Arithmetic Operations

Arithmetic and it's Discovery

What is arithmetic and who discovered it? How and when did we start using it? How do we perform basic mathematical operations? You must have a lot of these questions in your head. So what is it that you are waiting for? It is time to unravel the mystery. Arithmetic is a part of Mathematics which was founded by an Indian Mathematician and an astronomer, Brahmagupta, who is also known as the Father of Arithmetic and an extraordinary teacher Aryabhatta, who was also a scholar discovered “0” having immense knowledge about Mathematics and Astronomy.  Now, you would ask what is Mathematics? Mathematics is a science that basically deals with everything we do. It is everywhere. The logic of shape, quantity, structure, space, arrangements, changes, symbols. it is used in electrical devices, architecture, art, money, engineering and even sports. It is a building block for almost everything in our day to day life. It is so vast that it is almost impossible to define Mathematics in a specific definition. But we can talk about fundamental arithmetical operations or let us say the basic mathematical operations. So, what is arithmetic operations definition? The fundamental arithmetical operations can be divided into four parts. 

  1. Addition 

  2. Subtraction

  3. Multiplication 

  4. Division

These are the four main basic mathematical operations. 


Addition

The addition is the first among the 4 basic operations. Suppose it's your birthday and you invited your family and friends. Now, since it's a birthday party, they will bring you gifts. How will you have a count of so many gifts? Thus you add the gifts and find out. For example, if you got 10 gifts from your family and 15 gifts from your friends then you add 10 and 15 to get 25 and you can say that you got 25 gifts in all. In addition, we use the sign “+”. The first additional tool was the abacus which was invented by Tim Cranmer. 


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Know the Rules

There are few rules that we need to abide by before we do any fundamental arithmetical operations in addition. These rules are:


Rule 1) When we add two positive numbers, the sum(the result of addition) would be a positive number.

Rule 2) When we subtract( we will discuss it in the next heading) two negative numbers (having minus “-” sign), the result would be a negative number.   

Rule 3) While adding a negative and a positive number, we actually subtract the number and use the sign of the largest number. 


Subtraction

Subtraction is a fundamental arithmetical operation which is just the opposite of addition. In addition, the number keeps on increasing but in subtraction, the number keeps on decreasing. For example, if you have 100 rupees and you spent 20 rupees then you subtract 20 from 100 to get 80 which means you are now left with 80 rupees. If you further spend 50 rupees, then you subtract 50 from 80 to get 30, and thus you are now left with only 30 rupees. For subtraction, we use the sign “-”. 


Know the Rules

The rules of the fundamental arithmetical operations of subtraction are the same as the addition.


Rule 1) When we add two positive numbers, the sum(the result of addition) would be a positive number.

Rule 2) When we subtract( we will discuss it in the next heading) two negative numbers (having minus “-” sign), the result would be a negative number.   

Rule 3) While adding a negative and a positive number, we actually subtract the number and use the sign of the largest number. 


Multiplication

Multiplication is a shortcut method of a long addition of the same numbers. 


For example, 2 x 2 x 2 x 2 x 2 x 2 = 12 and 2 x 6 = 12. What did we just do? We counted the numbers of 2 occurring and multiplied it with 2. You can call it a repeated addition. 


For multiplication, we use the sign “x”.


Addition                                                   Multiplication

4 + 4 + 4 + 4 = 16                                         4 x 4 = 16

8 + 8 + 8 = 24                                               8 x 3 = 24

3 + 3 + 3 + 3 + 3 = 15                                   3 x 5 = 15


We can also multiply two different numbers such as 2 x 3 = 6. Given below are the multiplication tables from 1 to 10.


1 x 1 = 1

2 x 1 = 2

3 x 1 = 3

4 x 1 = 4

5 x 1 = 5

1 x 2 = 2

2 x 2 = 

3 x 2 = 6

4 x 2 = 8

5 x 2 = 10 

1 x 3 = 3

2 x 3 = 6

3 x 3 = 9

4 x 3 = 12

5 x 3 = 15

1 x 4 = 4

2 x 4 = 8

3 x 4 = 12

4 x 4 = 16

5 x 4 = 20 

1 x 5 = 5

2 x 5 = 10

3 x 5 = 15

4 x 5 = 20

5 x 5 = 25

1 x 6 = 6

2 x 6 = 12

3 x 6 = 18

4 x 6 = 24

5 x 6 = 30

1 x 7 = 7

2 x 7 = 14

3 x 7 = 21 

4 x 7 = 28

5 x 7 = 35 

1 x 8 = 8

2 x 8 = 16

3 x 8 = 24

4 x 8 = 32

5 x 8 = 40

1 x 9 = 9

2 x 9 = 18

3 x 9 = 27

4 x 9 = 36

5 x 9 = 45

1 x 10 = 10

3 x 10 = 20

3 x 10 = 30

4 x 10 = 40

5 x 10 = 50


6 x 1 = 6

7 x 1 = 7

8 x 1 = 8

9 x 1 = 9

10 x 1 = 10

6 x 2 = 12

7 x 2 = 14

8 x 2 = 16

9 x 2 = 18

10 x 2 = 20

6 x 3 = 18

7 x 3 = 21

8 x 3 = 24

9 x 3 = 27

10 x 3 = 30

6 x 4 = 24

7 x 4 = 28

8 x 4 = 32

9 x 4 = 36

10 x 4 = 40

6 x 5 = 30

7 x 5 = 35

8 x 5 = 40

9 x 5 = 45

10 x 5 = 50

6 x 6 = 36

7 x 6 = 42

8 x 6 = 48

9 x 6 = 54 

10 x 6 = 60

6 x 7 = 42

7 x 7 = 49

8 x 7 = 56

9 x 7 = 63

10 x 7 = 70

6 x 8 = 48

7 x 8 = 56

8 x 8 = 64

9 x 8 = 72

10 x 8 = 80

6 x 9 = 54

7 x 9 = 63

8 x 9 = 72

9 x 9 = 81

10 x 9 = 90

6 x 10 = 60

7 x 10 = 70

8 x 10 = 80

9 x 10 = 90

10 x 10 = 100


Know The Rules

Just like addition and subtraction, we also have rules for multiplications and they are:


Rule 1) On multiplying two positive numbers, the result would be a positive number

Rule 2) On multiplying two negative numbers, the result would be a negative number

Rule 3) On multiplying a negative with a positive number, the result would be a negative number.  


Division

Let us go back to the birthday example but this time you have to distribute chocolates to your classmate. Now, if there are 200 chocolates and 100 students, how many chocolates would each student get? This is where we will use the operation of division. The division is a method through which we can distribute a thing into equal parts. For division, we use the sign “”. This method has four parts:

  1. Divisor: It is the number that does the division.

  2. Dividend: It is the number to be divided.

  3. Quotient: It is the number we get after the division is done.

  4. Reminder: It is the number we are left with when the number cannot be further divided

So here 200 is the dividend which is to be divided, 100 is the divisor which will perform the division and 2 will be our quotient. And there is no remainder. 


The rule for the division is if two positive or negative numbers are divided, the result will be positive. However, if the signs of both the numbers are different then the result would be a negative number.

FAQ (Frequently Asked Questions)

Question 1) Who is Known as the Father of Mathematics in the World?

Answer 1) Archimedes is known as the father of Mathematics in the world. His father was an astronomer himself and encouraged his son to get a proper education. And thus, Archimedes loved maths, science, poetry, and many more.