Sum Definition

A summation or sum is the addition of different numbers or terms. It is one of the basic operations of Mathematics that everyone has to learn from their childhood. In simple words, the result we get after adding different terms in mathematics is called Sum


Read about Terms in Mathematics here.

In Mathematics, the sum is denoted by using a “+” symbol. This symbol is inserted between different terms that you want to add. Here is the pictorial representation of the Summation of two terms.

Sum of Numbers

You can find the summation of as many numbers as you want. There is no restriction over the maximum numbers that can be added to find the sum. You only have to put the addition symbol between all terms to show that these terms are going to add.

Example 1:

Find the Sum of the first five natural numbers.


1, 2, 3, 4, and, 5

Let us show you how to find the Sum of these numbers,

= 1 + 2 + 3 + 4 + 5
= 15 

Ways to find the sum of numbers

In general, there are two methods to find the summation of the given numbers. Here we are going to discuss them one by one.

  • Vertical Addition: In this method, you can write the numbers vertically and start adding from the first right term of the terms.
  • Horizontal Addition: In this method, you can write the numbers in a horizontal line as we have written in above Example 1.

Fun Facts of Sum

  • The addition of 0 with any other number will give the second number its resultant.
  • The sum of opposite sides of the Dice is 7.
  • Adding 1 in any number will give its successor.


What is the opposite of Sum?

The opposite method of Sum is Subtraction in which we minus different terms.

Is Sum related to the product?

Yes, both of these are related. Product means the addition of the given number of particular times.