 # Arithmetic Operations

Arithmetic is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises of operations such as Addition, Subtraction, Multiplication and Division. Let us understand each of the basic arithmetic operations in details.

## Basic Arithmetic Operations

The four basic arithmetic operations in Maths are:

• Subtraction
• Multiplication
• Division

Let us discuss all these four basic arithmetic operations with rules and examples in detail.

The addition is a mathematical process of adding thing together. The addition process is denoted by ‘+’ sign. It involves combining two or more numbers into a single term. In addition process, the order does not matter. It means that, the addition process is commutative. It can involve any type of number whether it be a real or complex number, fraction or decimals.

Example: 4.13 + 3.87 = 8

The addition of more than two numbers, values or terms is also known as a summation of terms and can involve n number of values.

The following are the addition rules for integers:

• Addition of two positive integer is a positive integer
• Addition of two negative integer is a negative integer
• While adding positive and negative integer, subtract the integers and use the sign of the largest integer number

## Subtraction Definition

Subtraction operation gives the difference between two numbers. Subtraction is denoted by ‘-‘ sign. It is almost similar to addition but is the conjugate of the second term. It is the inverse process of addition. The addition of the term with the negative term is known as subtraction. This process is mostly used to find how many are left when some things are taken away.

Example: 15 – 7

The term can also be re-written as 15 + (-7)

### Subtraction Rules

The following are the subtraction rules for integers:

• If both the signs of the integers are positive, the answer will be the positive integer
• If both the signs of the integers are negative, the answer will be the negative integer
• If the signs of the integers are different, subtract the values, and take the sign from the largest integer value.

## Multiplication Definition

Multiplication is known as repeated addition. It denoted by ‘×’ or by ‘*’. It also combines with the two or more values to result in one a single value. The multiplication process involves multiplicand, multiplier. The result of the multiplication of multiplicand and the multiplier is called the product

Example: 2 × 3 = 6

Here, “2” is the multiplier, “3” is the multiplicand, and the result “6” is called the product.

Product of two numbers says ‘a’ and ‘b’ results in a single value term ‘ab,‘ where a and b are the factors of the final value obtained.

### Multiplication Rules

The following are the multiplication rules for the integers.

• The product of two positive integers is a positive integer
• The product of two negative integers is a negative integer
• The product of positive and negative integer is a negative integer

## Division Definition

The division is usually denoted by ‘÷‘ and is the inverse of multiplication. It constitutes two terms dividend and divisor, where dividend is divided by the divisor to give a single term value. When the dividend is greater than the divisor, the result obtained is greater than 1, or else it would be less than 1.

Example: 4 ÷ 2 = 2

Here, “4” is the dividend, “2” is the divisor, and the result “2” is called the quotient.

### Division Rules

The following are the division rules for integers:

• The division of two positive integer is a positive integer
• The division of two negative number is a negative integer
• The division of integers with different signs results in the negative integer.