## ::Ratio

### ::concepts

**Ratio**::ratios ''p''::''q'' Quantity::''r'' Books::numbers Example::number Fraction::''a''

{{#invoke:Hatnote|hatnote}}
{{#invoke:Hatnote|hatnote}}
{{#invoke:redirect hatnote|redirect}}

In mathematics, a **ratio** is a relationship between two numbers indicating how many times the first number contains the second.<ref>Penny Cyclopedia, p. 307</ref> For example, if a bowl of fruit contains eight oranges and six lemons, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Thus, a ratio can be a fraction as opposed to a whole number. Also, in this example the ratio of lemons to oranges is 6:8 (or 3:4), and the ratio of oranges to the total amount of fruit is 8:14 (or 4:7).

The numbers compared in a ratio can be any quantities of a comparable kind, such as objects, persons, lengths, or spoonfuls. A ratio is written "*a* to *b*" or *a*:*b*, or sometimes expressed arithmetically as a quotient of the two.<ref>New International Encyclopedia</ref> When the two quantities have the same units, as is often the case, their ratio is a dimensionless number. A rate is a quotient of variables having different units. But in many applications, the word *ratio* is often used instead for this more general notion as well.<ref>*"The quotient of two numbers (or quantities); the relative sizes of two numbers (or quantities)"*, "The Mathematics Dictionary" [1]</ref>

**Ratio sections**

Intro History and etymology Number of terms and use of fractions Proportions and percentage ratios Reduction Irrational ratios Odds Units Triangular coordinates See also References Further reading External links

PREVIOUS: Intro | NEXT: History and etymology |

<< | >> |