# Quotient

In mathematics and in the natural sciences, the quotient referred to each other a ratio of two quantities, ie, the result of a division. The quotient of two integers ( dividend and divisor ) is always a rational number, and can be written as a fraction.

A quotient is often the assignment of a value to an overall scale, such as the intelligence quotient, which is determined by using an intelligence test number for a person with their age group corresponding " average intelligence " in relationship. The intelligence quotient 100 stands for the average. Ratios are often expressed as a percentage by the ratio normalized (ie extended or shortened) is that the denominator is 100.

Particular circumstances in this sense are:

- The slope as the ratio of the value added to the second coordinate axis to increase in value on the first coordinate axis.
- The trigonometric functions sine, cosine, etc.
- The scale as a ratio of two lengths
- Than twice the radius of the circular area and the ratio between circumference
- The fractal dimension of chaos theory as a ratio of two logarithms

## Proportions

Ratio equations or proportions are equations that equate the two ratios: a ÷ b = c ÷ d a and c are called the antecedents, b and d hind limbs of proportion. In addition, a hot and d outer links and inner links b and c. The proportion can be formed by cross- multiplication in an equation of the form a · d = c * b. Swapping the inner segments and the outer links of a proportion, new proportions: a ÷ c = b ÷ d and d ÷ b = c ÷ a Further, the laws of the corresponding addition and subtraction apply:

### Laws of the corresponding addition and subtraction

It should be given the proportion a ÷ b = c ÷ d. Then the proportions are

### Ongoing proportions

Occasionally, there is also the spelling of a ÷ b ÷ c = u ÷ v ÷ w. This continuous proportions are not to be understood as a single equation, but are rather a short form for the two equations a ÷ b = u ÷ v and b ÷ c = v ÷ w (or equivalently a ÷ u = b ÷ v and b ÷ v = c ÷ w).

### Examples

- The definition of the Golden Ratio
- The Law of Sines
- The radiation rates
- The law of refraction of the optical
- The octave of music