Step by Step tutorial on How to Solve Ratios In Mathematics

When we have to compare two or more than two numbers in mathematics then we can use ratios for the same as ratios can compare two or more quantitative numbers or amount or you can compare the portions of numbers of the larger numbers. Ratio is one of the tools of data analysts. This is why many people face difficulty in solving ratios so they are always in search of methods on how to solve ratios. If you are also stuck with solving ratios then this article will help you to understand the concept of ratios and methods on how to solve ratios.

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Concept of ratio

Before learning the steps on how to solve ratios one must be well versed with ratios. As you can’t mug up mathematics you have to understand the concepts then only you can solve ratios. 

First thing to learn is that ratios are used only in academics but also by data analysts for analysing the data in the form of comparison. Generally we think ratio compares only two numbers rather you can compare more than two numbers such as 3 or 4 through ratios. 

Second thing to learn on how to solve ratios is that ratio basically states the relation of two or more numbers with each other. 

Thirdly the sign of ratio is “:”. So if you want to tell someone that you got 75 marks in maths and your friend got 50 marks in maths then you can write it in the form of ratio as 75:50 that is 3:2.

Likewise you can write sex ratio of your class like 15 males and 10 females then you can write it as 15:10 that is 3:2.  And we read the ratio as “isto”. So you will read it as 3 isto 2. 

You can also write it in division form like 3/2. 

Thus there are 3 ways to write ratios. 

Steps – How to solve Ratios 

The first step on how to solve the ratio is to write the values you want to compare and you can write such values in any given form like using colon or through division sign or by writing isto. Let’s understand the steps through an example. Suppose you want to take out the ratio of your maths and physics marks. You have got 90 marks in maths and 70 marks in physics. So firstly I will write it in the form of a ratio. 

90 isto 70 or 90:70 or 90/70.

Second step on how to solve the problem is to reduce the values into their simplest way. So for that you can take out the common factors from the numbers. And then we can divide both of the numbers from such a common factor so that we can get the numbers in their simplest form. For example we have a number 90 : 70 then after writing it in the format of ratios now you have to bring out the common factors between the terms of ratios. So in this example we have 10 as a common factor. Thus you will divide both the numbers 90 and 70 by 10 so that you get the numbers in their simplest form so you will get 90/10:70/10 = 9:7.

Thus the ratio is 9:7.

Let’s take another example of three digits and three digits are 75 marks in biology, 25 marks in physics and 100 marks in maths. So let’s first write it in the form of ratio that is 

75 : 25 : 100

Now we need to follow the next step of how to solve ratios. That is to find out the common factor from all the numbers thus we can clearly see that 25 is the common factor so you will have to divide each number with 25. 

75/25 : 25/25 : 100/25 

= 3 : 1 : 4

Thus the answer is 3:1:4.

The important point to learn in ratio is that it does not change with the multiplication or division of same numbers. It will remain the same. For example if you multiply the above number with 2 then they will become 75 x 2 : 25 x 2 : 100 x 2 = 150 : 50 : 200. Now also the ratio is same if you convert it to the smallest form then like first you have to divide it by 50 then you will find get the same ratio that is 3:1:2. 

You can also find the value of variables if two ratios are equal. Let’s take an example to understand it better. Suppose you have one ratio 3:2 and other ratio 5:x and these two ratios are equal and now you are required to find the value of x song the equation will be 

3 / 4 = 3/X

3 x X = 3 x 2 

X = 6/3

X= 2.


Ratios are the mathematical expressions used to compare two or more numbers having common factors. We also use ratios one daily basis. Although ratio is a simple mathematical concept still many people ask how to solve ratios. So we have written this article in the simplest language and steps wise with examples to solve ratios. Get the best help for math homework from the leading experts.

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