Ratio and Proportions

Ratio and proportion are based on fractions. Proportions are defined as when two ratios are equal and the ratio is defined as when the fraction is written as a: b. Ratio and proportion i.e. a and b are the two integers. The ratio and proportion are the two crucial concepts in the sphere of Mathematics. Every day, the concept of ratio and proportion is highly used in our home i.e. while cooking, the measurement is done by using ratio and proportion.

Definition of Ratio

The ratio is a term that is highly used in mathematics, in simple words ratio is a mathematical term that is used for comparing two or more than two numbers that determine their magnitude in each other’s relation. While comparing the two or more numbers to each other the ratio is used for determining how larger or smaller a number is. Using division in ratio the two numbers are compared. Here, ‘antecedent’ is the term used for the dividend and ‘consequent’ is the term used for the divisor. For example, 12 students in a class prefer writing by pencil and the other 32 students prefer writing by pen. Therefore, the ratio between the students who prefer to write by pencil and the students who prefer to write with the pen are represented as 12:32, this is spelled out as 12 is to 32, ‘:’ this is called here as ‘is to’.

Define Proportions

Proportions are represented by the symbols ‘::’ or ‘=’. Proportions are used for stating that two different ratios are equal. Therefore, proportions are having at least four quantities. For example, suppose four numbers like 1, 2, 3, 4 are there which are written in the ratio as 1:2 and 3: 4 and let these ratios be equal to each other, therefore now we can express these ratios in proportions as 1:2:: 3:4. Two terms are needed to be remembered in proportions, these are means and extremes. Means are the expressions or the numbers which are near to each other of two different ratio sets when written in proportional form and extremes are the numbers or expressions that are away from each other in two different ratio sets when written in the proportional form. For example, 1:2:: 3:4, here 2 and 3 are the means and 1 and 4 are the extremes.

There are four different types of proportion, these are –

• Direct Proportions –

An example can explain direct proportion more clearly. Suppose the cost of one pen is Rs. 5. If Ram wants to buy 10 pens then he needs to pay Rs. 50 and if he buys 2 pens then he needs to pay Rs. 10. It is very clear from the example that the total cost of the pens rises as the number of pens rises and decreases as the number of pens decreases, depending on the number of pens Ram is buying the total cost of the pen will increase or decrease. So, it can be said that the price of the pens and the number of pens are directly proportional to each other and it can be said that they are directly related. 

• Inverse Proportions –

An example can explain the inverse proportion very accurately. Inverse proportion is just the opposite or reciprocation of direct proportion. Suppose the time required for one man to complete one particular work is 10 days, it is seen that when more than 4 men are added in the same work then the work is getting completed by 5 days. That is, the time taken by one man to complete the work is more than the time taken by 5 men to complete the same work. This represents that the number of men working for that particular work to get completed is inversely proportional to the number of days required for the completion of the work. Continued Proportions –

Proportions are said to be continued when the first quantity is to the second quantity, the second quantity is to the third quantity, and the third quantity is to the fourth quantity, and so on.

For example, 1/2 = 2/3 = 3/4 = 4/5 = 5/6………………………….

Ratio and proportion questions

Question 1.

6:5 was the age ratio of Sita and Geeta 6 years ago. After 4 years their age will be 11:10. Now, what is the present age of Geeta?

1. 15 years
2. 16years
3. 20years
4. 6 years
5. 12 years

Solution: 

Let the age of Sita be x

And the age of Geeta be y

ATQ, (x-6)/(y-6) = 6/5 …………… Equation (i)

(x+4)/(y+4) = 11/10……………Equation (ii)

Solving equations (i) and (ii) we get,

y = 16

Question 2 

If the first three terms in a proportion are 2, 8, and 11. Then find the next term.

1. 41
2. 40
3. 22
4. 44
5. 90

Solution:

(8 X 11)/2 = 44

Conclusion

It is to conclude that ratio is a term that is highly used in mathematics, in simple words ratio is a mathematical term that is used for comparing two or more than two numbers that determine their magnitude in each other’s relation. Proportions are represented by the symbols ‘::’ or ‘=’. Proportions are used for stating that two different ratios are equal.