Three ways to solve 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.

  • Vertical
  • Horizontal
  • Diagonal (often called "cross-products")

 

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: Cross-products

Are these two ratios equivalent?

Since the cross-products 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 cross-products.


 

Directions:

  1. Look at the proportion on the right.
  2. Solve it. (You may use the calculator below.)
  3. Then enter your answer and press the "Enter" or "Return" key on your keyboard.
  4. Press the "New problem" button to get a new problem. (Duh.)

 




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Self-Check


Q1: Find the missing value. $\,\,\,\frac{9}{12}=\frac{12}{m}\,\,\,$[show answer]


Q2: Find the missing value. $\,\,\,\frac{18}{12}=\frac{k}{4}\,\,\,$[show answer]


Q3: Find the missing value. $\,\,\,\frac{a}{24}=\frac{5}{20}\,\,\,$[show answer]