# Introduction to Arithmetic Operations

• Last Updated : 17 Aug, 2021

Arithmetic is a traditionally used mathematical operation concerned with numeral systems and their operations. It is applied to get a definite single value. The term got originated from the Greek word “arithmos” which simply means numbers. The traditional operations associated with arithmetic include summation, difference, multiplication, and division. These operations are being carried out for the purpose of trading, marketing, and monetization for centuries.

Arithmetic is the elementary branch of mathematics that specifically deals with the study of numbers and properties of traditional operations like addition, subtraction, multiplication, and division.

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Besides the traditional operations of addition, subtraction, multiplication, and division arithmetic also include advanced computing of percentage, logarithm, exponentiation and square roots, etc. The article is focused on the study and explanation of these basic types of arithmetic operations.

History  of Arithmetic

• The 17th-century Indian mathematician Brahmagupta is the “father of arithmetic“.
• Carl Friedrich Gauss in 1801, provided the Fundamental principle of number theory.

### Basic Operations in Arithmetic

The four basic operations of arithmetic i.e. addition, subtraction, multiplication, and division are discussed below:

The simple definition for addition will be that it is an operation to combine two or more values or numbers into a single value. The process of adding n numbers of value is called summation.

0 is said to be the identity element of addition as while adding 0 to any value it gives the same result. For example, if we add 0 to 5 the result would be the same that is 5.

0 + 5 = 5

And, the inverse element includes the addition of the opposite value. The result of adding inverse elements will be an identity element that is 0. For example, if we add 2 with its opposite value -2, then the result would be

2 + (-2) = 0

Subtraction(-)

Subtraction is the arithmetic operation that computes the difference between two values (i.e. minuend minus the subtrahend).In the condition where the minuend is greater than the subtrahend, the difference is positive. It is the inverse of addition.

4 – 2 = 2

While, if the subtrahend is greater than minuend the difference between them will be negative.

2 – 4 = -2

Multiplication(×)

The two values involved in the operation of multiplication are known as multiplicand and multiplier. It combines two values that is multiplicand and multiplier to give a single product.

The product of two values supposedly a and b is expressed in a.b or a × b form.

2 × 4 = 8

Division(÷)

The division is the operation that computes the quotient of two numbers. It is the inverse of multiplication. The two values involved in it are known as dividends by the divisor and if the quotient is more than 1 if the dividend is greater than the divisor the result would be a positive number.

4 ÷ 2 = 2

### Sample Questions

Question 1. The sum of the two numbers is 100, and their difference is 60. Find the numbers.

Solution:

Let the two numbers be x and y

Now, according to the question

x + y = 100…………..(I)

x – y = 60…………….(ii)

From equation (I)

=>x = 100 – y

Therefore, putting the value of x

=>100 – y – y = 60

=>100 – 2y = 60

=>2y = 40

=>y = 20

Putting the value of y in equation (ii)

=>x – y = 60

=>x = 60 + 20

=>x = 80

Therefore, the numbers are 80 and 20 respectively.

Question 2: Simplify 50 + 10(9) – 9

Solution:

=>50 + 10(9) – 9

=>50 + 90 – 9

=>140 – 9

=>131

Question 3: If the sum of two numbers x and a + 5 is 39. Find the value of x.

Solution:

According to the question,

=>x + (x + 5) = 39

=>2x + 5 = 39

Subtracting 5 on both sides,

=>2x + 5 – 5 = 39 – 5

=>2x = 34

x = 34/2 = 17

Therefore, the value of x is 17.

Question 4: The difference between the two numbers is given by finding the value of p.

Solution:

According to the equation,

=>p – 4 = 11

Adding 4 to the both sides,

=>p – 4 + 4 = 11 + 4

=>p = 15

Therefore, the value of p is 15.

Question 5: Find the value of y in the given equation y – 9 = 3.

Solution:

According to the question,

=>y – 9 = 3

=>y = 9 + 3

=>y = 12

Therefore, the value of y is 12.

Question 6: Simplify: -1[(3 – 28) ÷ 5] – 2 × 24 ÷ 6

=>-1[(3 – 28) ÷ 5] – 2 × 24 ÷ 6

=>-1 × [(-25) ÷ 5] – 2 × 24 ÷ 6

=>-1 × [-5] – 2 × 24 ÷ 6

=>5 – 2 × 24 ÷ 6

=>5 – 48 ÷ 6

=>5 – 8

=>-3

Question 7: Solve 2x = 10

Solution:

According to question,

=>2 × x = 10

Dividing both sides with 2

=>2 × x/2 = 10/2

=>x = 5

Therefore, the value of x is 5.

Question 8: Solve the given equation 5x/4 + 1/2 = 2x – 1/2

Solution:

=>5x/4 + 1/2 = 2x – 1/2

Multiplying both sides with 4

=>4(5x/4 + 1/2) = 4(2x – 1/2)

=>5x + 2 = 8x – 2

=>-3x + 2 = -2

Subtracting both sides with 2

=>-3x + 2 – 2 = -2 – 2

=>x = -4/-3

=>x = 4/3

Therefore, the value of x is 4/3.

Question 9: Find the value of unknown number 3/2y – 2/3 = 1/5y

Solution:

According to the question,

=>3/2y – 2/3 = 1/5y

Multiplying both sides with 30(LCM of 2, 3, and 5)

=>30(3/2y – 2/3) = 30(1/5y)

=>45y – 20 = 6y

=>45y – 20 + 20 = 6y + 20

=>45y = 6y + 20

=>39y = 20

=>y = 20/39

Therefore, the value of y is 20/39.

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