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'''Proportion''' in mathematics exists when two quantities vary in such a way that one of the quantities is a constant multiple of the other, or equivalently if they have a constant [[ratio]]. Proportion also refers to the equality of two ratios.

'''Proportion''' in mathematics exists when two quantities vary in such a way that one of the quantities is a constant multiple of the other, or equivalently if they have a constant [[ratio]]. Proportion also refers to the equality of two ratios.

[[File:Proportion1.jpg‎|center]]

[[File:Proportion1.jpg‎|center]]

is called the proportionality constant or constant of proportionality.

is called the proportionality constant or constant of proportionality.

===Examples===

===Examples===

* If an object travels at a constant [[speed]], then the distance traveled is proportional to the time spent traveling, with the speed being the constant of proportionality.

* If an object travels at a constant [http://en.wikipedia.org/wiki/Speed speed], then the distance traveled is proportional to the time spent traveling, with the speed being the constant of proportionality.

* The [[circumference]] of a [[circle]] is proportional to its [[diameter]], with the constant of proportionality equal to π.

* The [http://en.wikipedia.org/wiki/Circumference circumference] of a [[circle]] is proportional to its [http://en.wikipedia.org/wiki/Diameter diameter], with the constant of proportionality equal to π.

* On a map drawn to [[scale]], the distance between any two points on the map is proportional to the distance between the two locations that the points represent, with the constant of proportionality being the scale of the map.

* On a map drawn to [[scale]], the distance between any two points on the map is proportional to the distance between the two locations that the points represent, with the constant of proportionality being the scale of the map.

* The [[force]] acting on a certain object due to [[gravity]] is proportional to the object's [[mass]]; the constant of proportionality between the mass and the force is known as gravitational acceleration.

* The [[force]] acting on a certain object due to [[gravity]] is proportional to the object's [http://en.wikipedia.org/wiki/Mass mass]; the constant of proportionality between the mass and the force is known as gravitational acceleration.

===Properties===

===Properties===

[[File:Proportion2.jpg|center]]

[[File:Proportion2.jpg|center]]

Basically, the [[concept]] of inverse proportion [[Meaning|means]] that as the [[absolute]] [[value]] or magnitude of one variable gets bigger, the absolute value or magnitude of another gets smaller, such that their product (the constant of proportionality) is always the same.

Basically, the [[concept]] of inverse proportion [[Meaning|means]] that as the [[absolute]] [[value]] or magnitude of one variable gets bigger, the absolute value or magnitude of another gets smaller, such that their product (the constant of proportionality) is always the same.

For example, the time taken for a journey is inversely proportional to the [[speed]] of travel; the time needed to dig a hole is (approximately) inversely proportional to the number of people digging.

For example, the time taken for a journey is inversely proportional to the [http://en.wikipedia.org/wiki/ speed] of travel; the time needed to dig a hole is (approximately) inversely proportional to the number of people digging.

The graph of two variables varying inversely on the [http://en.wikipedia.org/wiki/Cartesiancoordinate Cartesian coordinate] plane is a [http://en.wikipedia.org/wiki/Hyperbola hyperbola]. The product of the X and Y values of each point on the curve will equal the constant of proportionality (k). Since k can never equal zero, the graph will never cross either axis.

The graph of two variables varying inversely on the [http://en.wikipedia.org/wiki/Cartesiancoordinate Cartesian coordinate] plane is a [http://en.wikipedia.org/wiki/Hyperbola hyperbola]. The product of the X and Y values of each point on the curve will equal the constant of proportionality (k). Since k can never equal zero, the graph will never cross either axis.