Proportions
 Lesson
 Topic Index | Grade 6 Math | Intermediate Test Prep | StudyZone
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 term (4 and 2) are called the extremes. 
The second and third terms (8 and 1) are called the means.

 
In simple proportions,  all you need to do is examine 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

.
In simple proportions, you can use this same approach when solving for a missing part of a proportion.  Remember that both fractions must reduce to the same value.   
To alter the denominator 3 to become 15 requires multiplying by 5.  The SAME must be done to the top to keep the fractions equal.  Answer: x = (1)(5) = 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!!
Rule:
In a true proportion, the product of the means equals the product of the extremes.

 

 Example:

Solve for x in this proportion:

 

Solution: 

Apply the rule that the product of the means 
equals the product of the extremes.
5x = (25)(2)
5x = 50
x=10  Answer


 
Topic Index | Grade 6 Math | Intermediate Test Prep | StudyZone

Created by Donna Roberts
Updated by Carol Carroll
Copyright © 2001-06 Oswego City School District