Comparing Ratios

Ratios used for comparisons in math and science. In order to determine if one ratio is greater or lesser than another, we usually have to change or manipulate the ratios to make the comparison. There are 3 basic methods used for comparing ratios: use cross products, use a common denominator or change the ratios to decimals. Let’s explore each method.

Use Cross Products

This method is fairly simple. It is easier to use if the ratios are fractions. In order to get cross products, you multiply the denominator of one ratio to the numerator of the other ratio. If the ratios are the same than the ratios are equivalent. If the ratios are different than the greater cross product can be used to determine the greater ratio.

cross roducts

Use a Common Denominator

If the ratios are written as fractions and the denominators are different, you can change the ratios to a common denominator and then make the comparison.

common denominator

Change the Ratios to Decimals

if the ratios are written as fractions, you can easily change those to decimals by dividing the numerator by the denominator. If the ratio is 2/9 than divide 2 by 9. You change both ratios to decimals and then compare.

The Problem Determines Which Method You Use

The problem determines how you compare ratios. If the problem involves money, it is best to change the ratios to money since money is often written as decimals. If is easy to find a common denominator based on the ratios, than use a common denominator. Cross products can be used almost anytime with success. I recommend using one method to solve the math problem and use a different method to check your answers.

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