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The ratio is a widely used method of expressing one quantity in terms of other. Suppose there are two houses A and B. House A has a total number of 5 rooms and House B has a total number of 3 rooms. The ration of the rooms in House A to the room in House B is expressed as 5:3. The ratio is a simple and effective way of comparing two quantities that can be measured and expressed in the form of numerical values. Ratios are closely related to fractions but they are not same. The two terms in a fraction are always integers. However, ratios can be in the form of integers as well as decimals. Moreover, ratios are always positive while a fraction can be negative as well as positive.  Thus, we can say that ratios are simple or decimal fractions without any negative sign. Now that we have understood ‘What is Ratio in Mathematics’, lets us take some examples to learn more about ratios. 

Learning more about Ratios with the help of Examples

The ratio of two numbers expressing some measurable quantities is usually expressed A:B or A/B and is read as A is to B. 

                                                   

Suppose you have two shirts and three trousers, the ratio of shirts to trousers will be given by 2:3 and read as 2 is to 3. 

The ratio does not necessarily express the same absolute values as the ratio can be expressed in the form of an equivalent ratio in the simplest form. For example, if you have 20 pens and 10 pencils, the ratio of the number of pens to the number of pencils can be expressed as 20:10 or in the form of a simple equivalent ratio of 2:1. Thus, the ratio 2:1 does not mean that you have 2 pens and 1 pencil but it simply means that you have 2 pens for every 1 pencil.     

Let us now extend our understanding about ‘What is Ratio in Mathematics’ by learning about equivalent ratios with more examples. Suppose there are 10 windows and 5 doors in your house. Also, there are 4 fans and 2 ACs in your house. We can say that the ratio of windows to doors in your house is same as the ratio of fans to ACs in your house. Mathematically, 

Ratio of windows to doors in your house = 10:5

Ratio of fans to ACs in your house = 4:2

Both the ratios can be said to be equivalent to a simple equivalent ratio = 2:1. 

In general, all the three ratios 10:5, 4:2 and 2:1 are called as equivalent ratios and can be written as:
10:5 = 4:2 = 2:1

There can be infinite equivalent ratios for a given ratio.  

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