The conception of ratio, proportion, and variation is actually important in mathematics and in our day-to-day life. The word ratio means the quantitative relationship between two numbers. We can write ratio in two ways, one way is a fraction and another way is using a colon. Consider an example 3:4 or 3/4. Comparison of ratios is used when three or further quantities are required for comparison.

Suppose a ratio is mentioned between friends A and B on the marks scored and another relationship between B and C, by comparing both the ratios we can determine the ratios of all three friends A, B, and C. To compare ratios, we need to remember a few steps. On this page, you will learn about the definition of Comparison of ratios, how to compare ratios, methods of comparison ratios, solved problems, and so on.

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### Comparison of Ratios – Definition

Comparison of ratios means comparing the relationship between two or further ratios. The quantitative relationship of two amounts or numbers is called a ratio. The ratio is very frequently used to express as the percentages. When three or further quantities come into play, a comparison of ratios is necessary. So, whenever you are comparing two numbers, it becomes necessary to find out how multiple times one number is greater than the other number.

### How to Compare Ratios?

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

- Step 1: First, obtain the given ratios.
- Step 2: Now, we have to express each of the given ratios as a fraction in the simplest form.
- Step 3: Make the consequent of both the ratios equal – First, we want to find out the least common multiple (LCM) of both the consequent in ratios. Once the LCM is decided, then divide the LCM with both the consequent of the ratio. Finally, multiply both the consequent and antecedent of both ratios with the quotient that is obtained previously. Similarly, apply the same procedure to all other fractions.
- Step 4: Compare the 1
^{st}numbers that are the antecedent of both the ratios which are each other. Once step 3 is done, then we move forward to step 4 to find out the comparison between the two ratios. In other words, convert each fraction to its equivalent fractions with a denominator equal to the L.C.M (least common multiple). Thus, the denominators of all the fractions are the same. - Step 5: Compare the numerators of the equivalent fractions whose denominators are the same.

### Methods Used to Compare Ratios

The comparison of ratios can be done in two different and simple methods. The methods are given below:

**1. LCM Method of Comparing Ratios**

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

**2. Cross Multiplication Method of Comparing Ratios**

This method is where we multiply the antecedent of the first ratio with the consequent of another ratio and the consequent of the first ratio with the antecedent of another ratio. Consider an example 8:9 and 7:8, according to this approach we should multiply the numbers that are 8 x 8 and 9 x 7.

### Comparison of Ratios Examples | Comparing Ratios Problems with Solutions

**Problem 1:**

Compare the given ratios and find which of the following is greater, 12: 16 and 18: 20?

**Solution:**

As given in the question, the numbers are 12:16 and 18:20.

Now, we have to find the LCM of the consequents of both ratios.

So, the LCM of 16, 20 is 80.

Now, divide the LCM with the consequent that is 80/16 = 5, and 80/20 =4.

Multiply the values with the ratios.

So, the values is (12 x 5) : (16 x 5) = 60 and 80.

(18 x 4) : (20 x 4) = 72 and 80.

Hence, the value is 72 > 60, the ratio 18:20 is greater than 12:16.

**Problem 2:**

Using the Cross Multiplication method for comparison of ratios and finding the greater ratio value. The ratio values are 5:18 and 9:25?

**Solution:
**Given that, the ratio values are 5:18 and 9:25

Now, we have to compare given ratios using the cross multiplication method.

The ratios 5:18, and 9:25 can be written as 5/18, 9/25.

By using the cross multiplication method, we get

The values are 5 x 25 , 9 x 18 is125 and 162

Since 162 is greater than 125.

Therefore, the ratio value of 9:25 is greater than 5:18.

**Problem 3:**

Compare the ratios of 5:12 and 3:8. Write the which ratio is greater?

**Solution:**

Given that, the ratio values are 5:12, and 3:8.

Now, we have to compare the ratio and find the greater ratio value.

We can written as, 5:12 = 5/12 and 3:8 = 3/8.

First, we have to find the LCM of 12 and 8. So the LCM of 12 and 8 is 24.

Next, the value is (5 x 2)/(12 x 2) = 10/24 and (3 x 3)/(8 x 3) = 9/24.

So, the value 10 is greater than 9.

Therefore, the ratio is 10/24 > 9/24 = 5/12 > 3/8 = 5 : 12 > 3 : 8.

Hence, after Comparison the greater ratio is 5:12.

**Problem 4:**

Find the greater ratio using the comparison of ratios. The ratios are 7:6 and 24:6.

**Solution:
**As given in the question, the values are 7:6 and 24:6.

Now, we have to compare the given ratio and then find the greater ratio.

We can rewrite as 7 : 6 = 7/6 and 24 : 9 = 24/9.

First, we will find the LCM, then the LCM of 6 and 9 is 18.

So, the values are (7 x 3)/(6 x 3) = 21/18 and (24 x 2)/(9 x 2) = 48/18.

We observed clearly the value 21 is less than 48.

Therefore the ratio 21/18 < 48/18 = 7/6 < 24/9.

=7 : 6 < 24 : 9.

Hence, the greater ratio is 24:9.

### FAQ’S on Comparison of Ratios

**1.** **What does a Comparison of Ratio Mean?**

Comparison of ratios means comparing the relationship between two or further ratios. The quantitative relationship between two numbers is called a ratio and when three or additional quantities come into play, a comparison of ratios is required.

**2. When do we use Comparison of Ratios?**

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

**3. 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 significance of the comparison of ratios. In comparison, we can find out which ratio is higher and lesser among the given ratios.

**4. How two Ratios are compared?**

By chancing the LCM of the consequents of both the ratios, divide the LCM with the consequents, and eventually, multiply both the numerator and the denominator of both the ratios with that answer to find out the compared ratio. Suppose, if the ratio is 6:8 and 5:9. First, find the LCM of 8 and 9 which is 72, next divide the 72 with both 8 and 9, and then multiply the answer with the antecedents of the ratios.

**5. How can a Comparison of Ratios occur?**

Once the question is given, first we will identify the known ratio according to the information mentioned. Once both the ratios are ready, then use the cross multiplication method and work out the ratios to find out which ratio is greater or higher than the other.