Arithmetic operations are the basic mathematical operations that we use to work with numbers.
The four main arithmetic operations are: Addition, Subtraction, Multiplication and Division.
We can perform these four arithmetic operations for any kind of number including fractions, rational numbers, and complex numbers.
Addition
Addition is one of the basic arithmetic operations where two or more numbers (called addends) are combined to get a total (called the sum). When we combine two or more numbers or quantities we say are adding. It is represented by the plus sign (+).
Subtraction
Subtraction is the process of finding the difference between two numbers. It is represented by the (-) symbol and is the opposite of addition.
Multiplication
Multiplication is the process of adding a number to itself repeatedly for a specified number of times. Instead of lengthy addition, we multiply the number by the number of repetitions. Multiplication is represented by the cross (⨯) symbol.
Division
Division is the reverse operation of Multiplication. It is the method of reducing a number by continuous subtraction. Division is represented by the (÷) symbol.
Example,
if we divide 8 by 2, i.e. 8 ÷ 2, it means we continuously subtract 2 from 8 until we get a number less than 2. We perform this as
8 - 2 = 6
6 - 2 = 4
4 - 2 = 2
2 - 2 = 0
Here, in the fourth step, we get 0 which is less than two. Now we will stop the process here, and the number of steps involved is 4, hence the result of division is 4. Division has got its application from distributing sweets among your friends equally to calculate the per capita income of a country. Let's learn about the components of division.
Table of Arithmetic Properties
Let a, b be two integers.
Property | Addition | Subtraction | Multiplication | Division |
|---|---|---|---|---|
Closure Property | a + b ∈ Z | a - b ∈ Z | a ⨯ b ∈ Z | a / b ∉ Z |
Commutative Property | (a + b) = (b + a) | (a - b) ≠ (b - a) | (a ⨯ b) = (b ⨯ a) | (a / b) ≠ (b / a) |
Associative Property | a + (b + c) = (a + b) + c | a -(b - c) ≠ (a - b) - c | a ⨯ (b ⨯ c) = (a ⨯ b) ⨯ c | a / (b / c) ≠ (a / b) / c |
Distributive Property | a ⨯ (b + c) = a ⨯ b + a ⨯ c | a ⨯ (b - c) = a ⨯ b - a ⨯ c | Not applicable | Not applicable |
Identity | a + 0 = 0 + a = a | Not applicable | 1 ⨯ a = a ⨯ 1 = a | Not applicable |
Inverse | a + (-a) = 0 | Not applicable | a ⨯ 1 / a = 1 | Not applicable |