# What is Arithmetic? Definition, Basic Operations, Examples

• Last Updated : 19 Oct, 2021

Arithmetic most likely has the longest history at the time. It is a calculating approach that has been used since ancient times for routine calculations such as measurements, labelling, and other day-to-day computations to achieve precise results. The name derives from the Greek word “arithmos,” which meaning “numbers.”

Arithmetic is the fundamental area of mathematics that studies numbers and the characteristics of conventional operations such as addition, subtraction, multiplication, and division.

Aside from the standard operations of addition, subtraction, multiplication, and division, arithmetic also includes sophisticated computations such as percentage, logarithm, exponentiation, and square roots, among others. Arithmetic is a field of mathematics that deals with numbers and their conventional operations.

### Basic Operations of Arithmetic

Arithmetic has four basic operations that are used to perform calculations as per the statement:

2. Subtraction
3. Multiplication
4. Division

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 7 the result would be the same that is 7.

0 + 7= 7

• 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 4 with its opposite value -4, then the result would be:

4 + (-4) = 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 p and q is expressed in p.q or p × q form.

5 × 6 = 30

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.

12 ÷ 3 = 4

### What is Simple Arithmetic?

Arithmetic most likely has the longest history at the time. It is a calculating approach that has been used since ancient times for routine calculations such as measurements, labelling, and other day-to-day computations to achieve precise results. The name derives from the Greek word “arithmos,” which meaning “numbers.”

Arithmetic is the fundamental area of mathematics that studies numbers and the characteristics of conventional operations such as addition, subtraction, multiplication, and division.

Aside from the standard operations of addition, subtraction, multiplication, and division, arithmetic also includes sophisticated computations such as percentage, logarithm, exponentiation, and square roots, among others. Arithmetic is a field of mathematics that deals with numbers and their conventional operations.

### Sample Problems on Simple Arithmetic

Question 1: The sum of the two numbers is 30, and their difference is 20. Find the numbers.

Solution:

Let the numbers be a and b. Now, as per the situation,

a + b = 30                                                                                                                                                                                     ………(1)

and a – b = 20                                                                                                                                                                              ………(2)

We can write, a = 30 – b, from equation (1),

no put the value of a in equation (2), we get,

30 – b – b = 20

30 – 2b = 20

2b = 30 – 20 = 10

b = 10/2 = 5

b = 5

And

a = 30 – b

= 30 – 5

a = 25

Therefore, the two numbers are 25 and 5.

Question 2: Solve 45 + 2(36 ÷ 3) – 9

Solution:

45 + 2(36 ÷ 3) – 9

⇒ 45 + 2(12) – 9

⇒ 45 + 24 – 9

⇒ 69 – 9 = 60

Question 3: Find the value of a in the given equation 3a – 18 = 3.

Solution:

According to the equation,

3a – 18 = 3

3a = 18 + 3

3a = 21

a = 7

Therefore, the value of a is 7.

Question 4: Solve for the value of a:

3a – 2(15 ÷ 3) – 5 × 2 = 22

Solution:

3a – 2(15 ÷ 3) – 5 x 2 = 22

3a – 2(5) – 10 = 22

3a – 10 – 10 = 22

3a – 20 = 22

3a = 22 + 20

3a = 42

a = 14

Therefore the value of a is 14.

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