Comparison of Ratios

The word ratio means the quantitative relationship of two amounts or numbers. The concept of ratio, proportion, and variation is very important in math and in day-to-day life. The ratio is written in two ways - as a fraction and using a colon. For example - 2:3 or 2/3. Comparison of ratios is used when 3 or more quantities are required for comparison. Suppose a ratio is mentioned between friends J and K on the marks scored and another relationship between K and S, by comparing both the ratios we can determine the ratios of all three friends J, K and S. To compare ratios, we need to remember two steps. Let us see what they are.

There are two steps to be remembered while comparing ratios. They are as follows:

Step 1: Make the consequent of both the ratios equal - First, we need to find out the least common multiple (LCM) of both the consequent in ratios. Once the LCM is determined, divide the LCM with both the consequent of the ratio. Finally, multiply both the consequent and antecedent of both the ratios with the quotient that is obtained previously.

Step 2: Compare the 1^st numbers i.e. the antecedent of both the ratios with each other. Once step 1 is done, then we move forward to step 2 to find out the comparison between the two ratios. 

For example, compare the ratios of the given quantities 2:6 and 5:4. Which of the ratios is greater?

Solution: First find out the LCM of both the consequent in the ratios i.e. 6 and 4. LCM of 6 and 4 is 12 

Once the LCM is determined, divide it with both the numbers i.e. 12 ÷ 6 = 2 and 12 ÷ 4 = 3

Therefore, (2 x 2):(6 x 2) = 4 and 12  (5 x 3):(4 x 3) = 15 and 12

Since 15 > 4, the ratio 5:4 is greater than 2:6.

Comparison of ratios can be done in two different and simple methods. Let us see both the methods below:

LCM Method of Comparing Ratios

This method involves the 2 steps where we first find the LCM of the consequent, divide it by the consequents, and then multiply the quotient obtained with the ratios. 

Comparing Ratios by Cross Multiplication Method

The second method is where we multiply the antecedent of the first ratio with the consequent of the second ratio and the consequent of the first ratio with the antecedent of the second ratio. For example - 8:9 and 7:8 according to this method we multiply the numbers. 8 x 8 and 9 x 7.

Comparison of Ratios Related Topics

Check out these interesting articles to know more about the comparison of ratios and their related topics.

• Ratio
• Percentage
• Fractions
• Least Common Multiple

Important Points

• Remembering the two steps while comparing ratios is necessary. 
• The methods of comparing ratios are very simple and are used at all times. 

What does a Comparison of Ratio Mean?

Comparison of ratios means comparing the relationship between two or more ratios. The quantitative relationship of two amounts or numbers is called ratio and when 3 or more quantities come into play, a comparison of ratios is necessary. 

How are Two Ratios Compared?

By finding the LCM of the consequents of both the ratios, divide the LCM with the consequents, and finally, multiply both the numerator and the denominator of both the ratios with the answer to find out the compared ratio. For example, if the ratio is 6:8 and 5:9. Find the LCM of 8 and 9 which is 72, divide 72 with both 8 and 9, and multiply the answer with the antecedents of the ratios. 

What are the Two Methods of Comparing Ratios?

There are two methods for comparing ratios and those are:

• LCM method
• Cross Multiplication Method

LCM Method of Comparing Ratios: This method involves the 2 steps where we first find the LCM of the 2nd numbers, divide it by the consequents, and then multiply it with the antecedents of the ratios. 

Comparing Ratios by Cross Multiplication Method: The second method is where we multiply the antecedent of the ratio with the consequent of the second and consequent of the first ratio with the antecedent of the second ratio. For example - 1:9 and 5:8 according to this method we multiply the numbers. 1 x 8 and 9 x 5

What is the Importance of Comparison of Ratios?

A ratio tells us the value of one quantity for a given value of the other quantity, this is the main importance of comparison of ratios. Through comparison, we can find out which ratio is greater or lesser among the given ratios.

When do we Use Comparison of Ratios?

A ratio is a method to compare two numbers or quantities of the same kind. Ratios are used to compare things of the same type. For example, we may use a ratio to compare the number of boys to the number of girls in two different classrooms. Then, we can compare those ratios to find out which class has a greater ratio as compared to another.

How can Comparison of Ratios occur?

Once the question is given, identify the known ratio according to the facts mentioned. Once both the ratios are ready, use the cross multiplication method and solve the ratios to find out which ratio is greater than the other.

For example - Kenji feeds his cats a mixture of wet and dry food at every meal. He mixes 8 spoonfuls of dry food and 10 spoonfuls of wet food for Tiger, his adult cat. He mixes a smaller meal with 2 spoonfuls of dry food and 7 spoonfuls of wet food for his kitten, Smokey. Do the two meals have the same ratio of dry food to wet food?

Solution - The ratios are 8:10 and 2:7. The LCM of 10 and 7 is 70. Multiplying 8/10 with 7 and 2/7 with 10 to get the common denominators. 

(8 x 7) / (10 x 7) = 56/70 

(2 x 10) / (7 x 10) = 20/70 

Since one ratio is greater than the other. Therefore, the two meals do not have the same ratio.