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Direct and inverse proportion contrast as follows: in direct proportion the variables increase or decrease together. With inverse proportion, an increase in one variable is associated with a decrease in the other. For instance, in travel, a constant speed dictates a direct proportion between distance
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distances, the distance between any two points on the map is directly proportional to the beeline distance between the two locations represented by those points; the constant of proportionality is the scale of the
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The net force acting on an object is proportional to the acceleration of that object with respect to an inertial frame of reference. The constant of proportionality in this,
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and time travelled; in contrast, for a given distance (the constant), the time of travel is inversely proportional to speed:
784:, is directly proportional to the object's mass; the constant of proportionality between the force and the mass is known as
1011:; the two coordinates correspond to the constant of direct proportionality that specifies a point as being on a particular
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if corresponding elements have a constant product, also called the coefficient of proportionality.
40:
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Students' Overuse of
Proportionality on Missing-Value Problems: How Numbers May Change Solutions
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The relation is often denoted using the symbols "∝" (not to be confused with the Greek letter
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This definition is commonly extended to related varying quantities, which are often called
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If several pairs of variables share the same direct proportionality constant, the
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458:) or "~", with exception of Japanese texts, where "~" is reserved for intervals:
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1343:. Journal for Research in Mathematics Education, 40.2, 2009, p. 187–211.
1198:
740:
712:
190:); these two different concepts share the same name for historical reasons.
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of inverse proportionality that specifies a point as being on a particular
1053:∝, ∝, ∝, ∝, ∝
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values of each point on the curve equals the constant of proportionality (
1334:. Mathematics Teaching in the Middle School, 13.3, 2007, p. 140–142.
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765:
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121:
88:
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Van Dooren, Wim; De Bock Dirk; Evers
Marleen; Verschaffel Lieven :
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1325:. Mathematics Teaching in the Middle School 8.8 (2003), p. 392–396.
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1302:
Merriam-Webster's Guide to
Everyday Math: A Home and Business Reference
1131:
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spent traveling, with the speed being the constant of proportionality.
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proportion lead to the location of points in the
Cartesian plane by
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A Look at the
Development of Ratios, Rates, and Proportionality
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834:) if each of the variables is directly proportional to the
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is not the common meaning of the term in mathematics (see
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Property of two varying quantities with a constant ratio
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PROPORTIONALITY: A Unifying Theme for the Middle Grades
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1100:∼, ∼, ∼, ∼
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The graph of two variables varying inversely on the
838:(reciprocal) of the other, or equivalently if their
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of a sufficiently small geographical area, drawn to
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expressing the equality of these ratios is called a
969:is non-zero), the graph never crosses either axis.
1035:characters for proportionality are the following:
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688:A direct proportionality can also be viewed as a
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751:, with the constant of proportionality equal to
842:is a constant. It follows that the variable
679:{\displaystyle \{(a,b)\in A\times B:a=kb\}.}
670:
625:
846:is inversely proportional to the variable
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112:is inversely proportional to the variable
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732:traveled is directly proportional to the
381:
372:). Proportionality is closely related to
96:is directly proportional to the variable
76:Learn how and when to remove this message
803:
103:
87:
39:This article includes a list of general
1319:Lanius, Cynthia S.; Williams Susan E.:
780:by a nearby large extended mass due to
140:if their corresponding elements have a
1349:
795:, is the classical mass of the object.
776:, acting on a small object with small
808:Inverse proportionality with product
1026:
850:if there exists a non-zero constant
25:
724:If an object travels at a constant
100:with proportionality constant ~0.6.
13:
1328:Seeley, Cathy; Schielack Jane F.:
45:it lacks sufficient corresponding
14:
1373:
300:{\textstyle {\frac {f(x)}{g(x)}}}
159:) and its reciprocal is known as
883:{\displaystyle y={\frac {k}{x}}}
747:is directly proportional to its
602:∝ with proportionality constant
576:{\displaystyle k={\frac {y}{x}}}
415:if there is a positive constant
116:with proportionality constant 1.
30:
547:can be expressed as the ratio:
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150:coefficient of proportionality
1:
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1187:Basic proportionality theorem
711:> 0, which corresponds to
7:
1167:Rule of three (mathematics)
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718:
592:constant of proportionality
10:
1378:
992:
786:gravitational acceleration
480:{\displaystyle y\propto x}
385:
18:
1304:. Merriam-Webster, 1998,
1291:Higher math for beginners
1272:– A Wolfram Web Resource.
1230:– A Wolfram Web Resource.
594:. Given such a constant
399:and a dependent variable
162:constant of normalization
1357:Mathematical terminology
1266:"Inversely Proportional"
1209:
965:can equal zero (because
692:in two variables with a
545:proportionality constant
156:proportionality constant
1224:"Directly Proportional"
800:Inverse proportionality
536:{\displaystyle x\neq 0}
506:{\displaystyle y\sim x}
60:more precise citations.
1009:hyperbolic coordinates
995:Hyperbolic coordinates
989:Hyperbolic coordinates
922:. Hence the constant "
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884:
836:multiplicative inverse
820:inversely proportional
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598:, the proportionality
586:It is also called the
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382:Direct proportionality
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188:variable (mathematics)
173:inversely proportional
147:. The ratio is called
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945:. The product of the
943:rectangular hyperbola
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885:
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588:constant of variation
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409:directly proportional
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171:). Two sequences are
138:directly proportional
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1115:GEOMETRIC PROPORTION
939:Cartesian coordinate
926:" is the product of
915:{\displaystyle xy=k}
897:
861:
622:
616:equivalence relation
554:
521:
491:
465:
444:{\displaystyle y=kx}
426:
394:independent variable
262:
247:{\displaystyle g(x)}
229:
218:{\displaystyle f(x)}
200:
168:normalizing constant
19:For other uses, see
1285:Ya. B. Zeldovich,
1264:Weisstein, Eric W.
1241:"Inverse variation"
1222:Weisstein, Eric W.
793:Newton's second law
1152:Inverse-square law
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880:
832:inverse proportion
818:Two variables are
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182:. This meaning of
128:of numbers, often
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1204:Hyperbolic growth
1157:Proportional font
1142:Eudoxus of Cnidus
1027:Computer encoding
957:). Since neither
893:or equivalently,
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828:inverse variation
824:varying inversely
606:between two sets
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368:(for details see
309:constant function
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130:experimental data
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999:The concepts of
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1049:PROPORTIONAL TO
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1199:Linear growth
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822:(also called
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713:linear growth
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108:The variable
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92:The variable
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49:
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28:
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1290:
1287:I. M. Yaglom
1269:
1260:
1248:. Retrieved
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1235:
1227:
1218:
1147:Golden ratio
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978:
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256:proportional
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134:proportional
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63:
44:
1250:October 31,
1172:Sample size
1137:Correlation
1119:∺
941:plane is a
728:, then the
618:defined by
419:such that:
388:Equals sign
122:mathematics
66:August 2021
58:introducing
1351:Categories
1280:References
1182:Trairāśika
1177:Similarity
1132:Linear map
1082:PROPORTION
854:such that
697:-intercept
386:See also:
320:proportion
41:references
1314:p. 85–101
1270:MathWorld
1228:MathWorld
1021:hyperbola
650:×
644:∈
528:≠
498:∼
472:∝
392:Given an
375:linearity
195:functions
180:variables
126:sequences
1295:p. 34–35
1245:math.net
1126:See also
1112:∺
1093:∼
1079:∷
1046:∝
1017:constant
1015:and the
749:diameter
730:distance
719:Examples
600:relation
322:, e.g.,
316:equation
184:variable
142:constant
1033:Unicode
1005:inverse
840:product
782:gravity
614:is the
361:
345:
341:
325:
54:improve
1362:Ratios
1308:
1193:Growth
1109:
1107:U+223A
1090:
1088:U+223C
1076:
1074:U+2237
1065:~
1062:
1060:U+007E
1043:
1041:U+221D
1001:direct
745:circle
703:and a
363:= ⋯ =
132:, are
124:, two
43:, but
1210:Notes
1162:Ratio
1068:TILDE
830:, in
826:, in
813:= 1 .
774:force
766:scale
760:On a
743:of a
726:speed
705:slope
456:alpha
370:Ratio
307:is a
145:ratio
1306:ISBN
1252:2021
1031:The
1003:and
961:nor
949:and
930:and
778:mass
772:The
769:map.
739:The
734:time
610:and
543:the
517:For
487:(or
254:are
225:and
193:Two
165:(or
153:(or
1013:ray
811:x y
762:map
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699:of
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411:to
407:is
136:or
120:In
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977:×
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