. Distillate hydrotreater unit: Uses hydrogen to desulfurize some of the other distilled fractions from the crude oil distillation unit (such
Petroleum_refining_processes
Sum of an infinite series, about 0.6434
constant is defined as the value of the following infinite series of unit fractions with alternating signs: C = ∑ i = 0 ∞ ( − 1 ) i s i − 1 = 1 1 − 1 2
Cahen's_constant
Comparison of various scales
expressed as fractions and arranged so that any dimensional unit appearing in both the numerator and denominator of any of the fractions can be cancelled
Conversion_of_units
Mathematical group that can be generated as the set of powers of a single element
unit fraction, the inverse of their lowest common denominator, and generates as a subgroup a cyclic group of integer multiples of this unit fraction.
Cyclic_group
Square matrix where a[i,j]=1/(i+j-1)
introduced by Hilbert (1894), is a square matrix with entries being the unit fractions H i j = 1 i + j − 1 . {\displaystyle H_{ij}={\frac {1}{i+j-1}}.} For
Hilbert_matrix
Unconventional units of measurement intended as humor
"any obscure unit", furlongs per fortnight have also served frequently in the classroom as an example on how to reduce a unit's fraction. The speed of
List of humorous units of measurement
List_of_humorous_units_of_measurement
Ancient Egyptian mathematical manuscript
overlines denote the unit fraction having that number as denominator, e.g. 4 ¯ = 1 4 {\displaystyle {\bar {4}}={\frac {1}{4}}} ; unit fractions were common objects
Moscow_Mathematical_Papyrus
SI unit of time
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
Second
1356 mathematical treatise by Narayana Pandita
examples. Contains rules for writing a fraction as a sum of unit fractions. 22 rules and 14 examples. Unit fractions were known in Indian mathematics in
Ganita_Kaumudi
Modern form of the metric system
more subtle example is mass fraction. A silicon sample with small amounts of copper should be reported as with no units, for example, w ( Cu ) = 1.3
International_System_of_Units
Central computer component that executes instructions
machine (VM). Each VM is allocated a virtual central processing unit [...] which is a fraction of the blade's CPU. Fifield, Tom; Fleming, Diane; Gentle, Anne;
Central_processing_unit
Numerals used in Ancient Egypt
only as sums of unit fractions, i.e., sums of reciprocals of positive integers, except for 2⁄3 and 3⁄4. The hieroglyph indicating a fraction looked like a
Egyptian_numerals
Slanting line punctuation mark (/)
modern period and comma, the slash is now used to represent division and fractions, as a date separator, in between multiple alternative or related terms
Slash_(punctuation)
Mathematical puzzle
chosen to divide n + 1 {\displaystyle n+1} , all of these fractions simplify to unit fractions. When combined with the judge's share of the animals, 1 /
17-animal_inheritance_puzzle
Atmospheric-pressure oil separation process
separation of the different hydrocarbons present in crude oil into useful fractions and the conversion of some of the hydrocarbons into products having higher
Atmospheric distillation of crude oil
Atmospheric_distillation_of_crude_oil
Ratio between two related quantities in different units
often represented as a fraction. If the divisor (or fraction denominator) in the rate is equal to one expressed as a single unit, and if it is assumed
Rate_(mathematics)
Relationship between two numbers of the same kind
of numbers, a fraction with the first number in the numerator and the second in the denominator, or as the value denoted by this fraction. Ratios of counts
Ratio
Natural number
also a full reptend prime, meaning that the decimal expansion of the unit fraction 1/229 repeats periodically with as long a period as possible. With 227
229_(number)
Building block of a polymer chain
involves tetrafunctional structural units. For example, in the synthesis of cross-linked polystyrene, a small fraction of monomeric styrene (or vinylbenzene)
Structural_unit
Mixture fraction ( Z {\displaystyle Z} ) is a quantity used in combustion studies that measures the mass fraction of one stream of a mixture formed by
Mixture_fraction
Cold-pressed essential oil
yellow, bergamot essential oil consists of a volatile fraction (average 95%) and a non-volatile fraction (5% or residual). Chemically, it is a complex mixture
Bergamot_essential_oil
Indicates multiples or fractions of a unit
unit prefix is a specifier or mnemonic that is added to the beginning of a unit of measurement to indicate multiples or fractions of the units. Units
Unit_prefix
One of the seven units of measurement that define the metric system
The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now
SI_base_unit
Number or ratio expressed as a fraction of 100
nonetheless a unit of measurement in its orthography and usage. For example, 45% (read as "forty-five percent") is equal to the fraction 45/100, or 0
Percentage
Political movement
Fractionism (Angolan Portuguese: fraccionismo), also called Nito's Group or Nitism (Angolan Portuguese: nitismo), and self-called MPLA Action Committee
Fractionism
Units of measurement commonly used in the U.S.
of metric units in carpentry and the building trades, on the basis that it is easier to remember an integer number of inches plus a fraction, rather than
United_States_customary_units
Administration of a total dose of radiation in parts, at intervals
and minimizes the negative side effects. A typical fractionation scheme divides the dose into 30 units delivered every weekday over six weeks. Experiments
Dose_fractionation
Mass per unit volume
the void fraction. Sometimes this can be determined by geometrical reasoning. For the close-packing of equal spheres the non-void fraction can be at
Density
Unit for the arithmetic difference of two percentages
treatment. For measurements involving percentages as a unit, such as growth, yield, or ejection fraction, statistical deviations and related descriptive statistics
Percentage_point
Increasing sequence of reduced fractions
sequence of order n {\displaystyle n} is the sequence of completely reduced fractions which have denominators less than or equal to n {\displaystyle n} , arranged
Farey_sequence
Lower bound on radii in circle packings
Then the minimum radius of any circle in the ring is at least the unit fraction 1 F 2 n − 3 − 1 {\displaystyle {\frac {1}{F_{2n-3}-1}}} where F i {\displaystyle
Ring_lemma
Surname list
first name that may refer to: Cahen's constant, an infinite series of unit fractions, with alternating signs, derived from Sylvester's sequence Cahen–Mellin
Cahen
ISBN 978-0-691-24410-5. (Boyer 1991, "Egypt" p. 11) Egyptian Unit Fractions at MathPages Egyptian Unit Fractions "Egyptian Papyri". www-history.mcs.st-andrews.ac
History_of_mathematics
Logarithmic unit expressing the ratio of physical quantities
subtraction (C/N0)dB = CdB − N0 dB. However, the linear-scale units still simplify in the implied fraction, so that the results would be expressed in dB-Hz. According
Decibel
Instrument used to study object movement
frequency of the flash is adjusted so that it is an equal to, or a unit fraction of the object's cyclic speed, at which point the object is seen to be
Stroboscope
Positive integer whose divisors have a harmonic mean that is an integer
and only if the average of its divisors is the product of M with a unit fraction 1/k. Ore showed that every perfect number is harmonic. To see this,
Harmonic_divisor_number
Mathematical sequence of numbers
arithmetic progression Harmonic series – Divergent sum of positive unit fractions Infinite series – Infinite sum Preferred number – Selection constraint
Geometric_progression
Quantity standard
numbers or small fractions easier to read, is to use unit prefixes. At some point in time though, the need to relate the two units might arise, and consequently
Unit_of_measurement
Structuring of armed forces of a state
larger units manning expensive equipment and only a fraction of personnel in infantry units. In western militaries, a joint force is defined as a unit or
Military_organization
Foam fractionation is a chemical process in which hydrophobic molecules are preferentially separated from a liquid solution using rising columns of foam
Foam_fractionation
Sum of pairwise divisible unit fractions
of numerators and denominators sharing the same fraction bar represents an ascending continued fraction: a b c d e f g h = d + c + b + a e
Engel_expansion
Mixture of solids suspended in liquid
ceramics and pottery. Slurry oil, the highest boiling fraction distilled from the effluent of an FCC unit in an oil refinery. It contains a large amount of
Slurry
addition, the methods used in the Reisner and RMP to convert vulgar fractions to unit fraction series look similar to the conversion methods used in the Egyptian
Reisner_Papyrus
Signed odd unit fractions sum to π/4
be a power of ten, each term in the right sum becomes a finite decimal fraction. The formula is a special case of the Euler–Boole summation formula for
Leibniz_formula_for_π
Ancient Egyptian mathematical document
taken up by the 2/n table. The fractions 2/n for odd n ranging from 3 to 101 are expressed as sums of unit fractions. For example, 2 15 = 1 10 + 1 30
Rhind_Mathematical_Papyrus
Crystallography concept
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}
Atomic_packing_factor
SI unit of amount of substance
charge of one mole of electrons Mole fraction – Proportion of a constituent in a mixture Dalton (unit) – Standard unit of mass for atomic-scale entities
Mole_(unit)
SI unit of temperature
also held in Resolution 4 that "The kelvin, unit of thermodynamic temperature, is equal to the fraction 1/273.16 of the thermodynamic temperature of
Kelvin
Integer-valued polynomial Rational number Unit fraction Irreducible fraction = in lowest terms Dyadic fraction Recurring decimal Cyclic number Farey sequence
List_of_number_theory_topics
be factored algebraically) for which no generalized repunit primes are known. 210 Smallest base such that all unit fractions 1/2 to 1/10 terminate.
List_of_numeral_systems
Number whose sums of distinct divisors represent all smaller numbers
Egyptian fractions. Fibonacci does not formally define practical numbers, but he gives a table of Egyptian fraction expansions for fractions with practical
Practical_number
Ancient Egyptian texts
1/80, 1/90 and 1/100 fractions to binary quotient and 1/1320 (ro) remainder unit fraction series. Problem 80 gave 5 Horus eye fractions of the hekat and equivalent
Akhmim_wooden_tablets
Traditional system of measurement used by Han Chinese
unit system'). The ROC government then promulgated the "market unit" (Chinese: 市制) system in 1930, redefining traditional units as simple fractions of
Chinese_units_of_measurement
Integer whose multiples are digit rotations
Cyclic numbers are related to the recurring digital representations of unit fractions. A cyclic number of length L is the digital representation of 1/(L +
Cyclic_number
British mathematician
NT]. Bloom, Thomas F. (2021-12-07). "On a density conjecture about unit fractions". arXiv:2112.03726v2 [math.NT]. Cepelewicz, Jordana (2022-03-09). "Math's
Thomas_Bloom
SI derived unit of visible light emission
The lumen (symbol: lm) is the SI unit of luminous flux, which quantifies the perceived power of visible light emitted by a source. Luminous flux differs
Lumen_(unit)
Negative integer two units from the origin in mathematics
Sequences. OEIS Foundation. Kyle Bradford; Eugen J. Ionascu (2014). "Unit Fractions in Norm-Euclidean Rings of Integers". Acta Mathematica Universitatis
−2
Natural number
rendering support, you may see question marks, boxes, or other symbols. 1 (one, unit, unity) is a number, numeral, and grapheme. It is the first and smallest
1
Topics referred to by the same term
non-sparse matrix Hilbert matrix, a square matrix with entries being the unit fractions Hollow matrix, a square matrix or related classes of matrix Routh–Hurwitz
H-matrix
Form of distillation
distillation, where the mixture is added to the unit at the start of the distillation, distillate fractions are taken out sequentially in time (one after
Continuous_distillation
Definition of the units kg, A, K and mol
In 2019, four of the seven SI base units specified in the International System of Quantities were redefined in terms of natural physical constants, rather
2019_revision_of_the_SI
accumulation of the subtrahends 1 x {\textstyle {\frac {1}{x}}} into a unit fraction, that is, m x = 1 n {\textstyle {\frac {m}{x}}={\frac {1}{n}}} for m
List of logarithmic identities
List_of_logarithmic_identities
System of measurement used in Ancient Greece
from theory is as follows: Athenians measured the day by sundials and unit fractions. Periods during night or day were measured by a water clock (clepsydra)
Ancient Greek units of measurement
Ancient_Greek_units_of_measurement
Ratio of two consecutive integers
a unit fraction) are exactly the rational numbers whose simple continued fraction terminates after two terms. The numbers whose continued fraction terminates
Superparticular_ratio
Difference between logarithm and harmonic series
plus the difference between Boya's expansion and the series of exact unit fractions ∑ k = 1 ∞ 1 T k {\displaystyle \textstyle \sum _{k=1}^{\infty }{\frac
Euler's_constant
System of measurements
pound the primary unit of mass. In all the systems, the fundamental unit is the pound, and all other units are defined as fractions or multiples of it
Imperial_units
Map of most or all of the surface of the Earth
impossible because less than half of Earth's coastlines and only a small fraction of its continental interiors were known to any culture. With exploration
World_map
Open source web server and a reverse proxy server
software, released under the terms of the 2-clause BSD license. A large fraction of web servers use nginx, often as a load balancer. A company of the same
Nginx
travel, tourism, insurance
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