What Is A Ratio
This article is about the mathematical concept. For the Swedish institute, see Ratio Institute. For
the academic journal, see Ratio (journal). For the philosophical concept, see Reason. For the
legal concept, see Ratio decidendi.
In mathematics, a ratio is a relationship between two numbers of the same kind (e.g., objects,
persons, students, spoonfuls, units of whatever identical dimension), usually expressed as "a to b"
or a:b, sometimes expressed arithmetically as a dimensionless quotient of the two which explicitly
indicates how many times the first number contains the second (not necessarily an integer).
In layman's terms a ratio represents, simply, for every amount of one thing, how much there is of


another thing. For example, suppose I have 10 pairs of socks for every pair of shoes then the ratio
of shoes:socks would be 1:10 and the ratio of socks:shoes would be 10:1

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Examples
The quantities being compared in a ratio might be physical quantities such as speed or length, or
numbers of objects, or amounts of particular substances. A common example of the last case is
the weight ratio of water to cement used in concrete, which is commonly stated as 1:4.
This means that the weight of cement used is four times the weight of water used. It does not say
anything about the total amounts of cement and water used, nor the amount of concrete being
made. Equivalently 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..
Older televisions have a 4:3 "aspect ratio", which means that the width is 4/3 of the height;
modern widescreen TVs have a 16:9 aspect ratio.
Percentage ratio
If we multiply all quantities involved in a ratio by the same number, the ratio remains valid. For
example, a ratio of 3:2 is the same as 12:8. It is usual either to reduce terms to the lowest
common denominator, or to express them in parts per hundred (percent).
If a mixture contains substances A, B, C & D in the ratio 5:9:4:2 then there are 5 parts of A for
every 9 parts of B, 4 parts of C and 2 parts of D. As 5+9+4+2=20, the total mixture contains 5/20
of A (5 parts out of 20), 9/20 of B, 4/20 of C, and 2/20 of D.


If we divide all numbers by the total and multiply by 100, this is converted to percentages: 25% A,
45% B, 20% C, and 10% D (equivalent to writing the ratio as 25:45:20:10).

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Proportions
If the two or more ratio quantities encompass all of the quantities in a particular situation, for
example two apples and three oranges in a fruit basket containing no other types of fruit, it could
be said that "the whole" contains five parts, made up of two parts apples and three parts oranges.
In this case, 2/5, or 40% of the whole are apples and 3/5, or 60% of the whole are oranges. This
comparison of a specific quantity to "the whole" is sometimes called a proportion. Proportions are
sometimes expressed as percentages as demonstrated above.
Dilution ratio
Ratios are often used for simple dilutions applied in chemistry and biology. A simple dilution is one
in which a unit volume of a liquid material of interest is combined with an appropriate volume of a
solvent liquid to achieve the desired concentration. The dilution factor is the total number of unit
volumes in which your material will be dissolved.
The diluted material must then be thoroughly mixed to achieve the true dilution. For example, a
1:5 dilution (verbalize as "1 to 5" dilution) entails combining 1 unit volume of solute (the material to
be diluted) + 4 unit volumes (approximately) of the solvent to give 5 units of the total volume.
(Some solutions and mixtures take up slightly less volume than their components.)
The dilution factor is frequently expressed using exponents: 1:5 would be 5e-1 (5-1 i.e. one-
fifth:one); 1:100 would be 10e-2 (10-2 i.e. one hundredth:one), and so on.
There is often confusion between dilution ratio (1:n meaning 1 part solute to n parts solvent) and


dilution factor (1:n+1) where the second number (n+1) represents the total volume of solute +
solvent.

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In scientific and serial dilutions, the given ratio (or factor) often means the ratio to the final volume,
not to just the solvent. The factors then can easily be multiplied to give an overall dilution factor.
In other areas of science such as pharmacy, and in non-scientific usage, a dilution is normally
given as a plain ratio of solvent to solute.
Different units
Ratios are unitless when they relate quantities which have units of the same dimension.
For example :-
the ratio 1 minute : 40 seconds can be reduced by changing the first value to 60 seconds. Once
the units are the same, they can be omitted, and the ratio can be reduced to 3:2.
In chemistry, mass concentration "ratios" are usually expressed as w/v percentages, and are
really proportions.
For example :-
a concentration of 3% w/v usually means 3g of substance in every 100mL of solution. This cannot
easily be converted to a pure ratio because of density considerations, and the second figure is the
total amount, not the volume of solvent

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