Introduction to Ratios and Proportions

There is a 20 over cricket match going on between India and Zimbabwe. India scores 200 runs with Kohli playing a good knock of 76* runs. Zimbabwe gets bowled out at 100 runs. So India wins by a good margin. That’s a qualitative definition. But by how much did India win? This is answered by the concept of ratios and proportions. So come, let us know more about ratios and proportions.

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Ratios and Proportions

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 which are similar to each other in terms of units. For example, we can compare the length of a pencil to 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 Kamal is 5okg and the weight of Hassan is 100kg. A ratio of Kamal’s weight to Hassan’s weight can be found out by dividing Kamal’s weight to Hassan’s weight and vice versa. The ratio between Kamal’s and Hassan’s weight is 50/100= 1:2.

A ratio is denoted by ‘:’. In the above case, we can say that 2 times the weight of Kamal equals the weight of Hassan or Kamal’s weight is half of Hassan’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 the 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 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.

Download Ratios and Proportions Cheat Sheet by clicking on the button below

Solved Examples for You

Question 1: Divide 90 Rs. in ratio 1:2 between Ram and Karan.

Answer : There are two parts, 1 and 2, the sum of which is 3 parts. Hence among the 3 parts, Karan gets 2 and Ram gets 1. Therefore for 90 Rs (considered equivalent to 3 parts here)  –

• Karan’s share = 2/3 ×90 = 60 Rs.
• Ram’s share = 1/3 ×90 = 30 Rs.

Here we have added the ratios as parts and then divided the total parts according to the ratio. Thus the sum of ratios is assumed to be equal to the total sum of rupees that needs to be divided among Karan and Ram.

Question 2: Are 30, 40, 45 and 60 in proportion?

Answer : Ratio of 30 and 40= 30/40= 3:4

Ratio of 45 and 60= 45/60= 3:4

The ratio of 30 and 40 is equal to the ratio of 45 and 60. Hence they are proportionate to each other or 30:40::45:60.

Question 3: What are ratio and proportion examples?

Answer: Proportion refers to an equation with a ratio on each side.  Moreover, it is a statement that two ratios are equal. Such as ¾ = 6/8 is an example of proportion. In addition, when one of the four numbers in a proportion is unknown, cross products may be used to find the unknown number.

Question 4: What is the formula for proportion?

Answer: Simply, a proportion is a statement that has two ratios that are equal. In addition, we can write it in two ways; first as two equal fractions a/ b = c/ d; or the other way is using colon that is a: b = c: d.

Question 5: Is the proportion of percent?

Answer: If the proportion is a percentage then 1 would be 10%, however, the proportion is a ratio, as in this case 10/100 = 1/10 = 1. Although 10% is not a ratio in of itself, then it is a proportion of 10). Besides, % means of one hundred. In addition, a proportion is a number to another number.

Question 6: Are ratio and proportion the same?

Answer: The main difference between ratio and proportion is that ratio is the comparison of sizes of two quantities of the same unit. On the other hand, proportion refers to the equality of two ratios.