|
A ratio is a comparison of two (or more) quantities.
|
The ratio of one number to another number is the quotient of the first number divided by the second number, where the second number is not zero. (A ratio is a fraction.) |
|
While a ratio is most commonly written as a fraction, it may also appear in other forms:
Since a ratio can be written as a fraction, it can also be written in any form that is equivalent to that fraction. All of the following statements are equivalent:
Equivalent ratios are ratios that can be reduced to the same value: 
A continued ratio refers to the comparison of more than two quantities: a : b : c.
When working with ratios in an algebraic setting, remember that 3 : 4 : 7
may need to be expressed as 3x : 4x : 7x (an equivalent form).
The sides of a pentagon are in the ratio of 2 : 3 : 5 : 1 : 4. If the perimeter of the pentagon is 90 units, find the lengths of the five sides.
Solution: Represent the sides of the pentagon as 2x, 3x, 5x, x, and 4x, an equivalent form.
Since 2 + 3 + 5 + 1 + 4 does not equal 90, we know that the side lengths will be an equivalent form of this continued ratio.
2x + 3x + 5x + x + 4x = 90
15x = 90
x = 6
The sides of the pentagon are 12, 18, 30, 6 and 24 units.
|
A proportion is an equation stating that two ratios are equivalent (equal), written in the form  . |
|
Proportions always have an equal sign!
A proportion can be written in two forms: 
For example, 
where both are read "6 is to 9 as 2 is to 3".
In each proportion, the first and last terms (6 and 3) are called the extremes.
The second and third terms (9 and 2) are called the means.
or 
 RULE: In a proportion, the product of the means
equals the product of the extremes.
(You may see this rule referred to as "cross multiply" or "cross product".) |
 |
Properties of Proportions:
Notice that all of these proportions "cross multiply" to yield the same result.
a • d = c • b
Some additional properties:
Keep in mind that there are many different ways to express
equivalent proportions.
Solve for x: 
Solution: Apply the rule that "in a proportion, the product of the means equals the product of the extremes."
gives (5)•(12) = 8 • x; 60 = 8x; x = 7.5 ANSWER
In Geometry, we also use this rule when working with similar triangles.
