Method Of Case Study Solving Proportions
Finding the missing value in a proportion is much like finding the missing value for two equal fractions. There are three main methods for determining whether two fractions (or ratios) are equivalent.

Method 1: Vertical Are these two ratios equivalent? Since the numerator and denominator are related (by multiplying or dividing by 2), we know these two ratios are equivalent.  Method 2: Horizontal Are these two ratios equivalent? Since the numerators are related (by multiplying or dividing by 3) to each other and the denominators are related to each other, we know these two ratios are equivalent.  Method 3: Crossproducts Are these two ratios equivalent? Since the crossproducts are equal to each other, the two ratios are equivalent. 
All three methods work for every problem, but often one method is easier to use than the others. Always watch for the easiest method to use!
Example 1
The following two ratios are equivalent. Find the missing value.
Answer: Let's use the vertical method on this. Since 3 x 4 = 12, then 5 x 4 = 20. So the missing value is 20.
Example 2
The following two ratios are equivalent. Find the missing value.
Answer: We will use the horizontal method on this one. Since 5 x 2 = 10, then 4 x 2 = 8. So, the missing value is 8.
Example 3
The following two ratios are equivalent. Find the missing value.
Answer: In this problem it is easiest to look at the crossproducts.
Directions:
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SelfCheck
Q1: Find the missing value. $\,\,\,\frac{9}{12}=\frac{12}{m}\,\,\,$[show answer]
$m=16$
Q2: Find the missing value. $\,\,\,\frac{18}{12}=\frac{k}{4}\,\,\,$[show answer]
$k=6$
Q3: Find the missing value. $\,\,\,\frac{a}{24}=\frac{5}{20}\,\,\,$[show answer]
$a=6$
What is a Proportion?There are a few different ways to define a proportion. One way to describe a proportion is that it's an equation with two equal ratios. In other words, a proportion is when you have two fractions with an equals sign in the middle. Some proportions just have two fractions set equal to each other. Proportions can also have variables in one or both of the fractions. This lesson will show you how to solve for a variable that's in a proportion.

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