Ratio And Proportion Concept , Tricks , Examples

Ratio And Proportion

In Mathematics ratios and proportion is a very important concept. Let us understand the concepts with the help of examples and solved questions.

Ratios

Ratios are the mathematical numbers used to compare two things that are similar to each other in terms of units. For example, we can compare the length of a pencil to the length of a pen likewise distance to a unit that denotes distance. We can’t compare two things that are not similar to each other. Similarly, we can’t compare the height of a person to the weight of another person.
As an illustration, suppose the weight of Rohan is 150 kg and the weight of Sohan is 300kg. A ratio of Rohan’s weight to Sohan’s weight can be found out by dividing Rohan’s weight to Sohan’s weight and vice versa. The ratio between Rohan’s and Sohan’s weight is 150/300= 1:2.
A ratio is denoted by ‘:’. In the above case, we can say that 2 times the weight of Rohan equals the weight of Sohan or Rohan’s weight is half of Sohan’s weight. Ratios can help in such deductions. Note how only the weights, which are similar to each other, are compared.

Proportions

Ratios compare things similar to each other. Further, these ratios are compared with each other using proportions. The purpose of comparing ratios is to deduce whether two distributions are equal or not. It additionally helps us to find out a more suitable proportion. When two ratios are the same, they are said to be proportionate to each other. A proportionate relation is represented by ‘::’ or ‘=’ sign.

Let’s assume you and your friend go out to buy notebooks. You both buy a total of 8 notebooks, which amount to 200 Rs. Your friend pays 50 Rs. while you pay 150 Rs. Now while returning your friend suggests that both of you receive 4 notebooks each. On the other hand, since you paid more, you suggest that you must receive 6 notebooks while your friend gets 2 notebooks.
To decide which of you is correct, we can determine whether ratios of money paid and notebook distribution are equal or not. Here, the ratio of money you paid to that your friend paid is 150/50 = 3:1. The ratio according to your friend’s distribution is 4/4 = 1:1. Whereas, the ratio according to your distribution is 6/2= 3:1. Since the ratio of money paid and ratio according to your distribution is proportionate, your distribution will be correct.