### Ratio

A **ratio** shows the relationship between two quantities. You write it often with a colon as

a:b

and you call it the quotient of *a* and *b*.

##### Explanation

In general you can write

Numerator = Dividend = Quotient = Fraction = Ratio Denominator Divisor

##### Example 1

Ratios can be calculated by cross-multiplication

a:b=c:d

gives then

a×d=b×c

##### Example 2

Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities

where *a* > *b* > 0.

##### Example 3

The number π = 3.1415… describes the ratio between the circumference and the diameter of a circle

π = circumference diameter

and cannot be written by any pair of whole numbers. It is an irrational number.

##### Example 4

The number √2 = 1,4142... is the ratio between the side and the diameter of a square, and cannot be written by any pair of whole numbers. It is an irrational number.

##### Example 5

A probability is the ratio between the number of favorable outcomes and the number of possible outcomes

P(G) =number of favorable outcomes number of possible outcomes