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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:
795:, is directly proportional to the object's mass; the constant of proportionality between the force and the mass is known as
1022:; 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.
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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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469:) or "~", with exception of Japanese texts, where "~" is reserved for intervals:
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1354:. Journal for Research in Mathematics Education, 40.2, 2009, p. 187–211.
1209:
751:
723:
201:); 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
1064:∝, ∝, ∝, ∝, ∝
964:
values of each point on the curve equals the constant of proportionality (
1345:. Mathematics Teaching in the Middle School, 13.3, 2007, p. 140–142.
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398:
132:
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Van Dooren, Wim; De Bock Dirk; Evers
Marleen; Verschaffel Lieven :
1340:
1336:. Mathematics Teaching in the Middle School 8.8 (2003), p. 392–396.
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1313:
Merriam-Webster's Guide to
Everyday Math: A Home and Business Reference
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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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155:
845:) 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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27:
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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1111:∼, ∼, ∼, ∼
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The graph of two variables varying inversely on the
849:(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
980:is non-zero), the graph never crosses either axis.
1046:characters for proportionality are the following:
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699:A direct proportionality can also be viewed as a
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762:, with the constant of proportionality equal to
853:is a constant. It follows that the variable
690:{\displaystyle \{(a,b)\in A\times B:a=kb\}.}
681:
636:
857:is inversely proportional to the variable
810:
123:is inversely proportional to the variable
999:
743:traveled is directly proportional to the
392:
383:). Proportionality is closely related to
107:is directly proportional to the variable
87:Learn how and when to remove this message
814:
114:
98:
50:This article includes a list of general
1330:Lanius, Cynthia S.; Williams Susan E.:
791:by a nearby large extended mass due to
151:if their corresponding elements have a
14:
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806:, is the classical mass of the object.
787:, acting on a small object with small
819:Inverse proportionality with product
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861:if there exists a non-zero constant
36:
735:If an object travels at a constant
111:with proportionality constant ~0.6.
24:
1339:Seeley, Cathy; Schielack Jane F.:
56:it lacks sufficient corresponding
25:
1384:
311:{\textstyle {\frac {f(x)}{g(x)}}}
170:) and its reciprocal is known as
894:{\displaystyle y={\frac {k}{x}}}
758:is directly proportional to its
613:∝ with proportionality constant
587:{\displaystyle k={\frac {y}{x}}}
426:if there is a positive constant
127:with proportionality constant 1.
41:
558:can be expressed as the ratio:
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161:coefficient of proportionality
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1:
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1198:Basic proportionality theorem
722:> 0, which corresponds to
7:
1178:Rule of three (mathematics)
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729:
603:constant of proportionality
10:
1389:
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797:gravitational acceleration
491:{\displaystyle y\propto x}
396:
29:
1315:. Merriam-Webster, 1998,
1302:Higher math for beginners
1283:– A Wolfram Web Resource.
1241:– A Wolfram Web Resource.
605:. Given such a constant
410:and a dependent variable
173:constant of normalization
1368:Mathematical terminology
1277:"Inversely Proportional"
1220:
976:can equal zero (because
703:in two variables with a
556:proportionality constant
167:proportionality constant
1235:"Directly Proportional"
811:Inverse proportionality
547:{\displaystyle x\neq 0}
517:{\displaystyle y\sim x}
71:more precise citations.
1020:hyperbolic coordinates
1006:Hyperbolic coordinates
1000:Hyperbolic coordinates
933:. Hence the constant "
927:
895:
847:multiplicative inverse
831:inversely proportional
826:
691:
609:, the proportionality
597:It is also called the
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393:Direct proportionality
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199:variable (mathematics)
184:inversely proportional
158:. The ratio is called
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956:. The product of the
954:rectangular hyperbola
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599:constant of variation
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420:directly proportional
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182:). Two sequences are
149:directly proportional
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1126:GEOMETRIC PROPORTION
950:Cartesian coordinate
937:" is the product of
926:{\displaystyle xy=k}
908:
872:
633:
627:equivalence relation
565:
532:
502:
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455:{\displaystyle y=kx}
437:
405:independent variable
273:
258:{\displaystyle g(x)}
240:
229:{\displaystyle f(x)}
211:
179:normalizing constant
30:For other uses, see
1296:Ya. B. Zeldovich,
1275:Weisstein, Eric W.
1252:"Inverse variation"
1233:Weisstein, Eric W.
804:Newton's second law
18:Direct relationship
1163:Inverse-square law
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891:
843:inverse proportion
829:Two variables are
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193:. This meaning of
139:of numbers, often
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1215:Hyperbolic growth
1168:Proportional font
1153:Eudoxus of Cnidus
1038:Computer encoding
968:). Since neither
904:or equivalently,
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839:inverse variation
835:varying inversely
617:between two sets
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379:(for details see
320:constant function
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141:experimental data
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16:(Redirected from
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1010:The concepts of
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1060:PROPORTIONAL TO
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724:linear growth
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119:The variable
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1298:I. M. Yaglom
1280:
1271:
1259:. Retrieved
1255:
1246:
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1229:
1158:Golden ratio
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267:proportional
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145:proportional
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83:
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55:
1261:October 31,
1183:Sample size
1148:Correlation
1130:∺
952:plane is a
739:, then the
629:defined by
430:such that:
399:Equals sign
133:mathematics
77:August 2021
69:introducing
1362:Categories
1291:References
1193:Trairāśika
1188:Similarity
1143:Linear map
1093:PROPORTION
865:such that
708:-intercept
397:See also:
331:proportion
52:references
1325:p. 85–101
1281:MathWorld
1239:MathWorld
1032:hyperbola
661:×
655:∈
539:≠
509:∼
483:∝
403:Given an
386:linearity
206:functions
191:variables
137:sequences
1306:p. 34–35
1256:math.net
1137:See also
1123:∺
1104:∼
1090:∷
1057:∝
1028:constant
1026:and the
760:diameter
741:distance
730:Examples
611:relation
333:, e.g.,
327:equation
195:variable
153:constant
1044:Unicode
1016:inverse
851:product
793:gravity
625:is the
372:
356:
352:
336:
65:improve
1373:Ratios
1319:
1204:Growth
1120:
1118:U+223A
1101:
1099:U+223C
1087:
1085:U+2237
1076:~
1073:
1071:U+007E
1054:
1052:U+221D
1012:direct
756:circle
714:and a
374:= ⋯ =
143:, are
135:, two
54:, but
1221:Notes
1173:Ratio
1079:TILDE
841:, in
837:, in
824:= 1 .
785:force
777:scale
771:On a
754:of a
737:speed
716:slope
467:alpha
381:Ratio
318:is a
156:ratio
1317:ISBN
1263:2021
1042:The
1014:and
972:nor
960:and
941:and
789:mass
783:The
780:map.
750:The
745:time
621:and
554:the
528:For
498:(or
265:are
236:and
204:Two
176:(or
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773:map
718:of
710:of
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