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Last updated on July 4th, 2025

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Comparison of Ratios

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

Comparison of Ratios for Vietnamese Students
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What are Ratios?

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, 5/6 or 5:6. In word form, a ratio can be expressed as a to b, that is, 5 to 6.

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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. So, we find the LCM of the second terms of both ratios and then divide the LCM by each of the second terms. The respective quotient is used to multiply both terms of each ratio. 

 

Step 2: Compare the first terms of the ratio

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

 

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

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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. In this method, 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. At last, we compare the first term to compare the ratios.

 

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

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Comparing Ratios by Cross-Multiplication

In the cross-multiplication method, always cross-multiply the ratios to compare them. In other words, we first multiply the antecedent of the first ratio by the consequent of the second ratio, and vice versa. Then we compare the product to compare the ratios.

 

  • 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
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Comparing Ratios to Decimal Numbers

In this method, we convert each ratio to a decimal by dividing the first number by the second number. Then we compare the decimals.
 
For example, comparing 12:7 and 9:5

First, we convert the ratios to decimals, 

For 12:7, we divide 12 by 7; 12/7 = 1.714

For 9:5, we divide 9 by 5; 9/5 = 1.8

Here, 1.8 is greater than 1.714.

Therefore, 9:5 is greater than 12:7
 

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Comparing Ratios to Decimal Numbers

In this method, we convert each ratio to a decimal by dividing the first number by the second number. Then we compare the decimals. 

For example, comparing 12:7 and 9:5

First, we convert the ratios to decimals, 

For 12:7, we divide 12 by 7; 12/7 = 1.714

For 9:5, we divide 9 by 5; 9/5 = 1.8

Here, 1.8 is greater than 1.714.

Therefore, 9:5 is greater than 12:7

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Comparing Ratios to Percentages

When comparing the ratios to percentages, we first convert the ratios to percentages. To convert, we divide the first number by the second and multiply by 100. That is, a:b can be converted to a percentage as a/b ×100%.

For example, comparing 6:8 and 5:6

Converting 6:8 to percentage = 6/8 × 100 = 75%

Converting 5:6 to percentage = 5/6 × 100 = 83.333%

As 83.33% is greater than 75%, we can conclude that 5:6 is greater than 6:8.

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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 comparing ratios to measure ingredients and adjust them according to the number of servings. 

 

  • We use comparative ratios in the arts for creating visually appealing art forms.

 

  • To form new colors by mixing colors, we use comparing ratios to achieve the required tone.

 

  • Ratios are used to compare prices and determine the best deal.
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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. 

Mistake 1

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Comparing the ratios in different units

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When comparing ratios, it is important to check whether they are in the same unit or not. As we cannot compare the ratios of different units.

 

For instance, if one ratio is in kg and another is in grams, we cannot directly compare. Instead of comparing, we convert it to one unit and then compare it.

Mistake 2

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Not simplifying the ratios in the simplest form

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Students often forget to simplify the ratios to the simplest form, which leads to errors. It is always important to simplify the ratio if they have common factors. 

Mistake 3

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Using cross addition instead of cross multiplication

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When comparing ratios using the cross-multiplication method, sometimes students do add the terms instead of multiplying them, which is wrong. So, always use the cross-multiplication method: multiply the first term of the first ratio by the second term of the second ratio, and vice versa. Then compare the ratios. 

Mistake 4

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Confusing ratio with a fraction

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Students often consider that both ratios and fractions are the same, but they are not. This is because the ratio is the relationship between the two different quantities, whereas the fraction is the representation of part of a whole. 

Mistake 5

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Thinking that order doesn’t matter in ratios

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Students shouldn’t think that 5:4 and 4:5 are equivalent, as it is wrong, as order matters in fractions. 4:5 is not the same as 5:4

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Solved Examples of Comparison of Ratios

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Problem 1

Compare 4:5 and 3:4

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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

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Problem 2

Compare 7:9 and 5:6

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5:6 is greater than 7:9

Explanation

We use the comparison of ratios to the percentage method

Converting 7:9 to percentage, 7/9 × 100 = 77.778%

Converting 5:6 to percentage, ⅚ × 100 = 83.333%

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

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Problem 3

Compare 5:10 and 10:20

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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.

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Problem 4

Compare 4:7 and 5:8

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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 = 4/7 = 0.571

Converting 5:8 to decimal = 5/8 = 0.625

As 0.625 is greater than 0.571

We can conclude that 5:8 > 4:7

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Problem 5

Compare 3:8 and 2:5

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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

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FAQs on Comparison of Ratios

1.What is the comparison of ratios?

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2.What is a ratio?

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3.List the different methods to compare ratios.

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4.Can two ratios be the same?

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5.What are the applications of comparing ratios?

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6.How can children in Vietnam use numbers in everyday life to understand Comparison of Ratios?

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7.What are some fun ways kids in Vietnam can practice Comparison of Ratios with numbers?

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8.What role do numbers and Comparison of Ratios play in helping children in Vietnam develop problem-solving skills?

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9.How can families in Vietnam create number-rich environments to improve Comparison of Ratios skills?

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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.

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Fun Fact

: She loves to read number jokes and games.

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