Proportion

In mathematics, two quantities are proportional if they vary in such a way that one of them is a constant multiple of the other.

A proportion is an equation with a ratio on each side. It is a statement that two ratios are equal.

3/4 = 6/8 is an example of a proportion.

When one of the four numbers in a proportion is unknown, cross products may be used to find the unknown number. This is called solving the proportion. Question marks or letters are frequently used in place of the unknown number.

y is directly proportional to x




Example:

Solve for n: 1/2 = n/4.

Using cross products we see that 2 × n = 1 × 4 =4, so 2 × n = 4. Dividing both sides by 2, n = 4 ÷ 2 so that n = 2.

The mathematical symbol '∝' is used to indicate that two values are proportional. For example, A ∝ B. In Unicode this is symbol U+221D.

Direct Proportionality

Given two variables x and y, y is (directly) proportional to x (x and y vary directly, or x and y are in direct variation) if there is a non-zero constant k such that

The relation is often denoted



and the constant ratio


is called the proportionality constant or constant of proportionality.

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.

- The circumference of a circle is proportional to its 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.

- 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.

Reference:
http://en.wikipedia.org/wiki/Proportionality_(mathematics)