Editing Ratio (section)

== Notation and terminology ==
The ratio of numbers ''A'' and ''B'' can be expressed as:<ref>New International Encyclopedia.{{full citation needed|date=April 2025}}</ref>
* the ratio of ''A'' to ''B''
* ''A'':''B''
* ''A'' is to ''B'' (when followed by "as ''C'' is to ''D''"; see below)
* a [[fraction (mathematics)|fraction]] with ''A'' as numerator and ''B'' as denominator that represents the quotient (i.e., ''A'' divided by ''B, or'' <math>\tfrac{A}{B}</math>). This can be expressed as a simple or a decimal fraction, or as a percentage, etc.<ref>Decimal fractions are frequently used in technological areas where ratio comparisons are important, such as aspect ratios (imaging), compression ratios (engines or data storage), etc.</ref>

When a ratio is written in the form ''A'':''B'', the two-dot character is sometimes the [[Colon (punctuation)|colon]] punctuation mark.<ref name="MathWorld-colon">{{cite web |url=https://mathworld.wolfram.com/Colon.html |title=Colon |last=Weisstein |first=Eric W. |author-link=Eric W. Weisstein |website=[[MathWorld]] |date=2022-11-04 |access-date=2022-11-26 }}</ref> In [[Unicode]], this is {{unichar|3a|colon}}, although Unicode also provides a dedicated ratio character, {{unichar|2236|ratio}}.<ref name="Unicode">{{cite web |url=https://www.unicode.org/charts/PDF/U0000.pdf |publisher=Unicode, Inc. |website=The Unicode Standard, Version 15.0 |title=ASCII Punctuation |date=2022 |access-date=2022-11-26 |quote=[003A is] also used to denote division or scale; for that mathematical use 2236 {{not a typo|∶}} is preferred.}}</ref>

The numbers ''A'' and ''B'' are sometimes called ''terms of the ratio'', with ''A'' being the ''[[Antecedent (grammar)|antecedent]]'' and ''B'' being the ''[[consequent]]''.<ref>[http://www.britannica.com/topic/ratio ratio]. Encyclopædia Britannica.</ref>

A statement expressing the equality of two ratios ''A'':''B'' and ''C'':''D'' is called a '''proportion''',<ref>Heath, p. 126.</ref> written as ''A'':''B'' = ''C'':''D'' or ''A'':''B''∷''C'':''D''. This latter form, when spoken or written in the English language, is often expressed as
:(''A'' is to ''B'') as (''C'' is to ''D'').

''A'', ''B'', ''C'' and ''D'' are called the terms of the proportion. ''A'' and ''D'' are called its ''extremes'', and ''B'' and ''C'' are called its ''means''. The equality of three or more ratios, like ''A'':''B'' = ''C'':''D'' = ''E'':''F'', is called a '''continued proportion'''.<ref>New International Encyclopedia.{{full citation needed|date=April 2025}}</ref>

Ratios are sometimes used with three or even more terms, e.g., the proportion for the edge lengths of a "[[Dimensional lumber|two by four]]" that is ten inches long is therefore
:<math>\text{thickness : width : length } = 2:4:10</math>
:(unplaned measurements; the first two numbers are reduced slightly when the wood is planed smooth);
a good concrete mix (in volume units) is sometimes quoted as
:<math>\text{cement : sand : gravel } = 1:2:4.</math><ref>{{cite book
 | last = Surahyo | first = Akhtar
 | contribution = Proportioning of Concrete Mixes
 | doi = 10.1007/978-3-030-10510-5_4
 | isbn = 9783030105105
 | pages = 89–103
 | publisher = Springer International Publishing
 | title = Concrete Construction
 | year = 2019}}</ref>

For a (rather dry) mixture of 4/1 parts in volume of cement to water, it could be said that the ratio of cement to water is 4:1, that there is 4 times as much cement as water, or that there is a quarter (1/4) as much water as cement.

The meaning of such a proportion of ratios with more than two terms is that the ratio of any two terms on the left-hand side is equal to the ratio of the corresponding two terms on the right-hand side.