Comparing Ratios is an important topic to solve real-time problems. Check various problems involved in the comparison of ratios and also know the definition, rules, and solved examples. We are providing the step-by-step procedure to solve various problems in the below sections. Get the free pdf of ratios, proportions, and comparison from here. Follow the easy steps and change the ratio concepts and important topics.
Are you feeling difficulty in solving Ratios Comparision problems? if yes, then check this article and you will come to know various tips and tricks by which you can solve the problems easily. There is a procedure to be followed to compare two or more ratios and the final conclusion will be given at the end of the problem. Know what are the equivalent ratios and proportions and their effect in real life.
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Comparison of Ratios – Definition
Ratios help in comparing quantities. They also help in determining the relation between two or more quantities. Comparison of ratio is considered as the comparison of both similar quantities which is obtained by dividing one quantity by another quantity. A ratio is an abstract number as it is the relation or comparison between various quantities.
Representation of Ratios:
The ratios of quantities are represented with the symbol “:”. First, one quantity is written then the symbol “:” is written and then another quantity is written.
If two quantities have different units or cannot be expressed in the same unit terms, then no ratios will exist between them. Therefore, whenever two quantities are compared, they must have the same quantities.
For example, To find the ratio of 5 km to 500 m. First, we have to convert the distances to the same units and then compare them.
Ratios Comparision
Ratios are expressed as comparisons or relations among two numbers or quantities. They can be expressed as the fractions like 5/8 or as colon between two numbers such as 5:8. Ratios are used in day-to-day life like science, technology, finance, and business.
Ratios have to be calculated on paper because calculating them mentally is difficult. If you have to compare 5/8 to 12/21. You have to compare them by converting ratios to decimal numbers. It is not the same scenario in all the cases. In some cases, you come across ratios that are perfectly divisible. The time factors should also be kept in mind while dealing with ratios.
Imagine you are assigning a simple task to someone, where the task focuses on ratios. You are doing this just to know their capability to respond to a problem in a fast and flexible manner. In some scenarios like these, don’t go for ratios that have a decimal fraction.
Use the simple ratios and assign the task. This makes you easily understand the capability of the person or individual. If you want to test the in-depth knowledge of an individual then go for decimal ratios. These are some of the day-to-day things where you can improve the knowledge of ratios in a better way.
Now, here you are assigned to compare two ratios. Generally, a ratio has two numbers separated by a colon(:). This means that the first number is divided by the second number. Now, the case is that we need to compare two ratios. So the task here becomes some more time taking. Here we are not sure that both the ratios leave the same ratio on comparing.
So we need to convert these ratios in a comparable manner. For example, the first ratio is 2:3 and the second ratio is 4:5. Here we have no clue of how to compare both these ratios. So, here we use simple mathematics to compare both these ratios by converting the ratios to simple dividends. Below is a procedure that is used to compare both ratios.
It is necessary to find how many numbers of times is one number greater than other numbers. Generally, the number x ratio is considered as the quotient of both the numbers x and y. The numbers which are used in the ratio formation are called the ratio terms. These ratios are often used to express the percentages.
How to Compare 2 Ratios?
Follow the simple and easy guidelines on how to compare two ratios. They are listed in the below way.
Step 1:
First look at the question and Include both the ratios as fractions.
Step 2:
Find the LCM(least common multiple) of both the denominators of both fractions. This process has to be performed if the denominators are different or not the same.
Step 3:
In this step, you have to make both the denominators of fractions as the same value of LCM which is found out in step 1 using the multiplication process.
Step 4:
Once you get the fractions with the same denominator, compare the numerators and then decide the greatest fraction among the two. The fraction of the ratio with a larger numerator value is greater in value.
Example Problems on Comparing Ratios
Problem 1:
The ratio of water filled in buckets A and B is 5:12. The ratio of water filled in buckets B and C is 3:8. Compare these two ratios and define which is greater or smaller or equal?
Solution:
The ratio of water to be filled in buckets A and B = 5:12
The ratio of water to be filled in buckets B and C = 3:8
Let,
Ratio 1 = 5:12
Ratio 2 = 3:8
Multiply both the ratios with a common divisor(that is denominator).
When we observe both the divisors, the common divisor would be 24.
For Ratio1, we need to multiply the numerator and denominator with 2 in order to get the divisor as 21.
Then,
Ratio1 = 10:24
In the same way, Ratio2 should be multiplied by 3 in order to get the divisor as 24.
Then,
Ratio 2=9:24
Now, comparing the two ratios can be done by separating the two ratios by a double colon(::). It will be as 10:24::9:24. Name it as Ratio.
Then Ratio=(Ratio1)::(Ratio2), which implies
Ratio=(Ratio 1)/(Ratio 2)
After comparing these ratios, we observe that Ratio1 is greater than Ratio2.
Here, we can conclude that ratio of water to fill buckets A and B is more.
This is the general method used to compare the ratios. There is also a Shorthand method which makes our task easier. We solve the above problem using the Shorthand method
Shorthand Method
Solution:
The ratio of water to be filled in buckets A and B = 5:12
The ratio of water to be filled in buckets B and C = 3:8
Let,
Ratio1 = 5:12
Ratio2 = 3:8
Apart from the general method, multiply the extremities that is 5 and 8.
So, 5*8=40.
Now, multiply 3 and 12
So, 3*12=36.
Of these two multiples 40 and 36, 40 is greater.
40 is obtained by multiplying 5 with 8.
So, 5 ratio is greater
That implies 5:12 is greater
If we get the second multiple greater, then the second ratio is greater.
If both the multiples are equal then the ratio is the same.
Hence we conclude that the ratio of water to fill buckets A and B is more.
Problem 2: The ratio of sales of apple and banana in a store is 3:4. The ratio of sales of bananas and cherries in a store is 9:16. Compare the ratios and define which ratio is greater or smaller or the same.
Solution:
The ratio of sales of apple and banana in a store = 3:4
The ratio of sales of banana and cherry in a store = 9:16
Let,
Ratio 1 = 3:4
Ratio 2 = 9:16
Multiply both the ratios with a common divisor(that is denominator).
When we observe both the divisors, the common divisor would be 16.
For Ratio1, we need to multiply the numerator and denominator with 4 in order to get the divisor as 16.
Then,
Ratio 1 = 12:16
In the same way, Ratio 2 should be multiplied by 1 in order to get the divisor as 16.
Then,
Ratio 2=9:16
Now, comparing the two ratios can be done by separating the two ratios by a double colon(::). It will be as 12:16::9:16. Name it as Ratio.
Then Ratio=(Ratio 1)::(Ratio 2), which implies
Ratio=(Ratio 1)/(Ratio 2)
After comparing these ratios, we observe that Ratio1 is greater than Ratio2.
Here, we can conclude that the ratio of sales of apple and banana in a store is more.
This is the general method used to compare the ratios. There is also a Shorthand method which makes our task easier. We solve the above problem using the Shorthand method
Shorthand Method
Solution:
The ratio of sales of banana and apple in a store = 3:4
The ratio of sales of apple and cherry in a store = 9:16
Let,
Ratio 1 = 3:4
Ratio 2 = 9:16
Apart from the general method, multiply the extremities that is 3 and 16.
So, 3*16=48.
Now, multiply 9 and 4.
So, 9*4=36.
Of these two multiples 48 and 36, 48 is greater.
48 is obtained by multiplying 3 with 16.
So, 3 ratio is greater
That implies 3:4 is greater
If we get the second multiple greater, then the second ratio is greater.
If both the multiples are equal then the ratio is the same.
Hence we conclude that the ratio of sales of apple and banana in a store is higher.