What does sum mean in math?

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Sum: Sum in common terms is a way of putting things together or getting a total. In maths, sum is the answer that we get on adding two or more numbers.

Symbol Used:

The symbol used to represent a sum is ‘+’, also known as plus.

Common Terms used:

Some common alternative terms that are used other than sum or depict a need to add to or more numbers are “total”, “together”, “all-together” and “in all”.

Representation:

a + b = c

Here, ‘a’ and ‘b’ are known as addends and ‘c’ is known as sum.

The terms or numbers that participate in the addition or sum are called addends. The minimum number of addends is two.

For example:

12 + 13 = 25;

In this mathematical expression, 12 and 13 are addends and 25 is the sum.

How to calculate a sum?

Sum can be calculated in two ways. Let’s discuss:

Problem: Find the sum of 8 + 3?

Way 1: Pictorial representation

Here you need to draw pictures/lines as per the number of addends and the count them together.

So, for 8 =

For 3 =

Now, count all the stars together. They come out to be 11.

So, the sum of 8 + 3 is 11.

This method turns out to be very tedious if large numbers are involved as drawing so many pictures would be very difficult. But, if you have just started learning about sum then, this is the ideal way to learn.

Way 2: Count on fingers

This approach makes use of your ten fingers to calculate the sum.

Here you need to keep the biggest addend in your mind which is 8 in this case. Now, open the fingers equal to the second added.

Here, our second addend is 3. So, open three fingers.

Now start counting ahead of the number in your mind and start closing the open fingers one by one.

Start from 9 (next number of 8) and close your first open finger.

10, close your second finger.

Finally, 11 close your third finger. Now, stop when all fingers are closed.

So, on adding 8 and 3, the sum comes out to be 11.

Now, Let’s practice another problem:

Find the sum of 11 + 5?

Way 1

11= | | | | | | | | | | |

5 = | | | | |

On counting all the pipes the sum comes out to be 16.

Way 2

11 in the mind and open 5 fingers
on counting ahead of 11 and simultaneously closing the five open fingers we get 16.

So, the sum of 11 and 5 is 16 or, 11 + 5 = 16.

Real-world application

We use sum to add individual item prices when we go to shopping and pay the sum to the shopkeeper.

Sum Trivia

Adding zero to any number will result in the same number. This is also called Additive Identity Property. For example : 19 + 0 = 19
On adding 1 to any number, the sum would be the successor of that number. Example: 6 + 1 =7
The sum remains the same irrespective of the order of addends. Example: 4 + 15 = 15 + 4
The sum is always greater than individual addends.

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