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196:{\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\text{term}}\,+\,{\text{term}}\\\scriptstyle {\text{summand}}\,+\,{\text{summand}}\\\scriptstyle {\text{addend}}\,+\,{\text{addend}}\\\scriptstyle {\text{augend}}\,+\,{\text{addend}}\end{matrix}}\right\}\,=\,}
359:
549:{\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\frac {\scriptstyle {\text{dividend}}}{\scriptstyle {\text{divisor}}}}\\\scriptstyle {\frac {\scriptstyle {\text{numerator}}}{\scriptstyle {\text{denominator}}}}\end{matrix}}\right\}\,=\,}
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1149:
The quotient is most frequently encountered as two numbers, or two variables, divided by a horizontal line. The words "dividend" and "divisor" refer to each individual part, while the word "quotient" refers to the whole.
871:
785:
1224:{\displaystyle {\dfrac {1}{2}}\quad {\begin{aligned}&\leftarrow {\text{dividend or numerator}}\\&\leftarrow {\text{divisor or denominator}}\end{aligned}}{\Biggr \}}\leftarrow {\text{quotient}}}
426:{\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\text{factor}}\,\times \,{\text{factor}}\\\scriptstyle {\text{multiplier}}\,\times \,{\text{multiplicand}}\end{matrix}}\right\}\,=\,}
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311:{\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\text{term}}\,-\,{\text{term}}\\\scriptstyle {\text{minuend}}\,-\,{\text{subtrahend}}\end{matrix}}\right\}\,=\,}
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1400:
Outside of arithmetic, many branches of mathematics have borrowed the word "quotient" to describe structures built by breaking larger structures into pieces. Given a
1382:
923:
59:
699:{\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\text{base}}^{\text{exponent}}\\\scriptstyle {\text{base}}^{\text{power}}\end{matrix}}\right\}\,=\,}
1844:
1704:
614:{\displaystyle \scriptstyle \left\{{\begin{matrix}\scriptstyle {\text{fraction}}\\\scriptstyle {\text{quotient}}\\\scriptstyle {\text{ratio}}\end{matrix}}\right.}
1299:
is rational, if and only if it can be expressed as a quotient of two integers with a nonzero denominator. A real number that is not rational is irrational.
1696:
1392:—numbers that are not a quotient of two integers—was first discovered in geometry, in such things as the ratio of the diagonal to the side in a square.
988:
of two numbers. The quotient has widespread use throughout mathematics. It has two definitions: either the integer part of a division (in the case of
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negative. For example, the divisor 3 may be subtracted up to 6 times from the dividend 20, before the remainder becomes negative:
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resulting from the quotient of a physical quantity by mass, volume, or other measures of the system "size".
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1697:"NIST Guide to the SI, Chapter 7: Rules and Style Conventions for Expressing Values of Quantities"
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Special
Publication 811 | The NIST Guide for the use of the International System of Units
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866:{\displaystyle \scriptstyle \log _{\text{base}}({\text{anti-logarithm}})\,=\,}
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1412:" may be created which contains those equivalence classes as elements. A
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of times a divisor may be subtracted from a dividend—before making the
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1826:
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1125:(mass divided by mass, in kg/kg or in percent) is a "ratio".
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1570:"ISO 80000-1:2022(en) Quantities and units — Part 1: General"
1073:), "quotient" refers to the general case with respect to the
1238:
The quotient is also less commonly defined as the greatest
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1621:"IEC 60050 - Details for IEV number 102-01-22: "quotient""
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1646:"IEC 60050 - Details for IEV number 102-01-23: "ratio""
1671:"IEC 60050 - Details for IEV number 112-03-18: "rate""
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1103:, especially when the divisor is a duration (e.g., "
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is 6 (with a remainder of 2) in the first sense and
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1428:may be formed in a similar process by breaking a
1315:is rational if and only if there exists integers
1208:
336:{\displaystyle \scriptstyle {\text{difference}}}
891:{\displaystyle \scriptstyle {\text{logarithm}}}
1705:National Institute of Standards and Technology
1838:
1695:Thompson, A.; Taylor, B. N. (March 4, 2020).
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917:
452:{\displaystyle \scriptstyle {\text{product}}}
53:
8:
1291:A more detailed definition goes as follows:
724:{\displaystyle \scriptstyle {\text{power}}}
30:The quotient of 12 apples by 3 apples is 4.
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1288:(as long as the denominator is non-zero).
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805:{\displaystyle \scriptstyle {\text{root}}}
71:
60:
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1675:International Electrotechnical Vocabulary
1650:International Electrotechnical Vocabulary
1625:International Electrotechnical Vocabulary
1599:. Springer Science & Business Media.
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1091:quotients of two quantities of the same
1047:{\displaystyle 6{\tfrac {2}{3}}=6.66...}
1784:"Irrationality of the square root of 2"
1513:
1752:Discrete mathematics with applications
1284:can be defined as the quotient of two
1258:20 − 3 − 3 − 3 − 3 − 3 − 3 − 3 < 0.
1145:Division (mathematics) § Notation
1121:) is said to be a "quotient", whereas
1004:). For example, when dividing 20 (the
1117:(mass divided by volume, in units of
7:
1067:International System of Quantities
14:
1351:{\displaystyle r={\tfrac {a}{b}}}
1262:In this sense, a quotient is the
1897:
1866:
1810:
984:) is a quantity produced by the
954:
1250:20 − 3 − 3 − 3 − 3 − 3 − 3 ≥ 0,
1171:
1095:. Quotients with a non-trivial
16:Mathematical result of division
1750:Epp, Susanna S. (2011-01-01).
1478:, also left and right quotient
1213:
1194:
1179:
854:
846:
1:
1476:Quotient of a formal language
1266:of the ratio of two numbers.
1071:International System of Units
952:'how many times', pronounced
1754:. Brooks/Cole. p. 163.
1416:may be formed by breaking a
1593:James, R. C. (1992-07-31).
2068:
1273:
1142:
1000:(in the case of a general
18:
1937:
1895:
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1492:Quotient space (topology)
1432:into a number of similar
1420:into a number of similar
21:Quotient (disambiguation)
1270:Quotient of two integers
1199:divisor or denominator
1087:is the special case for
1502:Quotition and partition
1377:{\displaystyle b\neq 0}
1234:Integer part definition
1184:dividend or numerator
1058:) in the second sense.
1596:Mathematics Dictionary
1396:More general quotients
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39:Arithmetic operations
29:
1819:at Wikimedia Commons
1406:equivalence relation
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1307:Given a real number
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19:For other uses, see
1539:Weisstein, Eric W.
1303:Or more formally:
1128:Specific quantities
1079:physical quantities
1874:Division and ratio
1727:Weisstein, Eric W.
1541:"Integer Division"
1408:defined on it, a "
1390:irrational numbers
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1815:Media related to
1788:www.math.utah.edu
1606:978-0-412-99041-0
1451:Quotient category
1388:The existence of
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1107:"), are known as
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2016:Musical interval
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2006:Just intonation
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1471:Quotient object
1466:Quotient module
1442:
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1282:rational number
1278:
1276:Rational number
1272:
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1203:
1202:
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1187:
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1141:
1113:. For example,
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321:
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159:
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138:
137:
117:
116:
92:
86:
85:
66:
37:
24:
17:
12:
11:
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1456:Quotient graph
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1426:quotient space
1414:quotient group
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1295:A real number
1274:Main article:
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1143:Main article:
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1101:compound units
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851:anti-logarithm
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627:Exponentiation
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1089:dimensionless
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1487:Quotient set
1430:vector space
1410:quotient set
1399:
1387:
1320:
1316:
1312:
1308:
1302:
1296:
1290:
1279:
1264:integer part
1261:
1253:
1240:whole number
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1082:
1060:
1013:
1009:
1008:) by 3 (the
1005:
941:
935:
736:
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405:multiplicand
1994:Irreducible
1924:Denominator
1710:October 25,
525:denominator
233:Subtraction
2026:Percentage
2021:Paper size
1930:= Quotient
1793:2020-08-27
1730:"Quotient"
1681:2023-09-13
1656:2023-09-13
1631:2023-09-13
1579:2023-07-23
1550:2020-08-27
1522:"Quotient"
1508:References
1424:, while a
1323:such that
1105:per second
938:arithmetic
395:multiplier
329:difference
290:subtrahend
2052:Quotients
1999:Reduction
1957:Continued
1942:Algebraic
1918:Numerator
1854:Fractions
1817:Quotients
1770:970542319
1735:MathWorld
1369:≠
1244:remainder
1214:←
1195:←
1180:←
1097:dimension
1063:metrology
884:logarithm
844:
817:Logarithm
518:numerator
400:×
379:×
285:−
264:−
2046:Category
1972:Egyptian
1907:Fraction
1889:Quotient
1881:Dividend
1440:See also
1404:with an
1286:integers
1218:quotient
1139:Notation
1069:and the
1014:quotient
1006:dividend
1002:division
994:fraction
986:division
950:quotiens
942:quotient
760:radicand
659:exponent
588:quotient
577:fraction
494:dividend
465:Division
76:Addition
1989:Integer
1962:Decimal
1927:
1915:
1885:Divisor
1574:iso.org
1115:density
1042:6.66...
1012:), the
1010:divisor
992:) or a
739:th root
501:divisor
445:product
280:minuend
133:summand
123:summand
1982:Silver
1977:Golden
1967:Dyadic
1952:Binary
1947:Aspect
1858:ratios
1768:
1758:
1603:
1422:cosets
1254:while
1084:Ratios
944:(from
766:degree
384:factor
374:factor
175:addend
165:augend
154:addend
144:addend
1418:group
1358:and
1110:rates
998:ratio
946:Latin
819:(log)
717:power
677:power
599:ratio
2031:Unit
1856:and
1766:OCLC
1756:ISBN
1712:2021
1601:ISBN
1319:and
1131:are
1119:kg/m
1099:and
1093:kind
940:, a
839:base
798:root
672:base
654:base
269:term
259:term
112:term
102:term
2011:LCD
1402:set
1077:of
1061:In
1054:(a
996:or
936:In
835:log
741:(√)
629:(^)
467:(÷)
350:(×)
235:(−)
214:sum
78:(+)
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