Proportion is two equal ratios considered
simultaneously. An example proportion is
1:3::3:9
This proportion is expressed as “1 is to 3 as 3 is to 9.” Since
the ratios are equal, the proportion may also be written
1:3 = 3:9
Terms of Proportion
The first and fourth terms (the terms on the ends)
are called the extremes. The second and third terms
(middle terms) are called the means.
In a proportion, the product of the means equals the
product of the extremes; therefore, when three terms are
known, the fourth (or unknown) term may be determined.
Application of Proportion
The important factor when working proportions is
to put the right values in the right places within the
proportion. By following a few basic rules, you can
accomplish this without difficulty and solve the
problem correctly.
In numbering the four positions of a proportion
from left to right (i.e., first, second, third, and fourth,
observe the following rules):
Let X (the unknown value) always be in the
fourth position.
Let the unit of like value to X be the third
position.
If X is smaller than the third position, place the
smaller of the two leftover values in the second
position; if X is larger, place the larger of the two
values in the second position.
Place the last value in the first position. When
the proportion is correctly placed, multiply the
extremes and the means and determine the value
of X, the unknown quantity.
615
When we add water to a solution, the strength is
diluted; consequently, the 70% strength of this
solution will be lessened when we add the extra
150 ml of water. Therefore, of the two remaining
given quantities (650 ml and 500 ml), the smaller
(500 ml) will be placed in the second position,
leaving the quantity 650 ml to be placed in the first
position:
2^{nd} position:
500 ml
1^{st} position:
650 ml
The proportion appears as follows:
650 : 500 :: 70 : X
Multiplying the extremes and the means, we arrive
at:
650X = 35,000, or
X = 53.8
When 150 ml of water is added to 500 ml of 70%
alcohol, the result is 650 ml of 53.8% solution.
Example #1: What is the percent strength of 500 ml of
70% alcohol to which 150 ml of water has been added?
Solution: When adding 150 ml to 500 ml, the total
quantity will be 650 ml; consequently, our four values
will be 500 ml, 650 ml, 70%, and X (the unknown
percent). Following the rules stated above, the problem
will appear as follows:
4^{th} position:
X (%)
3^{rd} position:
70% (like value to X)
Example #2: When 1000 ml of 25% solution is
evaporated to 400 ml, what is the percent strength?
Solution:
4^{th} position:
X(%)
3^{rd} position:
15% (like value to X)
When we evaporate a solution, it becomes stronger.
Therefore, the larger of the two remaining given
values (1000 ml and 400 ml), will be placed in the
second position, leaving the quantity 400 ml to be
placed in the first position:
2^{nd} position:
1000 ml
1^{st} position:
400 ml
The proportion appears as follows:
400 : 1000 :: 15 : X
Multiplying the extremes and the means, we arrive
at:
400X = 25,000, or
X = 62.5
When 1000 ml of water is evaporated to 400 ml, the
result is a 62.5% solution.

