Comparison of Ratios
2026-02-28 17:40 Diff
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Last updated on December 9, 2025

The comparison of two or more numbers is done using a ratio, which can be represented using a fraction bar or a colon. For example, 5/2 or 5:2.

What are Ratios?

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A ratio represents the proportion or relative amount of two or more quantities. It can be expressed in a colon or fractional notation, a/b or a:b. For example, \(\frac56\) or 5:6. In word form, a ratio can be expressed as 'a to b', for example, '5 to 6'.

How to Compare Ratios?

Now, let’s learn how to compare ratios. Comparing ratios involves two main steps. Here we can learn the process in detail. 

Step 1: Make the second term of both ratios the same

To compare two ratios, first we need to make the second terms of both ratios the same. We find the LCM of the second terms and divide the LCM by each second term. The respective quotient is used to multiply both terms of each ratio. 

Step 2: Compare the first terms of the ratio

Now that both second terms of the ratios are the same, we simply compare the first terms.


Example:
 

For example, let’s now compare 7:9 and 5:6

Step 1: Make the second terms the same.

The second terms of the ratios are 9 and 6

The LCM of 9 and 6 is 18

  • Dividing 18 by 9 is 2, and dividing 18 by 6 is 3
     
  • Multiplying the first ratio, 7:9, by 2, we get 14:18
     
  • Multiplying the second ratio, 5:6, by 3, we get 15:18

Step 2: Compare the first terms.

  The second terms in both ratios are the same (18), so we compare the first terms. As 15 is greater than 14, we conclude that 5:6 is greater than 7:9.

What are the methods to compare ratios?

To compare ratios, we have different methods. Commonly used methods are:

  • Comparing ratios using the LCM method
     
  • Comparing ratios by cross-multiplication 
     
  • Comparing ratios to decimal numbers
     
  • Comparing ratios to percentages

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Comparing Ratios Using the LCM Method

Comparing ratios using the LCM method was discussed earlier. To compare ratios using the LCM method, follow the steps given below:

  • If the second terms of the ratios are different, we find the LCM of the second terms.
     
  • Then we divide the LCM by the second term, and then multiply the ratio by the quotient.
     
  • Finally, we compare the first terms to determine which ratio is greater.

For example, comparing 5:8 and 4:6

The LCM of 8 and 6 is 24.

  • Dividing 24 by 8 is 3, and dividing 24 by 6 is 4
     
  • Multiplying the ratio 5:8 by 3, we get 15:24
     
  • Multiplying the ratio 4:6 by 4, we get 16:24


As the second numbers are the same, we compare the first numbers of the ratios. As 16 is greater than 15, we conclude that 4:6 is greater than 5:8

Comparing Ratios by Cross-Multiplication

In the cross-multiplication method, we first multiply the antecedent of the first ratio by the consequent of the second ratio, and vice versa. Then we compare the products to determine which ratio is greater.

  • If the products of the cross-multiplication are the same, then the two ratios are the same. This means if ad = bc then a:b = c:d
     
  • If ad < bc, then a:b is less than c:d
     
  • If ad > bc, then a:b is greater than c:d

Comparing Ratios to Decimal Numbers

A comparison between two or more ratios can be done by converting them to decimal form. Follow these steps to convert a ratio into its decimal number representation.

Step 1: Let us divide the numerator and the denominator. 

Step 2: Since most ratios are not whole numbers, the final answer after the division will be a decimal.

Step 3: If the decimal is repeating or non-terminating, round off the value. 

Let us try to understand this with an example. 

What is the relationship between the ratios 5:3 and 7:2?

Let’s convert the given ratios to decimal values.

  5:3 = \(\frac53\) = 1.667

7:2 = \(\frac72\) = 3.5

Since 3.5 is greater than 1.667, we can conclude that 7:2 > 5:3.

Comparing Ratios to Percentages

We can compare two ratios by converting them into percentages. Follow these steps to learn how to convert ratios to percentages. 

Step 1: Convert the given ratio to its fractional form.

Step 2: Multiply the fractions by 100 to convert them to percentages.

Step 3: Now, we can compare the values.

Let us try to understand this with an example. 

What is the comparison between the ratios 4:5 and 7:10?

\(4:5 = \frac{4}{5}\\[1em] 7:10 = \frac{7}{10}\)

Multiply by 100.

\(\frac{4}{5} \times 100 = 80 \%\)

\(\frac{7}{10} \times 100 = 70 \%\)

Since 80% is greater than 70%, we can conclude that 4:5 > 7:10.

Tips and Tricks to Master Comparison of Ratios

Comparison of ratios can be confusing for younger students. Here are some tips and tricks to easily remember the concept of ratios and to master it:

  • To convert a fraction into decimals that has a power of 10 (10, 100, 1000,…) in the denominator. Count the number of zeroes. Place the decimal before the digits having place value equal to the number of zeroes.
     
  • Always reduce the ratio to its simplex form for easy calculation.
     
  • For comparing ratios, relate the fraction to items. For example, 1/2 is half of the pizza, and 1/4 is a quarter of a pizza. Now, checking the amount, you will 1/2 is greater.
     
  • Use prime factorization methods for calculating LCM.
     
  • To convert ratio to percentage, multiply the fraction by 100.
     
  • Teachers and parents should use visual representations to compare boys-to-girls ratios, apples-to-oranges ratios, etc. Through this method, children can see the ratio immediately and understand the ideal connection between the two ratios.
     
  • Teach learners that ratios can be compared just as fractions are. Fractions can be converted to decimals and percentages, which makes it easier to find their relation.
     
  • Parents should encourage their children to scale up to their equal second terms. To compare two ratios like 2:5 and 3:7, we can find the LCM of 5 and 7 to multiply all the terms by it. Upon scaling up, the ratios will become 14:35 and 15:35. Now it is easier for us to compare these two ratios. 3:7 is greater than 2:5.
     
  • Parents can help their children learn this concept by giving them real objects to build ratios. We can provide them with buttons, LEGO blocks, beads, candies, etc. We have to encourage them to create ratios.

Common Mistakes and How to Avoid Them in Comparison of Ratios

When working with ratios, we all make mistakes. In this section, we will discuss some common mistakes that students make. But by learning from these mistakes and the ways to avoid them, students can easily avoid these errors next time. 

Real-World Applications of Comparison of Ratios

In real life, we compare ratios in the fields of cooking, art, science, and finance. Let’s learn how we use comparing ratios in real life. 

  • In cooking, we use ratios to measure ingredients and adjust them according to the number of servings. For example, a recipe requires half a cup of milk, which is \(\frac12.\)
     
  • We use ratios in art to create visually appealing compositions. For example, The Golden ratio (1.618:1) is known to be used in famous arts like Mona Lisa and The Last Supper. It is also found in nature. 
     
  • To form new colors, we use ratios to achieve the desired tone. For example, mixing yellow and blue paint in 1:1, it will give a balanced green color.
     
  • Ratios are used to compare prices and determine the best deal. For example, if a store has 20% which is \(\frac15\) off the price of shoes and another have a 25% discount (1/4) on the same shoes, then it is profitable to buy from the second store. 
     
  • We use ratios to convert measurements from one unit to another.

    Example: Converting 1cm into m.

    \(1cm = \frac{1}{100} m\)

Download Worksheets

Problem 1

Compare 4:5 and 3:4

Okay, lets begin

4:5 is greater than 3:4.

Explanation

To compare the ratios, we find the LCM of the second terms
 

  • LCM of 5 and 4 is 20
     
  • Multiply 4:5 by 4, that is 16:20
     
  • Multiply 3:4 by 5, that is 15:20
     
  • When comparing the first terms of both ratios, 16 is greater than 15 

So, we can conclude that 4:5 is greater than 3:4.

Well explained 👍

Problem 2

Compare 7:9 and 5:6

Okay, lets begin

5:6 is greater than 7:9.

Explanation

We use the comparison of ratios to the percentage method
 

  • Converting 7:9 to percentage, \(\frac 79 × 100 = 77.778\%\)
     
  • Converting 5:6 to percentage, \(\frac56 × 100 = 83.333\%\)


As 83.33% is greater than 77.78%, we conclude that 5:6 is greater than 7:9

Well explained 👍

Problem 3

Compare 5:10 and 10:20

Okay, lets begin

Both 5:10 and 10:20 are the same.

Explanation

When simplifying both ratios:
 

  • 5:10 can be simplified to 1:2
     
  • 10:20 can be simplified to 1:2


Therefore, both ratios are the same.

Well explained 👍

Problem 4

Compare 4:7 and 5:8

Okay, lets begin

5:8 is greater than 4:7.

Explanation

Here, we use the decimal method.

We convert the ratios to decimals by dividing the first term by the second.

  • Converting 4:7 to decimal = \(\frac47\) = 0.571
     
  • Converting 5:8 to decimal = \(\frac58\) = 0.625
     
  • As 0.625 is greater than 0.571


We can conclude that 5:8 > 4:7.

Well explained 👍

Problem 5

Compare 3:8 and 2:5

Okay, lets begin

2:5 is greater than 3:8.

Explanation

Comparing ratios using cross-multiplication

That is 3 × 5 = 15

8 × 2 = 16

As 15 < 16, 2:5 > 3:8

Well explained 👍

FAQs on Comparison of Ratios

1.How to explain comparison of ratios to children?

The process of comparing two or more ratios is the comparison of ratios. To check which ratio is greater, smaller, or equal. 

2.How to define ratio to my child?

The ratio is a way of comparing two or more quantities, expressed in the form a:b. 

3.What are the different methods to explain comparison of ratios to my child.

The different methods to explain comparison of ratios includes the LCM method, cross multiplication method, decimal method, and percentage method.

4.Can two ratios be the same?

Yes, the ratios of two numbers can be the same.

5.What are the applications of comparing ratios that I can give to my child?

Present a pizza infront of your child. Cut it in four slices and give 1 slice to him/her. Explain that each slice is 1/4 of the entire pizza.

Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.