## ::Ratio

### ::concepts

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

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The ratio of width to height of standard-definition television.

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

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