Digital Sum in Maths: JKSSB, SSC, Boost Calculation

This is going to be a game-changer article for all students. Competition has been growing daily, and students must develop a good understanding of each subject.

One of the most important subjects is Maths because it is used in most of the subjects for calculation purposes. As you know, the calculator is not allowed in any state or national examination. So it becomes very important to learn the calculation tricks to save time and improve calculation speed.

Digital Sum in Maths is one of the best concepts in maths which can be used to solve questions with 3X speed and get answers within a fraction of a second.

In this article, we will provide you with this concept in detail and believe me if you read this article to the end your calculation speed will increase for sure and it will help you to crack national level as well as state level exams.

What is Digital Sum in Maths

We will start with the basic definition: Digital Sum is a single digit which we obtain after adding all the digits of a number. You have to focus on the word Single Digit. Let’s understand this with a basic example.

Digital Sum of 262 = 2+6+2 = 10 = 1+0 = 1

Hence the digital sum of 262 = 1

From the above example, it is clear that you have to add continuously till a single digit is obtained.

From the above example, the concept is clear to you. Now let’s discuss some concepts and uses of Digital Sum.

Digital Sum in Maths – Overview

Digital Sum Important Concepts

Before discussing the uses of Digital Sum, we will first learn some important concepts. Let’s start one by one.

Digital Sum of L.H.S = R.H.S

This is the most important concept which is used to solve questions by the method of Digital Sum. Let’s take an example to illustrate this concept:

Q) Find the sum of 13 + 12?

a) 22

b) 27

c) 25

d) 20

This is a simple example. We will discuss complex examples later on. Now coming to the question, the digital sum of 13+12 = 1+3+1+2 =7

Now you have to select that option whose digital sum is also 7. From the options, it is clear that the digital sum of 25 = 2+5 = 7

Hence the correct answer is 25.

This means the digital sum of the left-hand side (L.H.S) = digital sum of the right-hand side (R.H.S) = 7

Digital Sum Output

The digital sum of a number can be any of the following numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9 or 0.

It is important to note here that you can treat 9 as 0 which means there is no effect on digital sum if you add 9. For example, the digital sum of 239 = 2+3+9 = 14 = 1+4 = 5. But this question can be solved directly by neglecting 9 and the digital sum will also become 2+3 = 5

This is an important trick to save your time while adding digits of a number.

Digital Sum of any Multiple of 9

The digital sum of any multiple of 9 is always 9. For example, if we multiply 9 by any number, let’s say 8 we will get 72. But the digital sum of 72 is 9. Hence we can say that all multiples of 9 have 9 as their digital sum.

Applications of Digital Sum

1. Addition

Suppose you have to add large numbers and you are provided with options to select the correct one. In that case, you can use the digital sum technique to solve the question in seconds. Let’s understand this with the help of an example.

Q) Add 23456 + 8799 + 35476?

a) 67731

b) 23678

c) 133687

d) 46906

Using ordinary addition techniques will cost you a lot of time. Now see how we can solve this in seconds.

Digital sum of 23456 + 8799 + 35476 = 2 + 6 + 7 = 15 = 1+5 = 6 [ when the sum of 2 digits equals 9 you can treat it as zero as in 23456, 2+3+4+5+6 = 2 + (6+3) + (4+5) = 2 + 0 + 0 = 2 ]

Now select that option whose digital sum is also 6.

Taking the first option which is 67731. It’s digital sum = 6+7+7+3+1 = 6

Hence our correct answer is 67731. We got this answer without actually adding the numbers.

Decimal Calculation

A lot of students find it difficult to add decimals. But with the help of this concept, you can quickly check the answers, saving a lot of time.

For decimals, the rule is the same but you have to ignore the decimal and add the digits in the same way as if there was no decimal. For example, the Digital sum of 3.225 = 3+2+2+5 = 3

Q) Add 2.73 + 3.62 + 2.33?

a) 8.68

b) 9.72

c) 1.02

d) 11.291

In the given question, the digital sum of 2.73 + 3.62 + 2.33 = 3 + 2 + 8 = 13 = 1+3 = 4

From the options, digital sum of 8.68 = 8+6+8 = 22 = 2+2 = 4

Hence the correct answer is 8.68

2. Subtraction

Like addition, subtraction can also be done within seconds by following the same method. The only condition to satisfy is that the digital sum of L.H.S = Digital Sum of R.H.S.

Let’s understand it with the help of a simple example. After learning the concept, the same approach can be used to solve complex questions.

Q) Subtract 88 – 13?

a) 75

b) 78

c) 79

d) 76

Digital Sum of 88 – 73 = 16 – 13 = 7 – 4 = 3

From the given options, digital sum of 75 = 7+5 = 12 = 1+2 = 3

Hence the correct option is 75.

NOTE: If the digital sum comes out negative value, then add 9 to it and you will get the actual answer. For example, if the digital sum of a number is -3 then you have to add 9 to it and the final answer will become = -3 + 9 = 6

3. Multiplication

Addition and subtraction are easy to do, but students find multiplication difficult. Hence this technique will help you to find the product of numbers within seconds.

Let’s solve a question on multiplication which will make your concept clear without any further explanation.

Q) Solve 15 x 13

a) 152

b) 142

c) 196

d) 195

Ans: To solve this question, we will multiply the digital sum of these 2 numbers and match it with the given options.

Digital Sum of 15 x 13 = 6 x 4 = 24 = 2+4 = 6

From the given options, the digital sum of 195 = 1+9+5 = 6

Hence the correct answer will be 195.

NOTE: You might be thinking that there may be another option with the digital sum = 6. You are right, but as far as competitive exams are concerned, they know which options are suitable for a particular question.

Further, there are a lot of calculation techniques which will help you to solve any question within seconds.

Division

While applying the digital sum technique to solve division questions, you need to take care of certain things.

• Always try to make the digital sum of the denominator 0. For example, if the digital sum of the denominator is 2 then multiply both the numerator and denominator by 5 so that the digital sum of the denominator becomes 1. Similarly, if the digital sum of the denominator is 4, then in that case multiply both the numerator and denominator by 7. And lastly, if the digital sum is 8, then multiply by 8.
• If the digital sum of the denominator comes to be 3,6 or 9, then this rule fails. In that case, try to cancel out 3,6, or 9 and then follow the above process.

Q) Solve 2343 divided by 11?

Ans: We have 2343/11

In this question, the digital sum of the denominator is 1+1 = 2 and that of the numerator is 3.

Hence, multiply both N & D by 5 so that the new digital sum of the denominator becomes 1 (because 5×2 = 10 whose digital sum is 1) and that of the numerator becomes 6.

Now match the answer with the 4 options. You will be able to tick the correct answer.

We will discuss and share all other methods and tricks with you in upcoming articles.

The remaining portion i.e. percentage will be updated soon in this article. Keep visiting our website for more such amazing articles.

If you want to learn this concept with the help of a video, then you can watch 2 lectures on Digital Sum from Aditi Ranjan Sir.

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