A proportion
is a comparison of ratios.
A proportion
is an equation that states
that two ratios are equal, such as


Proportions
always have an EQUAL sign! 



A
proportion can be written in two ways:
Both
are read "4 is to 8 as 1 is to 2".
In
each proportion the first and last terms (4 and 2) are
called the
extremes.
The second and third terms (8 and 1) are called the
means. 

You can tell if a
simple proportion is true by just examining the
fractions. If the fractions both reduce to the same value,
the proportion is true. 
This is a true
proportion, since both fractions reduce to 1/3. 
You can often use this same
approach when solving for a missing part of a simple proportion.
Remember that both fractions must represent the same value.
Notice how we solve this problem by getting a common denominator
for the two fractions. 
To change the
denominator of 3 to 15 requires multiplying by 5. The
SAME must be done to the top to keep the fractions equal.
Answer: x = 5 
This
simple approach may not be sufficient
when working with more complex
proportions.
You need a rule:

Some
people call this rule
Cross
Multiply!! 


A more precise statement of the
rule is:
RULE: In a true proportion, the
product of the means equals
the product of the extremes. 

Proportions can also be solved by
multiplying each side of the proportion by
the common denominator for both fractions. 
Example
1:
Solve for x
algebraically in this
proportion:
Solution:
Method 1:
Appling
the rule that the "in a true proportion, the product of the means equals the product of the extremes".
5x = (25)(2)
5x = 50
x = 10 Answer

Method 2:
Multiplying by the common
denominator, 2x.
2•25 = 5•x
50 = 5x
10 = x Answer

Example
2:
The length of a
stadium is 100 yards and its width is 75 yards. If 1 inch represents
25 yards, what would be the dimensions of the stadium drawn on a sheet of
paper?
Solution: This
problem can be solved by an
intuitive approach, such as:
100
yards by 75 yards
100 yards = 4 inches (HINT: 100 / 25)
75 yards = 3 inches (HINT: 75 / 25)
Therefore, the dimensions would be 4 inches by 3 inches.
Solution
by
proportion:
(Notice that the inches are all
on the top and the yards are all on the bottom
for this solution. Other combinations are possible.)
Length:
25x
= 100
x = 4 inches 
Width:
25y
= 75
y = 3 inches 
